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.

21 questions with no upvoted or accepted answers
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Capturing (perturbatively) non-equilibrium field theory effects using “elementary” methods

I am considering a system of two interacting scalar fields: $\psi$, and $\phi$. The Lagrangian is given by: \begin{equation} \mathcal{L}[\psi]=\frac{1}{2}\partial_\mu\psi\partial^\mu\psi+\frac{1}{2}\...
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258 views

Quantum critical region governed by quantum critical point

I am trying to understand the following statement about quantum critical regions associated with a quantum phase transition from page 4 of these lecture notes on holographic superconductors: The ...
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545 views

What is the interpretation of Matsubara frequencies?

In QFT, the Matsubara frequencies are defined as $$\omega_n=\dfrac{2n\pi}{\hbar\beta}\quad\text{(bosons)}\quad\text{or}\quad\omega_n=\dfrac{(2n+1)\pi}{\hbar\beta}\quad\text{(fermions)},$$ where $\beta=...
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21 views

How does thermalisation make incoherent waves into coherent ones?

Thermalisation is the process by which out-of-equilibrium systems reach equilibrium. Coherence refers to the phases of waves being a constant difference apart. While reading a paper on axion stars, I ...
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28 views

Proof of factorization at late times for chaotic systems

While reading the paper "A bound on Chaos - Maldacena et. al", https://arxiv.org/abs/1503.01409 in equation (23) of the paper they factorize a correlator of the form, $$ Tr [\rho^{1/2} W(t) V \rho^{1/...
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41 views

Boundary times and bulk time in eternal black hole duality

In AdS/CFT, a particular duality is the correspondence between an eternal black hole in AdS spacetime (a large maximally extended AdS-Schwarzschild black hole) and the thermofield double state, \begin{...
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70 views

Reference request for the calculation effective potential at finite temperature

I want to know how does the Higgs potential $V(\Phi,T)$ varies with temperature in the Standard model. But I'm not familiar with the finite temperature calculation of effective potential. Therefore, ...
2
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0answers
135 views

Matsubara sum for particle number

I am trying to derive the electron number equation for some thermal system. There is something wrong in my calculation. The action has the following form: $S = \sum_{k,n \in \rm{odd}} \bar{\psi}[-\...
1
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1answer
33 views

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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32 views

Classical chaos at finite temperature

Is there any finite temperature generalization of classical chaos? In quantum chaos, at least with regards to out-of-time-order correlators, the generalization is clear - one simply takes a thermal ...
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0answers
45 views

Reference for Feynman diagram technique(position space) in Thermal Field Theory

I am trying to study perturbative expansion of Sachdev-Ye-Kitaev model, where I know that the dominant terms are the Melonic diagrams. I am interested in seeing how perturbative corrections affect the ...
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30 views

Electroweak phase transition and finite temperature field theory formalism

We do our calculations in standard quantum field theory at zero temperature where we can derive pole mass and renormalized mass and ... Due to my understanding, pole mass is independent of any energy ...
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64 views

Thermal density matrix QFT

The density matrix of a system at finite temperature is give by $$\langle\psi_1|\rho|\psi_2\rangle=\frac{1}{Z}\langle\psi_1|e^{-\beta H}|\psi_2\rangle, $$ where $Z$ is a normalization constant. We ...
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25 views

Normal ordering in 2D thermal CFT

I am trying to understand the notion of normal ordering in thermal CFT in 2D CFT, for instance I consider a two-point function of scalar primary operator with $\Delta$ dimension at finite temperature $...
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47 views

How can we calculate the imaginary part of a fraction that has a term $i0_+$ in the denominator?

I have recently started dealing with thermal field theory for fermions and I am faced with a paper that, at some point, tries to calculate the imaginary part of a fraction that looks like: $$\frac{1}{...
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66 views

What effect does multiplying $\mathscr{L}$ by $-1$ have on the propagator?

I am following along Ashok Das' development of Thermofield dynamics in his book Finite Temperature Field Theory. Here you have two real scalar fields $\phi_1$ and $\phi_2$ with Lagrangian density $$ \...
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68 views

Thermal field theory of isolated electroweak plasma

I need to understand something specific. The theory of electroweak temperature says that when you have a plasma of particles at energy above the electroweak phase transition (100 GeV). The Higgs ...
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108 views

Fermion boundary condition for a thermal compact circle

Is this true that for fermion statistical systems in the thermal phase, with Euclidean time, $$ \beta=1/T=t_E $$ the Euclidean time will be chosen to be anti-periodic for fermion boundary ...
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191 views

What is the meaning of thermal spectral function and thermal decay width in thermal field theory?

In Kallen-Lehmann spectral representation of 2-point correlation function \begin{equation} \langle 0|T\phi(x)\phi(0)|0\rangle=\int_0^\infty \frac{dM^2}{2\pi}\rho(M^2)D_F(x-y;M^2),\quad (a) \end{...
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17 views

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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126 views

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 ...