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?
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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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1answer
90 views

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 ...
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146 views

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 ...
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1answer
35 views

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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General expression of time-ordered thermal average Green's function does not reproduce non-interacting limit (Fetter ch. 31 Eq. (31.24))

Hi I am going through Fetter's Quantum Theory of Many-Particle Systems Dover Edition. In ch. 31 he computed the relation between $\bar{G}(\mathbf{k},\omega)$, ${\bar{G}}^{R}(\mathbf{k},\omega)$ and $\...
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Coefficient of viscosity from Kinetic Theory of Gas

I have a confusion in the derivation of coefficient of viscosity from the book: 'Concepts in Thermal Physics' by Blundell-Blundell. I am adding highlighted part in which I have confusion (the full ...
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1answer
80 views

Green's function in Thermal Field Theory

Background information Let $\beta$ be the inverse temperature 1/T, and $H$ be the Hamiltonian. $H = H_0 + H_I$, where $H_0$ is the free Hamiltonian. Also $S(\beta) = e^{\beta H_0}e^{-\beta H}$ Let $\...
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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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161 views

Derivation of Thermally averaged cross sections

In many sources discussing neutrino decoupling I find the following claim: "The thermally averaged rate of weak interactions is given by: $\Gamma = n \langle\sigma |v|\rangle$, where $\langle\...
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What does the Temperature of a QFT physically mean?

In elementary statistical mechanics, one can think of temperature as arising from the average kinetic energy of particles in the ensemble. Is there a similar way to think about the temperature of a ...
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649 views

Why is Euclidean Time Periodic?

I've been reading a bit about finite temperature quantum field theory, and I keep coming across the claim that when one Euclideanizes time $$it\to\tau,$$ the time dimension becomes periodic, with ...
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Which is the state of the art of relativistic many-body QFT?

We have a class of relativistic quantum field theories, typically used to calculate particle interactions (scattering) or to extend the Standard Model. Typically one start with a "free" theory, then ...
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How does a thermal propagator work?

I am looking at a propagator in the Hubbard model (in the strong coupling limit) and my timescale is $\beta$. I see that for longer (imaginary) times $\tau$, the particle can propagate further away. ...
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How to calculate expectation value of exponentiation of number operator for coherent state?

I consider a quantum harmonic oscillator and regard $a$ and $a^\dagger$ is ladder operators. Let $|0\rangle$ be a vacuum, and a coherent state $|\alpha\rangle$ is defined as the eigenstate of the ...
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Temperature reduction in 4D QED

I would like to find references for the following topic. Consider QED with non-zero temperatures, which is naively constructed by Wick rotation. Then, consider the case of high temperatures, $\beta\...
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234 views

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 $\mathcal{M}_{cd\to ab}$...
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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 [1], I found that indeed most examples ...
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Free parameter in Bose Einstein Condensate

In Kapusta and Gale's Finite-Temperature Field Theory book, BEC is derived for a complex scalar by Fourier expanding $$\phi _1 = \sqrt2 \zeta \cos \theta + \sqrt{\frac{\beta}{V}}\sum_{n,\bar p}e^{i(\...
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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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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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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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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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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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108 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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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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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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206 views

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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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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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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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 ...
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“Contraction Property of thermal density matrix” in the Maldacena's paper of A Bound of Chaos

In the paper, https://arxiv.org/abs/1503.01409 (Maldacena, et al. “A Bound on Chaos.”) in equation (24), the authors write an inequality, $$ Tr( y^{1+\eta} V y^{3-\eta} V ) \leq Tr(y V y^2 V) $$Where $...
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Multiplying Distributions in finite-temperature Keldysh/Thermo-field field theory

In the real-time finite temperature formalisms (Schwinger-Keldysh or Thermo-field), the free propagators are often defined with terms like: $$ \mathrm{Dirac\ Delta}\ \times \ \mathrm{Thermal\ ...
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Is the thermal expectation value of a square of Hermitian operator always finite?

If $\mathcal{O}$ is an hermitian operator in a system given by Hamiltonian $H$ and inverse temperature $\beta$, is $$\langle \mathcal{O} \mathcal{O} \rangle = Tr (e^{-\beta H} \mathcal{O} \mathcal{O})...
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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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Polyakov Loop and Chemical Potential

I have read in a paper (http://arxiv.org/abs/1203.3556) that in a thermal field theory, the chemical potential is $\mu=T \ln P$ where $$T^{-1}=\int_{0}^{\beta} \sqrt{-\xi^2}dt,$$ $\xi$ is $\partial_t$,...