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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questions
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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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0answers
19 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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1answer
37 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 ...
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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
$$\phi _1 = \sqrt2 \zeta \cos \theta + \sqrt{\frac{\beta}{V}}\sum_{n,\bar p}e^{i(\...
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1answer
90 views
Confusion about trace in the vertex term of Lagrangian
I was reading through Mariano Quirós's lecture notes titled "Finite Temperature Field Theory and Phase Transitions". In Sec. 1.2, the author is calculating the one-loop effective potential at $T=0$. ...
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38 views
Understanding Matsubara summation
I'm trying to understand matsubara summation.
Let us say I have $f(i\omega) = 1$.
Obviously, the matsubara summation $\sum_{\omega_n} f(i\omega_n)$ diverges.
So, I use a weighing function. Let us ...
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1answer
35 views
How does one modify the decay width of a particle (QFT/Thermal Field theory style) when a particle is travelling through matter
I believe a particle's decay width/rate should depend on whether they are in matter or vacuum, but am unsure of where to find a prescription describing this phenomena. Please could someone point me in ...
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1answer
39 views
Guessing the temperature dependence of a decay rate $\Gamma(A\to B+B)$
For a two-body decay of the form $$A\to B+B$$ if the interaction strength controlling the decay is $\lambda$, the Feynman amplitude $\mathcal{M}$ will contain a factor of $\lambda$ from the vertex ...
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34 views
Classical chaos at finite temperature
Is there any finite temperature generalization of classical chaos? In quantum chaos, at least with regards to out-of-time-order correlators, the generalization is clear - one simply takes a thermal ...
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50 views
Reference for Feynman diagram technique(position space) in Thermal Field Theory
I am trying to study perturbative expansion of Sachdev-Ye-Kitaev model, where I know that the dominant terms are the Melonic diagrams. I am interested in seeing how perturbative corrections affect the ...
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32 views
Electroweak phase transition and finite temperature field theory formalism
We do our calculations in standard quantum field theory at zero temperature where we can derive pole mass and renormalized mass and ...
Due to my understanding, pole mass is independent of any energy ...
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How does thermalisation make incoherent waves into coherent ones?
Thermalisation is the process by which out-of-equilibrium systems reach equilibrium. Coherence refers to the phases of waves being a constant difference apart.
While reading a paper on axion stars, I ...
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70 views
Thermal density matrix QFT
The density matrix of a system at finite temperature is give by
$$\langle\psi_1|\rho|\psi_2\rangle=\frac{1}{Z}\langle\psi_1|e^{-\beta H}|\psi_2\rangle, $$
where $Z$ is a normalization constant. We ...
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27 views
Normal ordering in 2D thermal CFT
I am trying to understand the notion of normal ordering in thermal CFT in 2D CFT, for instance I consider a two-point function of scalar primary operator with $\Delta$ dimension at finite temperature $...
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0answers
48 views
How can we calculate the imaginary part of a fraction that has a term $i0_+$ in the denominator?
I have recently started dealing with thermal field theory for fermions and I am faced with a paper that, at some point, tries to calculate the imaginary part of a fraction that looks like:
$$\frac{1}{...
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1answer
122 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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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
$$
\...
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28 views
Proof of factorization at late times for chaotic systems
While reading the paper "A bound on Chaos - Maldacena et. al", https://arxiv.org/abs/1503.01409 in equation (23) of the paper they factorize a correlator of the form,
$$ Tr [\rho^{1/2} W(t) V \rho^{1/...
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1answer
69 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 ...
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135 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 ...
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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 $...
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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:
$$
\mathrm{Dirac\ Delta}\ \times \ \mathrm{Thermal\ ...
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3answers
197 views
Is the thermal expectation value of a square of Hermitian operator always finite?
If $\mathcal{O}$ is an hermitian operator in a system given by Hamiltonian $H$ and inverse temperature $\beta$, is $$\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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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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651 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
654 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 ...
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71 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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1answer
303 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
$$Z=\int\mathcal{D}\Phi\,e^{-S_E[\...
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126 views
Fermion boundary condition for a thermal compact circle
Is this true that for fermion statistical systems
in the thermal phase, with Euclidean time,
$$
\beta=1/T=t_E
$$
the Euclidean time will be chosen to be anti-periodic for fermion boundary ...
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1answer
84 views
Physical understanding of the change in scattering cross-sections at finite temperatures
I am familiar with the computation of scattering cross-sections in zero temperature quantum field theory.
How does a scattering cross-section typically behave at temperature $T$?
Let the cross-...
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2answers
460 views
Harmonic oscillator at finite temperature: taking expectation values of operators
I have the Hamiltonian of an harmonic oscillator (with $\hbar=1$)
$$
H = \omega \left(a^\dagger a + \dfrac{1}{2} \right) \;,
$$
and the associated (canonical) partition function
$$
Z = \text{Tr}\left[...
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1answer
2k views
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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1answer
268 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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1answer
196 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 ...
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1answer
188 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 $...
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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, ...
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1answer
145 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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1answer
110 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
682 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 ...
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0answers
141 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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1answer
223 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 ...
5
votes
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 ...
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1answer
336 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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0answers
196 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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0answers
478 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
159 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
485 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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votes
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 ...
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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.
