# 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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### 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 ...
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### Contour in real time formalism (thermal field theory)

The real-time formalism for thermodynamic systems involves a contour from $−T$ to $+T$ and then from $+T$ back to $−T$, with $T\rightarrow \infty$ and finally to $i\beta$. The question is why go from ...
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### Matsubara formalism

I am trying to understand qualitatively the Matsubara formalism. According to my current understanding, we just attach external legs to some matrix element then average it with the Fermi-Dirac or Bose-...
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### Finite temperature: lorentz invariance in imaginary time formalism

In the imaginary time formalism to model temperature, one analytically continues time to imaginary time i.e. $t \rightarrow i\tau$. In Minkowskii spacetime, spacetime obeys lorentz transformation i.e. ...
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### Lorentz boost of thermal propagator

Consider the propagators of two massive interacting scalar fields $(\phi_1(x),\phi_2(x))$, in 4 dimensional Minkowski spacetime $(x=\{t,\bar{x}_1,\bar{x}_2,\bar{x}_3\})$, which have been described ...
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### Quantum field theory at finite temperature

Is there any notion of causality in Quantum field theory at finite temperature?
1answer
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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 ...
1answer
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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 ...
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### How to view thermal spacetime in “Minkowski” picture?

For things such as the Page-Hawking phase transition, we perform a Wick rotation, and consider the Free energy of the metric of a Black Hole in AdS (which has a periodic time to avoid conical ...
3answers
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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 ...
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### Thermodynamic system and real time formalism: a basic $Q$

The real-time formalism for thermodynamic systems involves a contour from $-T$ to $+T$ and then from $+T$ back to $-T$, with $T \rightarrow \infty$. The contour path from $t = 0$ to $i\beta$ has a ...
1answer
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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 ...
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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 ...
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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) ...
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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 $\mathcal{M}_{cd\to ab}$...
1answer
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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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### Temperature and Witten index

Assume that the spectrum of some supersymmetric theory is discrete, then the Witten index is expected to be independent of temperature given by $T = 1/\beta$. However, it is well-known (see this) that ...
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### Estimate of trace of powers of density matrix

Given a very generic, lower bounded Hamiltonian, is there a estimate on how $Tr(\rho^{1/k})$ grows as $k>0$ increases? Does this quantity diverge as a function of $N$, the degrees of freedom of the ...
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### Finite temperature quantum mechanics and mixed states

Is it necessarily true that a quantum-mechanical system in thermal equilibrium is in a mixed state? If so, why is this the case? Is there any physical intuition as to why one cannot use a pure state ...
1answer
115 views