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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Symmetry restoration in accelerated frames
I am trying to understand the symmetry restoration in accelerated frames. I was reading 1 and 2. Can somebody help me to understand how they got Eq. 7.12 in 1 or Equation just after Eq.3.3 in 2? In ...
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Propagators in Quantum Field Theory at Finite Temperature
While reading section 5.8.2 of Quantum Field Theory An Integrated Approach by Fradkin, I had a few questions, not able to think them though myself. The thermal propagator is given as
$$G_{T}^{(0)}(\...
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Resummation of higher order in finite temperature
This is a question about the resummation of finite temperature quantum field theory. Take massless $\lambda\phi^4$ theory as an example. After doing the resummation of IR divergence, one express the ...
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Change in photon production rates due to finite temperature / a QED plasma?
I have the following question:
In a QED plasma, the photon technically gains a "mass" due to a change in its dispersion relations. I was wondering, if the photon also acts as massive during ...
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Evaluation of thermal average with path integral
I want to evaluate the thermal average
$$<\hat{\phi}(0)\hat{\phi}(0)\hat{\phi}(x)\hat{\phi}(x)>$$
with the path integral. $\phi$ is a real scalar field.
In general:
$$<\hat{\phi}(0)\hat{\phi}(...
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Relation of Wick theorems
In the context of quantum stat mech it is common to use Wick's theorem to refer to the factorisation
$$
\langle f_1 f_2 f_3 \cdots f_N\rangle = \sum_{\text{pairings}\, \pi} (\pm 1)^{|\pi|} \langle f_{\...
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Partition function for bosons with path integral
In this book the partition function for bosons is defined in eq. 2.17 as:
$$Z=\mathrm{Tr}[e^{-\beta (H-\mu_i N_i)}]=\sum_a\int d\phi_a\langle\phi_a|e^{-\beta(H-\mu_i N_i)}|\phi_a\rangle$$
The ...
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Harmonic oscillator propagator in Euclidean time
I'm following Nastase's book on Quantum Field Theory but this question is just about quantum mechanics in the path integral formalism. In chapter 8 he considers the propagator equation for a harmonic ...
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Fourier transform of Wick rotated functions
I am learning the imaginary time formalism of thermal field theory / reviewing the Euclidean formalism of quantum field theory. One thing that appears to be left implicit in many treatments is a ...
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Doubts about the "periodicity trick" to compute temperature
The "periodicity trick" is a mysterious way to compute some sort of temperature associated to a Rindler-like spacetime.
Suppose there exist coords $R\in(0,\infty), \eta\in(-\infty,\infty)$ ...
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How does SSB happen?
I've just finished studying for an exam on the Standard Model (so electroweak theory and symmetry breaking) and I can't figure out how this question never crossed my mind. I'm now studying the QCD ...
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$S$-matrix element for real photon production
In this book (Thermal field theory by Bellac) on page 109 the $S$-matrix element for the transition from an initial state to a final state plus photon $(i)\to(f,\gamma)$ is given:
$$S_{fi}^{(\lambda)}(...
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Interpreting the derivative of the effective potential with the tadpole
I am currently going through the Finite Temperature Field Theory notes by Mariano Quiros, and I stumbled upon a claim that I have seen often in the literature, namely that the first derivative of the ...
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Temperature of AdS-Schwarzchild black holes ? how physics is the same for different temperatures?
The five dimensional Schwarzchild-AdS black brane's metric is given by
$$
ds^2_5=-\left(\frac{r}{L}\right)^2h(r)dt^2+\frac{dr^2}{\left(\frac{r}{L}\right)^2h(r)}+\left(\frac{r}{L}\right)^2(dx^2+dy^2+dz^...
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Above the electroweak scale, is the Higgs ever effectively massless? (thermal field)
So before the Higgs attains a vev (i.e., above TeV scales), does the Higgs doublet become effectively massless?
The Higgs doublet $\Phi$ (not the physical higgs about the nonzero vev) gains an ...
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Quantum field theory at finite temperature
Is there any notion of causality in Quantum field theory at finite temperature?
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Yukawa interaction in QM (0+1D field theory)
This is a question about considering a simple ordinary quantum mechanics system from a quantum field theory perspective. Out of necessity the setup describing the problem is fairly long, but the ...
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E. Fradkin on thermal propagator of free scalar field
In his lecture, E. Fradkin performs a Matsubara sum to show that the finite temperature contribution to the thermal propagator of the free scalar field contains the Bose-Einstein factor (see 5.209 - ...
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Wick rotation on Ward identities
I'm having trouble performing a Wick rotation back to Minkowski spacetime ($\eta_{\mu\nu}=(-1,1,1,\dots)$), following page 19 in the lecture notes here by C.P. Herzog.
I have this expression (equation ...
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Matsubara sum with log term [closed]
How do I compute the Matsubara sum
$$\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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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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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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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 starts with a "free" ...
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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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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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Retarded Green's function is the same as time-ordered Green's function at zero temperature for $\omega>0$
Consider the equilibrium time ordered and retarded Green's function for two operators $A,B$, defined as follows
$$
G^T(t,t') \equiv -i\langle T A(t)B(t') \rangle=-i\theta(t-t')\langle A(t)B(t')\rangle ...
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Confusion about trace in the vertex term of Lagrangian
I was reading through Mariano Quirós's lecture notes titled "Finite Temperature Field Theory and Phase Transitions". In Sec. 1.2, the author is calculating the one-loop effective potential at $T=0$. ...
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Understanding Matsubara summation
I'm trying to understand matsubara summation.
Let us say I have $f(i\omega) = 1$.
Obviously, the matsubara summation $\sum_{\omega_n} f(i\omega_n)$ diverges.
So, I use a weighing function. Let us ...
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How does one modify the decay width of a particle (QFT/Thermal Field theory style) when a particle is travelling through matter
I believe a particle's decay width/rate should depend on whether they are in matter or vacuum, but am unsure of where to find a prescription describing this phenomena. Please could someone point me in ...
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Guessing the temperature dependence of a decay rate $\Gamma(A\to B+B)$
For a two-body decay of the form $$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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