# 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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### 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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### Partition function for bosons with path integral

In this book the partition function for bosons is defined in eq. 2.17 as: $$Z=\mathrm{Tr}[e^{-\beta (H-\mu_i N_i)}]=\sum_a\int d\phi_a\langle\phi_a|e^{-\beta(H-\mu_i N_i)}|\phi_a\rangle$$ The ... 1 vote
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### Harmonic oscillator propagator in Euclidean time

I'm following Nastase's book on Quantum Field Theory but this question is just about quantum mechanics in the path integral formalism. In chapter 8 he considers the propagator equation for a harmonic ...
1 vote
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### Fourier transform of Wick rotated functions

I am learning the imaginary time formalism of thermal field theory / reviewing the Euclidean formalism of quantum field theory. One thing that appears to be left implicit in many treatments is a ...
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### Doubts about the "periodicity trick" to compute temperature

The "periodicity trick" is a mysterious way to compute some sort of temperature associated to a Rindler-like spacetime. Suppose there exist coords $R\in(0,\infty), \eta\in(-\infty,\infty)$ ...
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### How does spontaneous symmetry breaking (SSB) happen?

I've just finished studying for an exam on the Standard Model (so electroweak theory and symmetry breaking) and I can't figure out how this question never crossed my mind. I'm now studying the QCD ...
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### Above the electroweak scale, is the Higgs ever effectively massless? (thermal field)

So before the Higgs attains a vev (i.e., above TeV scales), does the Higgs doublet become effectively massless? The Higgs doublet $\Phi$ (not the physical higgs about the nonzero vev) gains an ...
1 vote
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### Quantum field theory at finite temperature

Is there any notion of causality in Quantum field theory at finite temperature?
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### Yukawa interaction in QM (0+1D field theory)

This is a question about considering a simple ordinary quantum mechanics system from a quantum field theory perspective. Out of necessity the setup describing the problem is fairly long, but the ...
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### E. Fradkin on thermal propagator of free scalar field

In his lecture, E. Fradkin performs a Matsubara sum to show that the finite temperature contribution to the thermal propagator of the free scalar field contains the Bose-Einstein factor (see 5.209 - ...
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### Wick rotation on Ward identities

I'm having trouble performing a Wick rotation back to Minkowski spacetime ($\eta_{\mu\nu}=(-1,1,1,\dots)$), following page 19 in the lecture notes here by C.P. Herzog. I have this expression (equation ...
1 vote
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### Matsubara sum with log term [closed]

How do I compute the Matsubara sum $$\sum_n \log\left(-i\omega_n +\frac{k^2}{2m}+\mu\right)?$$ If I have sums like $\sum_n \frac{1}{i\omega_n -m}$, I can sum it up by calculating the sum of residues ...
1 vote
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### Broadening of spectral function: interaction and temperature effect

Consider a non-interacting fermion system with Hamiltonian \begin{equation} H = \sum_{\nu}\epsilon_{\nu}c^{\dagger}_{\nu}c_{\nu}, \end{equation} where $\nu$ is some single-particle quantum number. It ...
1 vote
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### Partition function for a system in local thermal equilibrium

For a system in equilibrium, the partition function is standard. But if the system is in local thermal equilibrium but stationary (i.e. zero or negligible time variation), but the temperature varies ...
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### How does QED at a finite temperature differ from QED at zero temperature?

Currently, I do not have any knowledge of finite temperature field theory. But I have learnt ordinary QFT calculations and I am reasonably familiar with Statistical mechanics. With this background, I ...
1 vote
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### Conceptual Problems in Understanding Thermal Field States in nonrelativistic QED

I have conceptual problems understanding the notion of thermal states in the context of nonrelatistic (cavity) QED. My main problem is the definition of temperature associated to the (quantized) ...
1 vote
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### Cross-sections at zero temperature and high temperature for a process and its reverse

If the Feynman amplitude for a $2-2$ forward scattering $ab\to cd$ is denoted by $\mathcal{M}_{ab\to cd}$ and that of the reverse scattering process, $cd\to ab$, is denoted by $\mathcal{M}_{cd\to ab}$...
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### Why is chaos a common property of thermal systems?

https://arxiv.org/abs/1811.06949 pg 3 mentions that chaos is a common property of thermal systems. Can someone please explain why that is? While looking at , I found that indeed most examples ...
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### Confusion about trace in the vertex term of Lagrangian

I was reading through Mariano Quirós's lecture notes titled "Finite Temperature Field Theory and Phase Transitions". In Sec. 1.2, the author is calculating the one-loop effective potential at $T=0$. ...
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### Understanding Matsubara summation

I'm trying to understand matsubara summation. Let us say I have $f(i\omega) = 1$. Obviously, the matsubara summation $\sum_{\omega_n} f(i\omega_n)$ diverges. So, I use a weighing function. Let us ...
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### How does one modify the decay width of a particle (QFT/Thermal Field theory style) when a particle is travelling through matter

I believe a particle's decay width/rate should depend on whether they are in matter or vacuum, but am unsure of where to find a prescription describing this phenomena. Please could someone point me in ...
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### Guessing the temperature dependence of a decay rate $\Gamma(A\to B+B)$

For a two-body decay of the form $$A\to B+B$$ if the interaction strength controlling the decay is $\lambda$, the Feynman amplitude $\mathcal{M}$ will contain a factor of $\lambda$ from the vertex ...
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