quantum field theory - What's the big difference between high energy physics and condensed matter physics?

Can anyone tell me the difference between high energy physics and condensed matter physics?

I am confused about how these concepts, such as second quantisation, Green's function and many others, in high energy physics are introduced into condensed matter physics?

Answer

A possible BIG difference was that condensed matter is non-relativistic (or Galilean relativistic) whereas high-energy physics is relativistic (or Lorentz-Poincaré relativistic). The tools are the same then, but writings are sometimes confusing for a few people. Some condensed matter physicists -- especially the young ones trained in condensed matter only -- are not well familiar with covariant notations (with greek indices everywhere !), and high-energy physicists are not necessarily familiar with the observables of condensed matter experiments. For instance, as a condensed matter physicist, I never calculated a cross section. I guess it is not natural for a high-energy physicist to calculate a magnetisation or a band structure... (please comment about it :-)

Also, for a few years (I would say in the 70's-80's but I could say something stupid), condensed matter physicists were interested in many-body problems at a given temperature, so they were using the real partition function (i.e. defined by statistical physics) and Matsubara frequency technique (in terms of the Green's functions it is a simple way to implement temperature in time-independent many body problems), whereas high-energy physicists were mainly concern by single particle processes, so their $Z$ function was mainly a tool to simplify calculations and was just marginally connected to a partition function.

At the present time, there is an emergent Lorentz relativity in modern condensed matter systems, such as topological systems and graphene, to cite a few of them, and high-energy physics is more and more concerned with many-body problems in order to elucidate the early times of the universe for instance, when there was a plasma of many high-energy particles. So in short there is a tendency for these two fields to overlap. Of course the energy ranges with which high-energy and condensed matter physicist play are not the same at all. At the high-energy level, there is no simple things as a solid that you can take in your hand ! In condensed matter, elementary particles are (dressed) electrons, not quarks for instance... Funnily enough, quantum field theory applies really well in condensed matter systems at low temperatures (quantum Hall, superconductivity, mesoscopic physics to cite a few nice applications), whereas high-energy physics is the realm of high temperatures (like collision particles, or the nuclear physics of stars for instance).

Historically, there has been a rich and interesting go and back movement in ideas between the two fields, like about the Green's function approach or diagrammatic (first applied in high-energy problems and adapted to many-body problems), phase transition (first applied in condensed matter and then adapted in high-energy), topological ideas (first considered in high-energy and recently applied to condensed matter problems), ... Each time it is not a simple copy of the ideas and methods from one sector to the other. Rather, the transition from one sector to the other requires adaptations which enrich both parts of the quantum field theory. That's mainly why it is working so well and nice since the mid XX's century !