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I'd really appreciate it if anyone clears my confusion here and point me to a good reference.

Thanks

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In summary, In order to find a good reference on QFT at finite temperature, you might need to look at books specifically about the subject or use a reference that discusses the theory in real-time.

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I'd really appreciate it if anyone clears my confusion here and point me to a good reference.

Thanks

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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.dextercioby said:

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.

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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?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.

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Can I find such calculations on every finite temperature field theory book? Does any of them do such calculations using path integrals?vanhees71 said:

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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

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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QFT at finite density is a branch of quantum field theory that studies the behavior of particles at non-zero densities. It takes into account the interactions between particles and their surrounding environment, and is used to understand the properties of matter at extreme conditions such as high pressures and temperatures.

QFT at finite density has many applications in various fields including condensed matter physics, nuclear physics, and astrophysics. It is used to study the behavior of matter in high-energy collisions, the properties of materials under extreme conditions, and the behavior of matter in the cores of neutron stars.

Some key concepts in QFT at finite density include the grand canonical ensemble, which describes a system at a fixed temperature and chemical potential, and the path integral formalism, which is used to calculate the probability of different particle interactions. Other important concepts include Fermi-Dirac statistics, which describe the behavior of fermions, and Bose-Einstein statistics, which describe the behavior of bosons.

There are many resources available for learning about QFT at finite density, including textbooks, online lectures, and research articles. Some recommended textbooks include "Quantum Field Theory at Finite Temperature and Density" by Jean-Paul Blaizot and "Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics" by Robert M. Wald. Online lectures can be found on platforms such as YouTube and Coursera, and research articles can be accessed through academic databases such as arXiv and ScienceDirect.

Current research topics in QFT at finite density include the study of strongly interacting matter, the behavior of quantum chromodynamics (QCD) at finite density and temperature, and the properties of matter in the early universe. Other areas of research include the application of QFT at finite density to condensed matter systems and the development of new theoretical frameworks for understanding the behavior of matter at extreme conditions.

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