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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2answers
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Proof of Loss of Lorentz Invariance in Finite Temperature Quantum Field Theory

In the standard quantum field theory we always take the vacuum to be a invariant under Lorentz transformation. For simple cases, at least for free fields, is very simple to actually prove this. Now ...
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4answers
2k views

temperature of electroweak phase transition

How does one estimate the temperature at which electroweak phase transition (EWPT) occurred? Somewhere I have read it is around 100GeV but the reason was not explained.
11
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1answer
2k views

What is the difference between quantum fluctuations and thermal fluctuations?

Start with a simple scalar field Lagrangian $\mathcal{L}(\phi)$ at zero temperature $T = 0$, which has a hidden symmetry and spontaneously break it. By the standard procedure a field $\phi$ is ...
11
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0answers
476 views

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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1answer
293 views

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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1answer
213 views

How it can be: separable Hilbert space in fundametial physics, and non-separable in condensed matter physics?

The fundamental QFT is formulated in a separable Hilbert space. But mostly approaches in condensed matter physics, e. g. thermal field dynamics, use a non-separable Hilbert space. It looks like it is ...
4
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1answer
266 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 ...
3
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1answer
195 views

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 ...
3
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2answers
2k views

What's the true reason behind thermal expansion?

Thermal expansion is a normal concept everyday. There are 2 explanations: 1, thermal expansion result in stress, then result in deformation 2, thermal expansion result in deformation, then result in ...
3
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1answer
35 views

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 ...
3
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1answer
67 views

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 ...
3
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2answers
76 views

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\ ...
3
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1answer
184 views

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 $...
3
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0answers
594 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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1answer
608 views

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 ...
2
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1answer
114 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 ...
2
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1answer
93 views

“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 $...
2
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1answer
649 views

Matsubara frequencies as poles of distribution function

Is there any deeper meaning to why the bosonic/fermionic Matsubara frequencies appear as poles of their corresponding distribution functions (with an additional $i$)? For example in the bosonic case ...
2
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1answer
88 views

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 $T=0$. ...
2
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1answer
143 views

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 ...
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0answers
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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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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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0answers
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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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0answers
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, ...
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138 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}[-\...
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3answers
155 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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1answer
478 views

Energy density and pressure in thermal quantum field theory

In QFT, energy density and pressure can be defined from Noether current due to Poincare translation invariance. What if we are considering a system at finite temperature? For a scalar field, we have ...
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1answer
56 views

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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1answer
331 views

Thermal mass and Thermal Width

I have a question about understanding the physical interpretation of the thermal mass and width of a particle. If we consider a particle in a plasma (which lets say is in the early universe and so ...
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1answer
155 views

Simple generalization of the Feynman rules for QFT to thermal QFT?

Assuming that one knows Feynman rules for QFT, what is the simplest way to generalize them for $T \neq 0$ case? What is the main difference? Can we just read them off from Lagrangian the same way as ...
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1answer
36 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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34 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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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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0answers
32 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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0answers
66 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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0answers
48 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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0answers
68 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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0answers
70 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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0answers
118 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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0answers
193 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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1answer
108 views

Role of thermal fluctuations in restoring the symmetry in finite systems

A symmetry is spontaneously broken in a system with infinite number of degrees of freedom (DOF), when the system finds itself in the ground state that breaks the symmetry of the Hamiltonian. For ...
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1answer
83 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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1answer
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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 ...
0
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1answer
27 views

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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0answers
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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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1answer
33 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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0answers
130 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 ...
0
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1answer
215 views

Thermal Expansion of Pump Shaft

To determine the thermal expansion of a pump shaft the following formula is available: $\Delta$L=$\alpha$L0$\Delta$T Below I also have a sketch of the situation: The shaft is constrained at the ...
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2answers
440 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[...