3 ms·

Thanks for the response, but I was mostly asking about your experience as someone working in this particular field. Do you have any guesses for what might be t

Thanks for the response, but I was mostly asking about your experience as someone working in this particular field. Do you have any guesses for what might be the connection between these two different scattering amplitudes in seemingly disconnected physical phenomenon?

joe__f 4y ago
I read the paper more carefully and had a think about this, and here are my thoughts; Dixon et al. find a duality linking form factors and scattering amplitudes. Scattering amplitudes are written as a 'loop expansion', which you could think of as a bit like a Taylor expansion, and I think a remarkable feature of their result is that it appears to hold for all orders of this expansion. I've seen some results relating form factors and scattering amplitudes at only the first order of this expansion before. Their result is based on a mathematical observation that the functions that the scattering amplitudes are built from at each loop order (called polylogarithms) have a natural operation on them called the 'antipodal map', and in applying this operation to every polylogarithm in the amplitude they recover the form factor. It's intuitive to me that if the mathematical building blocks of your amplitude behave nicely under some operation, you might expect the amplitude to have nice properties under that operation also. So it's clear mathematically why this new relationship exists, and I guess the question is, 'what does it mean physically?'. Dixon et al. comment that they don't know, and I don't really have any thoughts on this either. What I can say is that, over the last 20 or 30 years there have been many different discoveries of duality between seemingly disparate areas of mathematical physics. The first and most famous was the AdS-CFT relationship which relates gravity to gauge theory, and there is lots of work in amplitudes currently on a different relationship which writes gravitational physics as the square of physics in gauge theory. There are many others. So, my experience working in the field has taught me that there are many unexpected dualities and relationships between different physical theories, and that nature is more deeply connected at a fundamental level than is indicated by the initial (apparently disparate) mathematical formulations of those theories.
- mmazing 4y ago
  Thanks a bunch for the detailed reply! I would like to learn more about stuff like this.

joe__f 4y ago

I read the paper more carefully and had a think about this, and here are my thoughts; Dixon et al. find a duality linking form factors and scattering amplitudes. Scattering amplitudes are written as a 'loop expansion', which you could think of as a bit like a Taylor expansion, and I think a remarkable feature of their result is that it appears to hold for all orders of this expansion. I've seen some results relating form factors and scattering amplitudes at only the first order of this expansion before. Their result is based on a mathematical observation that the functions that the scattering amplitudes are built from at each loop order (called polylogarithms) have a natural operation on them called the 'antipodal map', and in applying this operation to every polylogarithm in the amplitude they recover the form factor. It's intuitive to me that if the mathematical building blocks of your amplitude behave nicely under some operation, you might expect the amplitude to have nice properties under that operation also. So it's clear mathematically why this new relationship exists, and I guess the question is, 'what does it mean physically?'. Dixon et al. comment that they don't know, and I don't really have any thoughts on this either. What I can say is that, over the last 20 or 30 years there have been many different discoveries of duality between seemingly disparate areas of mathematical physics. The first and most famous was the AdS-CFT relationship which relates gravity to gauge theory, and there is lots of work in amplitudes currently on a different relationship which writes gravitational physics as the square of physics in gauge theory. There are many others. So, my experience working in the field has taught me that there are many unexpected dualities and relationships between different physical theories, and that nature is more deeply connected at a fundamental level than is indicated by the initial (apparently disparate) mathematical formulations of those theories.

mmazing 4y ago
Thanks a bunch for the detailed reply! I would like to learn more about stuff like this.