# On equivalence of QFT and Quantum Statistical Physics

## Main Question or Discussion Point

Does fact that QFT in imaginary time is equivalent to QSP represents the proof that many-particle quantum physics is equivalent to quantum theory of fields?

To elaborate a little, I had some discussion with some engineers, and when I was explaining them Standard Model I had to invoke concepts of quantum fields and they immediately turned their noses in despise to "overly abstract" concept.

Since they didn't have problems with quantum particles and statistical physics I've thought of taking the route starting from many-particle quantum physics but I'm not sure that I can do that because I'm not certain how to treat equivalence of imaginary time with temperature. I mean, parameter t in QFT enters from space-time structure but parameter $$\beta$$ is inserted in partition function only to be shown after calculation, what is it's connection with kinetic energy.

In Minkowski space time-component of energy-momentum is energy but I cannot find any formal transformation which would transform it into median kinetic energy at corresponding temperature.

Related High Energy, Nuclear, Particle Physics News on Phys.org
malawi_glenn
Homework Helper
Why cast pearls before the swine ? ;-)

Why is the quantum field more abstract than the classical field of let's say electromagnetism?

Why is the quantum field more abstract than the classical field of let's say electromagnetism?
Well, beats me, but I kinda came to think of it as an interesting question. One of the first thing you are being taught about QFT is that you cannot do right single-particle relativistic QM because necessarily pair creation-annihilation comes into play. Now, what if we try doing quantum statistical mechanics of relativistic particles? Would we get QFT as a result of formal correspondence of temperature and imaginary time?

malawi_glenn