Oral History Interview with Stephen Parke, 2016 April 21
Transcript of interview with Fermilab theoretical physicist Stephen Parke by Fermilab Archivist and Historian Valerie Higgins on April 21, 2016.
HIGGINS: OK, today is April twenty first, 2016, it's 11 AM, I'm here at Wilson Hall, at Fermilab with Stephen Parke and I'm Valerie Higgins, the Fermilab archivist and historian. So, could you begin by briefly telling me where you grew up and how you first became interested in particle physics?
PARKE: OK, yes as Valerie said my name is Stephen Parke, I grew up in a very small town, in a very small country, in the middle of nowhere. I grew up in Gisborne, New Zealand, which if you look on the map is pretty hard to find. When I was in high school we moved to Auckland, which was the one big city in New Zealand, and there I was in high school and I got interested in physics by a teacher who was actually a French teacher, but he was teaching PSSC Physics. He had the PSSC Physics book, which was a text book, a course for physics, for high school students that was generated by a number of professors from MIT.
And of course, this was a great series of books for somebody who wanted to get into physics but was probably not so good for the students who were struggling, but I found them fantastic. And then I had a Chemistry teacher who started talking about orbitals and all this nonsense about quantum mechanics and I said, I tried to probe him about "well where did this all come from?" and he had no idea. So I figured that, you know, it has to come from somewhere, it's not just voodoo. So that, and special relativity, got me interested in physics, and then I ended up going to the University of Auckland and did an undergraduate degree in physics and mathematics, and then I enjoyed it so much that I wanted to do a PhD.
So, I applied to a number of universities all across the world, to do a PhD, and one of the universities that I was accepted in was Harvard University, and my parents were very upset with me because they were English and they wanted me to go to either Oxford or Cambridge, but Oxford or Cambridge acceptance date was after I had to already accept Harvard or turn it down. So basically I figured "a bird in a hand is worth anything in the bush," so I accepted to go to Harvard and I had a full scholarship to go to Harvard. And there I took some wonderful courses from some of the big luminaries in the field.
It's kind of interesting, what surprised me was, when I was an undergraduate, I thought all the people who wrote textbooks had to be dead, but when I came to Harvard, the people were teaching out of the textbooks that they just written. For example, Steve Weinberg had just finished his book on gravitation and cosmology and he was teaching the course on gravitation and cosmology, and of course he taught it out of his book, what else would you do? And then another professor, Sidney Coleman, gave a wonderful course on quantum field theory, and I really liked the way he thought, and I ended up doing my PHD with Sidney Coleman, who unfortunately is no longer with us, but he was one of these people that people liked to come and talk to about what they were doing. They would come into his office, and within five minutes of them explaining to him what they were working on, he would know more than what they were doing than they did. I mean he was just a phenomenal intellect and a tremendous resource for the field. People talked of him as a "physicist's physicist." Anyway, so I did my PhD with him, and then after I finished that I went off to SLAC, which was a part of Stanford University, and there I mainly worked with Sid Drell, who actually turns out to be a good friend of Sidney Coleman, so that was an interesting connection.
HIGGINS: Were you doing theory work at that time?
HIGGINS: Were you working on theory?
PARKE: Yeah, basically when I was doing my PhD I decided I wanted to be a theorist, and I found it more challenging, more interesting, and besides I wasn't that great with my hands, and I wasn't really wildly enthusiastic about computers. So I became a theorist, and when I was at SLAC, I wrote a paper  with Sid Drell on what super-heavy magnetic monopoles do to matter, and then an experiment in the Grand Sasso Tunnel, the MACRO Experiment, used this technique to try and look for super-heavy magnetic monopoles, and set a very tight bound on that they don't actually, we don't actually see hardly any of them in the universe. Maybe there aren't any, but they put a bound below, what's known as the "Parker" bound, so they set a limit below the Parker bound.
And that work got some attention and so after I finished my post-doc at SLAC, I had a three-year post-doc at SLAC, I was looking for another position and I was offered a post-doc at Berkeley, and I had decided to go to Berkeley, but then the Fermilab theory group offered me an associate scientist position, which is a tenure track position, and so in the end, I ended up coming to Fermilab, in what would have been the Fall of 1983, and I've been here ever since, been a long time. So that was the Fall of 1983 when I came to Fermilab and signed on as an employee. I then went back to SLAC for four months, so I actually didn't, even though I signed on to be an associate scientist, I didn't actually physically move here until February of 1984. And this was part of the agreement of me accepting the position and everything else, and Chris Quigg, who was head of the group at that time, was very generous and allowed this to happen.
