Questions tagged [thermal-field-theory]
Thermal Field Theory or Finite Temperature Field Theory deals with of methods to calculate expectation values of physical observables of a Quantum Field Theory at finite temperature.
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Intuition for imaginary time Greens function
I understand that $$G^M(0,0^+) = \operatorname{tr}\{\rho O_2 O_1\}$$ (I am not putting hats on the operators here because they don't render in the correct position) is simply the expectation value of ...
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Infrared regularizing the harmonic oscillator path integral
This is from Laine and Vuorinen’s Basics of Thermal Field Theory. I do not understand why the fact that the integral over $x(\tau)$ implies the following regularization scheme. That is, I don’t ...
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Naive approach to a path-ordered functional
For analytic functions, we know that
$$ \langle q'|F(\hat{q})|q\rangle = F[q]\,\langle q'|q\rangle\tag{1} $$
Now, suppose that $q$ depends on $\tau$, promote $F[\hat{q}]$ to a functional, and ...
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A tricky derivation accompanied by delta function
I have been reading a book on Thermal Field theory by Michel Le Bellac During the reading I have come into a seemingly trivial but indeed tricky derivation. On page 26(2.47), we are supposed too prove
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Thermal photon mass
I am currently researching the generation of thermal mass in photons within the framework of quantum field theory at finite temperature. In such as formalism, one can define longitudinal and ...
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Why theory at finite temperature is more sensitive to infrared physics than at zero temperature?
At large space-like distances thermal effects modify the behaviour of the correlation function in an essential way:
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Temperature
$G(0,x)$, $m x \to \infty$ and $x/T \to \infty$
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$\sim \frac{1}...
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Introductory material for effective potential in thermal QFT?
I'm looking for materials that systematically deal with both thermal and quantum corrections to the effective potential to all loop orders at a beginner-friendly level with prerequisites of QFT before ...
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Product of delta functions in fermion self-energy at finite temperature
In the calculation of the fermion self-energy at finite temperature, there seems to be a term containing the product of two delta functions which when combined equal zero, however I fail to see why ...
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Decay of metastable state in classical statistical mechanics
Suppose a classical system at temperature $T$ with one variable $m$ and a free energy $F(m)$ having a metastable and a stable minimum. Suppose the system is in the metastable equilibrium at $t=0$. My ...
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Questioning a calculation in Kapusta / Infinite entropy of a Fermi gas?
I am going through Kapusta's calculation of the free energy of a Fermi gas, and I find one of his steps dubious (and if I'm right, it would mean the free energy of a Fermi gas is either infinite or ...
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Coherent States and Temperature for Scalar QFT with Source
This is a follow-up question on a question I previously asked, namely Coherent states and thermal properties. The authors of the article I am referring to in the previous question (Thermodynamics of ...
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Temperature of quantum fields and periodicity
I have read this PSE post Finite Temperature Quantum Field Theory, saying that
In a QFT at finite temperature, we consider the Euclidean time to be periodic, i.e. we consider a theory on the manifold ...
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Taylor expansion in momentum integral
On Ashok Das' book "Finite temperature field theory", page 21, the book introduces the thermal mass correction to scalar field.
$$
\begin{aligned}
\Delta m^2 & =\Delta m_0^2+\Delta m_T^2 ...
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How to derive the Matsubara correlator?
So the Matsubara correlator for either bosons or fermions is given by
$$G(i \omega_n) = 1/(i \omega_n - \epsilon_k ), \quad (1)$$
with $\epsilon_k$ being the single particle energy and $\omega_n$ ...
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Troubles with Matsubara sum
In appendix C of Quantum Physics in One Dimension of Thierry Giamarchi, it is claimed that (See (C.22)) after performing the Matsubara sum over the bosonic frequencies $\omega_n=2\pi n/\beta$ in
$$\...
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