QFT at Finite Density: Refs & Resources for Zero T

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Discussion Overview

The discussion centers on the topic of quantum field theory (QFT) at finite density, specifically at zero temperature. Participants explore the availability of references and resources related to this area, distinguishing it from finite temperature QFT, and address the implications of field excitations in the ground state of interacting theories.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about finding references for QFT at zero temperature and finite density, suggesting that finite temperature resources may not be applicable.
  • Another participant notes that QFT at finite temperature is more commonly discussed and is akin to non-relativistic many-body theory, indicating a lack of familiarity with finite density QFT.
  • A participant attempts to clarify the concept of interacting QFT at zero temperature, mentioning the presence of field excitations at the ground state, which they acknowledge may seem contradictory.
  • One participant asserts that the vacuum state, defined as the ground state, has no excitations, but questions arise about approximating the interacting theory starting from the free theory.
  • Another participant discusses finite-temperature/density perturbation theory, emphasizing the correction of both the state and dynamics of fields, and mentions the use of diagrammatic rules.
  • A question is raised about the availability of calculations in finite temperature field theory books, particularly those using path integrals.
  • A participant shares a manuscript focusing on real-time formalism and provides several textbook references relevant to finite-temperature field theory.

Areas of Agreement / Disagreement

Participants express differing levels of familiarity with QFT at finite density, leading to a lack of consensus on the topic. While some agree on the existence of QFT at zero temperature, the implications and resources related to finite density remain contested.

Contextual Notes

There are unresolved assumptions regarding the definitions of states and excitations in the context of interacting theories versus free theories. The discussion also highlights the potential limitations of existing literature in addressing the specific needs of participants.

ShayanJ
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I need to take a look at some references about QFT at finite density but I can't find anything, or at least I don't know where to look. I should emphasize that what I need is QFT at zero temperature and finite density so it seems to me QFT in finite temperature books may not be what I need or maybe I'm not understanding what the title's representing.
I'd really appreciate it if anyone clears my confusion here and point me to a good reference.
Thanks
 
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One usually has QFT at finite temperature which is similar to non-specially relativistic QFT (many-body theory). I have never heard of QFT at finite density.
 
dextercioby said:
One usually has QFT at finite temperature which is similar to non-specially relativistic QFT (many-body theory). I have never heard of QFT at finite density.
Well, to be honest, I'm not sure what I'm talking about. But let me try to explain and then we'll see whether I make sense or not.
What I have in mind is an interacting QFT at zero temperature that has field excitations even at its ground state. Yeah, field excitations at ground state may seem contradictory but I guess that can be understood by comparing this theory to the corresponding free theory.
 
Well, of course there's QFT at ##T=0## but finite density, e.g., for cold nuclear matter. You get it as the limit of ##T \rightarrow 0^+## from the usual formalisms (Matsubara/imaginary time or Schwinger-Keldysh real-time). The vacuum by definition is the ground state, i.e., the state of lowest energy. There are by definition no excitations of anything if you have the system prepared in this state.
 
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vanhees71 said:
The vacuum by definition is the ground state, i.e., the state of lowest energy. There are by definition no excitations of anything if you have the system prepared in this state.
Yeah, but what if we approximate the interacting theory starting with the free theory? Then the approximate interacting ground state is actually a state with particles(free theory particles), right?
 
Yes, and in finite-temperature/density perturbation theory you correct for both the state (i.e., the (grand-)canonical statistical opertor) and the dynamics of the fields. This is, because the (grand-)canonical state is treated as time evolution for imaginary times, and the time evolution is perturbatively described with the diagrammatic rules (including the KMS conditions for the fields).
 
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vanhees71 said:
Yes, and in finite-temperature/density perturbation theory you correct for both the state (i.e., the (grand-)canonical statistical opertor) and the dynamics of the fields. This is, because the (grand-)canonical state is treated as time evolution for imaginary times, and the time evolution is perturbatively described with the diagrammatic rules (including the KMS conditions for the fields).
Can I find such calculations on every finite temperature field theory book? Does any of them do such calculations using path integrals?
 
Here's my manuscript (emphasizing the real-time formalism, using both operators and path integrals):

http://th.physik.uni-frankfurt.de/~hees/publ/off-eq-qft.pdf

Then there are three good textbooks:

J. I. Kapusta and C. Gale, Finite-Temperature Field Theory; Principles and Applications, Cambridge University Press, 2 ed., 2006.
M. LeBellac, Thermal Field Theory, Cambridge University Press, Cambridge, New York, Melbourne, 1996.
M. Laine and A. Vuorinen, Basics of Thermal Field Theory, vol. 925 of Lecture Notes in Physics, 2016.
http://dx.doi.org/10.1007/978-3-319-31933-9

For the real-time formalism, using path integrals, see the review article

N. P. Landsmann and C. G. van Weert, Real- and Imaginary-time Field Theory at Finite Temperature and Density, Physics Reports, 145 (1987), p. 141.
http://dx.doi.org/10.1016/0370-1573(87)90121-9
 
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