So, that was in, you know, in 1984, and so when I came here, I was looking around for different things to do, and one of the things that was very "hot" at that time was the SSC. People were starting to talk about the SSC and in the summer of that year there was the Snowmass Workshop, in Snowmass, where people looked at the physics capability of what the SSC could do. Just before that workshop there was a paper that came out, it was really a review  by Eichten, Quigg, Hinchliffe, and Lane, where they basically laid out the first pass of what the physics that could be done at the SSC or actually the Super Conducting Super Collider, not just the SSC, they even, if you look at that manuscript, they even talk about hundred TEV machines, so basically anything from the Tevatron on up. And so one of the things, one of the statements they made in that paper, was that these processes are multi parton processes, like two gluons goes to four gluons or more. People, in principle, didn't know how those could be calculated, and so Tomasz Taylor and I got interested in this question, and started thinking about how you could do such calculations.
And these are background processes to many things like the discovery of the Higgs or super-heavy particles, and just to give you an idea, if you wanted to calculate how hard it was using the techniques of the day, if you wanted to calculate two gluons goes to four gluons, what somebody would do at that time is, they'd write down all the Feynman diagrams, there are two hundred and twenty of them, and then they would write down what the analytic expression is for each of those Feynman diagrams, and there is six raised to the fourth power for every Feynman diagram, that's the number of terms, and there's two hundred and twenty Feynman diagrams. So the total number of terms, just writing down the amplitude, was about three hundred thousand, OK. And then the techniques of the day are that you would square that, and then you would use various identities to take care of the color sums and the sums over the polarization vectors of the gluons. But if you square something that has three hundred thousand terms, you end up with an expression that has ten to the eleven terms, and with the computers of 1985, you could not even write down those number of terms. There wasn't enough disc space on the planet to even write down all those terms. There may be today, but there certainly wasn't in 1985. So that just shows you how challenging this problem was with the techniques of the day, and so we realized that one had to be, do something different, and so the idea which has been around, known, for a long time, another way you try and calculate each helicity amplitude, separately, because then you don't have to square everything, and get this enormous number of terms.
So, you know, each gluon has two helicities either plus or minus, so you look at all the cases where all the gluons have the plus helicity separately from all the case where the gluons all have the minus helicity and so on, and you do all the possible cases, OK. And so we developed some techniques for doing that using super-symmetry. It turns out that if you're just looking at tree level gluon scattering, it doesn't matter whether the theory is just the gluons or you can bed it in a super-symmetric extension. And then there is a relationship between the amplitudes involving the quarks and the amplitudes involving just the pure gluons, and so you may have relationships between them. And these are what are now called the Supersymmetric Ward Identities that allow you to relate amplitudes with basically quarks, actually, they're really gluinos, but OK fine, doesn't matter, with the amplitude of pure gluons, and it's much, much easier to calculate the amplitudes with the quarks, and we made some progress on doing that, and we wrote a  paper summarizing these techniques. And in that paper we managed to calculate two gluons goes to three gluons and get an analytic expression. Now turns out that people have written down this analytic expression before, but had it only been checked numerically from other calculations, they actually hadn't derived that expression, it had just been checked by looking at arbitrary gluon momenta and showing that you get the same answer that they got numerically with the analytic formula, but we were actually able to derive the analytic expression, directly.
HIGGINS: Was this in 1986 or?
PARKE: This was 1985. So it was clear that these techniques were quite powerful and we pushed ahead, and managed to write a  paper where we did two gluons goes to four gluons, but to be honest with you that is a really ugly paper, it's horrible. I mean if you look at it, it's horrible. But the important thing about that paper, it was the first time that anybody had even calculated the amplitudes squared for two gluons goes to four gluons, and it's about nine pages long. So you've gone from something that you couldn't even write down before, to something that was nine pages long. And that same fall, this is in 1985, we also managed to do two quarks goes to four gluons. Which is a companion process that also needs to be taken in account. Alright, so and that again is another ugly paper, but it is also the first time that this is actually being calculated. So, but, the way that we had done these calculations, is we had done it helicity amplitude by helicity amplitude, and then summed them up at the end. And what we discovered was that some of the helicity amplitudes were zero, OK? The ones where all the gluons are positive, are zero, and all of the gluons are positive but one, one of them being negative, is also zero. And so that made us think about, well, "is it possible that the next amplitude, the one with two negatives and all the rest being positive, is simple?" Because the other one's a zero. And so we thought about this for a while, and we realized that what hadn't been observed by other people, is that even in two gluons scattering, two gluons goes to two gluons scattering, it is only this amplitude that appears, all the others are zero. The same for two gluons goes to three gluons, it will also, it's this one amplitude with two negative and three positive or two positive and three negative, is the only one that occurs, all the others are zero.
