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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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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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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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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25 views

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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42 views

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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55 views

Does finite temperature QFT partition function capture both quantum and statistical fluctuations?

I've been working on understanding finite temperature field theory and am stuck with the following concepts: For our thermal system in equilibrium we have the usual partition function \begin{equation} ...
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1answer
80 views

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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Higgs self-energy at finite temperature

Is there anybody know of a reference that calculates the Higgs self-energy at finite temperature, say in a Standard Model plasma?
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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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How to calculate thermal corrected masses of Higgs and Gauge bosons?

How are the self energies of scalars and gauge bosons at finite temperature calculated in the process of determining the 1-loop resummation of Debye masses? I have seen some papers where the explicit ...
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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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Time dependence of Drude-like correlation function obtained from Matsubara formalism

I'm trying to calculate the real time dependence of the correlation function that I've obtained in my effective model (it is closely related to the electron density correlation function), given in ...
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71 views

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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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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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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343 views

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 $\partial_t$,...
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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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What are thermal photons?

What is the difference between an ordinary photon and a thermal photon? Do thermal photons act as an exchange particle for any forces similar to an ordinary photon which acts as an exchange particle ...
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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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Is there any physical meaning for such a correlation function?

Consider a thermal scalar field theory, we have the partition functional $$Z={\rm tr}(e^{-\beta H}).$$ We can build this theory as an Euclidean quantum field theory $$Z=\int\mathcal{D}\Phi\,e^{-S_E[\...
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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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99 views

Physical understanding of the change in scattering cross-sections at finite temperatures

I am familiar with the computation of scattering cross-sections in zero temperature quantum field theory. How does a scattering cross-section typically behave at temperature $T$? Let the cross-...
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610 views

Harmonic oscillator at finite temperature: taking expectation values of operators

I have the Hamiltonian of an harmonic oscillator (with $\hbar=1$) $$ H = \omega \left(a^\dagger a + \dfrac{1}{2} \right) \;, $$ and the associated (canonical) partition function $$ Z = \text{Tr}\left[...
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is there any relation between the emissivity and the temperature?

I was just wondering if there is any relation between the emissivity and the temperature (i.e. temperature as a function of the emissivity). If yes, can you write the relation and cite a reference ...
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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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How did dark matter become a relic?

Why did the decay rate of the dark matter particles fall when the temperature of the Universe $T_U$ dropped below dark matter mass $M_{DM}$? In particular, why can it not decay into lighter particles ...
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Does non-unitarity necessarily imply the probability leakage?

I know that in quantum computing and also in the studies of the information loss inside black holes people often consider the following construction. The composite system, which consists of subparts $...
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How does one ensure that effective action includes all possible quantum corrections to the clasical action?

Consider a classical scalar field theory for a real scalar field $\phi$ given by $$\mathcal{L}=\frac{1}{2}(\partial_\mu\phi)^2-V(\phi)$$ where $V(\phi)$ is the classical potential. In quantum field ...