So we took that expression for those processes and tried to generalize it, and of course we made a number of guesses, and one of them we discovered numerically, that it was the correct answer for the two gluons goes to four gluons, OK? We would write down a random set of momenta, that conserved energy and momenta, and we would plug it numerically into our code, and we would calculate it both with our really complicated, messy calculation, and the simple formula, and we got the same answer, to fifteen significant figures. And then we would do it for a thousand different momenta sets, randomly chosen, and we would still get the same answer, they were identical, so we knew that this analytic expression, at least for two gluons goes to four gluons was correct, for this particular helicity amplitude, and then we guessed the generalization to n-gluons. And the way you do that is these amplitudes have to satisfy certain properties, nonlinear relationships, and there was one way that if we generalized this formula to n-gluons it satisfied all of these conditions. So with this in-hand, we decided, well, we have no idea how to prove this, we have no way to prove it. If we believed it, you know more than ninety-nine point nine-nine percent that this was the correct expression, because it satisfied all these conditions, so, and we also realized because it was so simple that we needed to publish it as soon as possible, or otherwise somebody else might discover it, and so that's what we did. So we wrote a paper  for PRL, and we sent it to PRL, and the couple of weeks afterward, the editor called Tomasz Taylor. Tomasz is the one who had submitted the paper, not me, but the editor called Tomasz Taylor and said, "you know, I got referee reports from your paper, and they're completely nonsense, so I've thrown them away, and I'm going to accept your paper, but you have to lengthen it because you need to put a general discussion at the beginning and the importance of why this was at the end." So we published the paper in PRL, and even with the additions that we add, its one and a half pages in PRL. Now, most people, the maximum number of pages you're allowed is five, and most people struggle to get their paper under five. But we really could only write, we can state what we'd done, and we could write down the simple formula, we had no proof, we could give our arguments why it was correct in a very short paper. So recently just for the fun of it, I took the preprint version and I typeset it in LaTeX, because now we have LaTeX, in the PRL Macro, and what I wanted to see was, is the original version greater than or less than one page? So, I did that, and I typeset it, and yes it's less than one page. If you turn off the camera, I will go and get it.
HIGGINS: Oh, sure
PARKE: Turn it off, I'll go get it.
PARKE: So here, are we back on?
PARKE: So here is the original version of the paper typeset with the PRL Macro, and as you can see, it fits on one page, including the references.
PARKE: The whole thing.
PARKE: And so uh, and so I recently reproduced this, and I gave a copy to my collaborator, Tomasz Taylor, for a workshop that we just had.
PARKE: So the fact that these processes were so complicated and we managed to get a simple answer for one helicity amplitude, we knew at the time was important. It was clearly important, because this kind of thing doesn't happen in physics unless there's a reason, so what's the reason? Well you know, this was one of the most frustrating papers that I've ever written, because, I have, by the time we finished writing this paper, we had far more questions than what we'd answered in this paper. And since we didn't really have a way of proving this, you know, we were in a very awkward position in some sense. It was not, so even though this is the most famous paper I'd ever written, it was also the most frustrating paper to write, because it opened up so many questions, and I didn't have any clue how to answer them, however I had some ideas. So this was in, we wrote this paper in a just, it was in March 1986, and earlier in the fall of 1985 I had gone to a workshop in China. I went to the Photon Lepton Conference, and then I went to China, OK? So this trip to the Photon Lepton Conference and to China was very adventuresome. Am I allowed to tell personal stories at this point?
HIGGINS: Yeah, anything you're comfortable with sharing.
PARKE: OK fine, so one of the things that happened on this trip to Japan and China is, I flew from here to Narita Airport, Japan, and then I was supposed to take a flight from Haneda Airport to Osaka, that was the plan. I had a confirmed reservation on these two airplane flights, OK? When I got to Narita, I knew that there was a flight from Narita to Osaka, so if I could get on that flight I wouldn't have to take a bus to the other airport, and then fly to Osaka. And since I had only carry-on baggage, I just asked the person at the desk, is there any possibility you can get me on that flight? I tried to get on that flight earlier, but it was completely sold out because there was a festival in Tokyo around this time, and everybody was trying to get to this festival, OK? So when I got to Narita Airport, I asked them and they said sure fine, no problem, we'll put you on the flight. That was the best thing I ever did. And I'll tell you why, because when I got to Osaka, I found out that the plane that I was supposed to take from Haneda had crashed into a mountain, and killed five hundred and sixteen people.
PARKE: So that was pretty damn close.
PARKE: So anyway, while I, that took a little while to recover, but while I was in China, I knew of some papers written by a Chinese physicist, actually a group of Chinese physicists, the one I got to know very well, his name was Zhan Xu. He had written a  paper on how to deal with the polarization vectors for gluons when you do multi-gluon processes. That was one of the pieces I needed to try and prove this expression that we had written down. The other piece I needed, was what to do with the color structures? How do we deal with the color structures? So after Tomasz and I wrote this paper, Tom got interested in doing other things, but later on that year I managed to get Michelangelo Mangano, who is now at CERN, and I managed to get this Chinese physicist to come to Fermilab for six months, I think he got here in 1986.
HIGGINS: What was his name again?
PARKE: Zhan Xu. Z-h-a-n, Zhan, and his last name is Xu, X-u.
PARKE: And so the three of us got together, and we worked on how do we attack this problem in a much more systematic way?, than Tomasz Taylor and I had done. And we figured out, Zhan Xu had the polarization vectors, and we figured out what to do with the color structure. It turned out that the problem with the color structure had been solved many years ago by string theorists. And so we rediscovered it, but then we discovered that they'd already done it twenty, thirty years ago. And, so this allowed us to, not only could we treat every helicity amplitude independently, is that we could break up every helicity amplitude into a sum of sub-amplitudes that were all independent of one another also. And these different sub-amplitudes had different color structures. And so then you reduce the problem into a much, much smaller problem, so, and each one of these sub-amplitudes has some beautiful properties also. And so if, I think, just let me see if I can get my dates right. So, in the beginning of 1987 we had basically been able to calculate two gluons goes to four gluons analytically from start to finish. There was no messy paper we wrote, what I consider to be one of my most beautiful papers, the three of us, an Italian, a Chinese, and a "Kiwi." We wrote this beautiful  paper on how these amplitudes really needed to be calculated, and in doing that, we were able to, in the paper that Tomasz Taylor and I had written, we had written down the amplitude squared for this special process of special helicity amplitude for two gluons going to n-gluons. We were able to write down the actual amplitude for this process, without the square. So that was a major step forward, and we also did some other things.
And then in 1991, Michelangelo Mangano, (and other people started to jump on this bandwagon), and then in 1991, Michelangelo and I wrote a  paper on this whole process, this whole multi-parton amplitudes, which has been very popular and is used a lot today. So you know that's, that's pretty much most of the story. And so what happened after that, I worked on these amplitudes for a while, and then it became clear that the Tevatron here at Fermilab was going to discover the top quark. That became, you know, there were hints, and everything. So I got much more interested in the top quark, and the physics of the top quark, and so instead of worrying about background processes, I became much more interested in signal processes, and even though many people have worked on this amplitude business since I worked on it, and they've done some truly amazing things, I sort of got distracted by signal, rather than background. But I mean it's clear that these theories which formed, the Yang-Mills theories, which formed the basis of all the forces. The strong force, the weak force, the electromagnetic force, and even gravity. And gravity in some sense is the square of one of these gauge theories. These theories, the amplitudes are much simpler than you would naively expect. If I was looking at say the simplest possible theory, Lambda Phi Four theory, it's you know, the kind of thing you learn first year in graduate school. I could not write down the amplitude for n of these scale particles, where as I can do it for gluons. Why is that? Well, there's a reason for that, and people are trying to understand that reason in the deepest possible sense. Nima Arkani-Ahmed, who came to Fermilab a couple of months ago, gave a nice colloquium, where he's trying to use these, our knowledge about these amplitudes to try and figure out what is the right principle that allows us to marry quantum mechanics and gravity. A notoriously difficult problem. So I mean what he's trying to do is, we know that there are many formulations of classical mechanics, but the one that allows you most simply to go to quantum mechanics and quantum field theory is the least action principle. And so the question is, what is the principle that allows us to go all the way to marrying quantum mechanics and gravity? And that's a problem for the century, and so OK, maybe I'll stop there. I'm sure you have questions.
HIGGINS: Yeah, I'm going to back up a little bit. When you were working with Tomasz Taylor and then later too with the other two physicists, could you tell me a little bit more about how that process worked, like how that collaboration worked? Did you do everything together or did you both kind of do independent things and then meet periodically to...
PARKE: We did a lot of things independently, but there were some things he did, and some things I did. I mean collaborations work in mysterious ways, you're trying to get to the answer, and it doesn't really matter how you get there you just want to get the answer. What we did was not really formal in any sense. We hadn't, didnt formally divide up the problem, I'll do this and you do that. We were all, we were both trying to push ahead to try and figure out how to get the answer from these problems. I mean probably some people naturally did things that they liked to do, rather than other things. But that sort of naturally happens. It was not, it was not dictated from above. I mean these, most collaborations in theoretical physics are not structured in any way. They just grow organically in a sense. "I'm interested in this part, Ill do that," etc.
PARKE: So it's not like a, its not like an experimental collaboration where somebody is assigned to do this, and somebody is assigned to do that. Doesn't work, theorists don't work that way.
PARKE: Well most, at least I've never been in a collaboration that works that way. I probably wouldn't enjoy it if I did.
HIGGINS: Yeah. So, what was the relationship between the work you were doing and sort of what was going on at Fermilab at the time? Was this something, like, were lots of other people aware that you were working on this? Was this something that, like, I know Lederman would have been director at that time, was he aware that...
PARKE: No, in fact, when we did this work, many people in the Perturbative QCD Community, this is the community that this was, were not really that interested. They were interested in a multiloop calculations for a various small number of particles, like you know, four, five max, you know they start to get very nervous when they have five particles. And so, you know, I would say that to first approximation that this work was kind of ignored when we did it. It wasn't until much, much later that people began to understand the utility of what we'd done, and that happened much, much later. I mean we were, we were both untenured associate scientists at the lab when this happened, and when we were working on this, on this stuff, and as you probably know, Tomasz Taylor is no longer at the lab, he's at Northeastern University, and that's because he wasn't promoted at the lab, and I am not going to discuss my promotion procedure here because, let me put it this way, it was not trivial. So...no people, I mean this paper that we wrote on n-gluon amplitudes, I think a number of the people in the community basically felt there's no way this could be right, it's too simple, and they were wrong.
HIGGINS: When do you think people started to realize the significance of, or when do you think that started to shift?
PARKE: Well, I would say the shift started in the mid 90's, when people started to realize the background processes for things like top quark production at the Tevatron, you needed to be able to calculate these things. And then other people, there were a few other people like Lance Dixon, Zvi Bern, and David Kosower started to use a lot of these techniques to do even, to even do loops with multi-parton amplitudes and they also made tremendous progress. But the real  paper that really got the, especially the more formal aspects, people in the field got interested in, was a paper that Ed Witten wrote in 2004, so this is eighteen years later. And he wrote a paper that showed that you can construct all of these amplitudes that we calculated from a twister string theory. And he showed the relationship between the two of them, and in fact I know that, I mean Ed had been interested in this problem from very early on, I remember talking to him in the early 90's about it. It was clear that he felt that there was something deep going on in this. And it wasn't this paper that he wrote just didn't pop out of nowhere. He had been working on this at the back burner for a long time, he been thinking about it. And that paper really triggered a lot of interest in many, many people in the field. That really triggered people beginning to realize that what had been done was important, and was changing the way people thought about these theories that are the basis of all the forces of nature. And so I mean if you look at the citations of this paper that Tomasz Taylor and I wrote, you know its relativity steady until 2004 and then in 2004 it really takes off.
PARKE: And I have to say, I'm very happy to have a paper that you know is, what is it, it will be thirty years, its thirty-years-old this year, and it's still receiving a significant number of citations. And the other thing that's happened is that, in a lot of papers they don't even bother to cite it anymore, they just call it the Parke Taylor amplitudes, and so it's like Yang Mills or Feynman Diagrams or the Dirac Equation, and you know, that's the step beyond citations, and I'm very happy about that.
HIGGINS: Yeah. So I know this is sort of asking you to speculate a bit, but what do you think, like, going forward what it's influence will be or how do you think that these ideas will sort of shape what's coming?
PARKE: Well, if people could truly understand why gauge theories are so simple, it will also help us understand why gravity, it will also imply that gravity is simple in some way, and so the real, you know if I was to dream that these ideas will eventually lead people to figure out a way to combine quantum mechanics and gravity, because that is the one area of particle physics that we really do not know, there are conceptual difficulties, and if you're not careful, you end up with paradoxes, and all sort of strange things that can't possibly be true happen. So there are a lot of people who are working on that area, I don't know how much progress they're making, but that is the one thing that we're sort of, conceptually, physics is stuck with, we don't know how to do that.
HIGGINS: What do you think some of your other most significant discoveries, ideas, or contributions to the field have been? I know that's a very big general question, but if there's other sort of things you want to highlight?
PARKE: Yeah that is a pretty big question, I suppose the other paper I'd like to mention, was a paper that I wrote a couple of months after I wrote the  paper with Tomasz Taylor on these amplitudes, and this paper was on a completely different topic, completely different. It was on, what's now known as, what's the solar neutrino problem, and people had, had some ideas that Wolfenstein's matter effects, that neutrinos when they propagated matter are affected by the matter, in a way that was unexpected, and I wrote a paper two months after this on basically a solution to the solar neutrino problem, and that is also another paper that's highly cited, and has basically, in there, I develop some concepts that I used in neutrino physics, even today.
So that was another piece of work that I'm very happy with because it's also getting citations thirty years later, not as many as the amplitudes paper but it still gets citations, so, and there are other things I could talk about but you know. I'm very happy about those two papers, and I wrote those two papers when I was an associate scientist at the lab, and one of them has had, you know the amplitudes paper has had a big impact, not only the way QCD is done, but has also had an impact on the formal aspects of the field. And the paper on neutrino physics is sort of you know, one of the classic papers on how neutrino masses can affect the way neutrinos do strange things.
HIGGINS: So I've know you mentioned how, with the upcoming discovery of the top quark back in the early 1990's that had drawn you into being interested in that, how did you become interested in neutrinos?
PARKE: Alright, how did I become interested in neutrinos, is because people started to talk about this effect, which has now been given the name “MSW,” Mikheev, Smirnov, and Wolfenstein. And when people first talked about that, I felt that what they were doing was confused, and I knew exactly how, and because I had written a paper with Sid Drell that mathematically had an even more complicated problem than this one, I knew exactly how to solve it analytically. So basically, in a period of one afternoon I wrote down the solution to this problem which was much more general than what other people were doing. I know, for example, at the same time there were three people in the Astro-particle Group also interested in this problem , and they were doing a numerical calculation, it was Rocky Kolb , Michael Turner, and Terry Walker.They, I think it was Terry Walker, wrote this numerical program, and they solved this problem numerically. And one afternoon, I wrote down a formula that basically did it all for them, and so I wrote my own paper. And, but I mean really the trigger was, is, I knew analytically how to solve this problem because I had used some of the techniques in a previous paper. And so, you know, theorists like to build on things that they've done in the past, but I mean this was completely unexpected. This was, you know neutrinos at that point in time, in 1986, early 1986, was a hot topic because people began to think that they had, that the solution to the solar neutrino problem was at hand, and I was able to make a significant contribution to that, just because I had done something earlier. So...
HIGGINS: So that pretty much covers all the questions that I had written down, is there anything else you'd like to mention that I haven't asked about?
PARKE: You know Fermilab has been a great place to do science, and you know the thirty years that I been here, you know, being able to do science every day, and interacting with other scientists has been truly fantastic.
PARKE: Thank you very much.
HIGGINS: Yeah, thank you so much.
 Zhan Xu, Da-Hua Zhang, Lee Cha. Helicity Amplitudes for Multiple Bremsstrahlung in Massless Nonabelian Gauge Theories Nucl.Phys. B291 (1987) 392-428 (Note: Zhan Xu won the ninth (2012-2013) Zhou Peiyuan Physics Award for related work.)