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Questions tagged [quantum-field-theory]

Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use this tag for many-body quantum-mechanical problems and the theory of [tag:particle-physics]. Don’t combine with [tag:quantum-mechanics].

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Quantum field theory, Dirac field interaction Yukawa theory

From this Phys.SE question: Please can someone answer me to get the scattering amplitude and the cross section
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Zee's explanation of expressing bare coupling by physical coupling

In terms of bare parameter $\lambda$, the $\phi\phi\to\phi\phi$ scattering amplitude is $\lambda\phi^4$ theory is given by $$\mathcal{M}=-i\lambda+iC\lambda^2\Big[\ln\Big(\frac{\Lambda^2}{s}\Big)+\ln\...
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Derivation of Feynman rules from generating functional for non-eq QFT

I consider Yukawa non-equilibrium theory with interaction $g\bar{\psi}\phi\psi$ with massive fermionic field $\psi$ with mass $m$ and massive scalar field $\phi$ with mass $M$. I would like to ...
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How does the instanton break the $U(1)_A$ symmetry in QCD?

The $U(1)_A$ symmetry in QCD is anomalous. Its supposed to be broken by the instantons. Can anyone physically describe how does that happen?
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Question about a “general” definition for a black hole and his validity outer General Relativity

Consider the following definition: A Black Hole in an asymptotically flat spacetime $\mathfrak{M} \equiv (\mathcal{M}, \mathrm{\textbf{g}})$ is the set of events that do not belong to the causal ...
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Are the ideals in two GNS constructions linked to the equivalence (or not) of the CCR representations?

Starting from the abstract C* algebra $A$ of canonical commutative relations, a state $\rho$ over this algebra enables to construct a Hilbert space $A/I$ where $I$ is the ideal of the elements $a$ ...
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Vanishing integral in deriving stress-energy tensor from action

In the derivation of the energy-stress tensor for a scalar field (context: Inflation Theory for Cosmology) by varying the action with respect to the metric, the integral over spacetime that is ...
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If Quantum entanglement occurs naturally [duplicate]

If we were to monitor a single particles that is naturally entangled with another some where in the universe. Would it be possible to affect the other entangled particle? If so would a second party ...
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Reference on instantons in gauge theories

Is there a reasonably detailed and systematic exposition of the theory of instantons in non-abelian gauge theories?
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Vacuum energy length scale detectable by Casimir effect?

According to Sean Carroll's The Cosmological constant (Eqn.20) cosmological observations imply that the magnitude of the vacuum energy density in natural units is given by $$|\rho^{(obs)}_\Lambda|\le (...
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How solitons are related to particle physics?

Recently, I read a paper about introduction to solitons. Author said that the solutions of sine-Gordon equation can be candidate for modeling elementary particles and there are some applications in ...
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Microcausality when quantizing the real scalar field with anticommutators

We know by the spin-statistics theorem that the real scalar field has to be canonically quantized by commutators. But if we try to use anticommutators, we would expand the field $$\phi(x)=\int\frac{d^...
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LSZ reduction derivation Srednicki

In the derivation of the LSZ reduction formula equation (5.21) Srednicki claims that in case of an interaction term in the Lagrangian density $a^{\dagger}(\textbf{k})$ will no longer be time dependent....
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Terminology: Infrared and Ultraviolet

I am new to high energy physics and string theory. I keep reading the terms infrared and ultraviolet in papers. I assume they aren't talking about electromagnetic radiation. For example, one paper ...
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Spatial position and 3 momentum relation between particle states in canonical quantization (QFT)

In the beginning of the chapter on LSZ reduction, in Srednicki's book, he says that the operator $a_1 ^{\dagger}:=\int d^3k\: \text{exp}\Big[-(\textbf{k}-\textbf{k}_{1})^2/4 \sigma^2\Big] a^{\dagger}(\...
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Writing Dirac field interaction [closed]

I am studying QFT and am struggling to write expressions for the scattering of pseudo-scalar particles (such as π mesons) of Dirac particles described by the Lagrangian of Dirac field interacting with ...
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Critical parameter for 1D quantum system corresponding to $T_c$ of 2D Classical model

Utilizing the fact that there is a correspondence between a $d$ dimensional quantum system and a $d+1$ dimensional classical system (c.f. Trotter Decomposition), my question regards what the critical ...
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Coulomb forces in String Theory

In QED electrostatic forces are mediated by field theoretic effects known as virtual "particles" if I am not mistaken, but I don't know how string theory explains electrostatic interactions between ...
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Do infinities occur when Quantum Field Theory is treated numerically?

What puzzles me regarding QFT and the occuring of infinte integrals when treated in a perturbatative manner is if these infinties would also occur when the theory is treated numerically, maybe even in ...
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Mismatch between conformal generators and conformal transformations as changes of variables

Introduction It is known that under changes of coordinates different fields transform according to their tensorial nature (scalar, vector, etc.) like$^{[1]}$ \begin{equation} \phi(x)\rightarrow\phi'...
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$\phi^3$ 2D 1-loop diagram disambiguation

I would like to calculate the 1-loop 1-PI correction to the propagator for $\phi^3$ scalar theory in 2 dimensions, where the integral is finite. Performing the usual procedure (Feynman trick, Wick ...
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Is Lorentz symmetry broken if SUSY is broken?

I have seemingly convinced myself that the entire Poincare group is spontaneously broken if one of the supersymmetric charges is spontaneously broken. We know that if one of the supersymmetric ...
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Ward identity for 'general' operator, higher point anomalies cancellation and current diagrams

This is actually about several related doubts and I hope is appropriate for a single question (if not, I will happily divide it). So, my problems are related to the analysis and calculation of chiral ...
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Quantization on (2,1)-signature hyperplane

QFT states, roughly speaking, belong to a certain subset of functionals over the field configuration on the space-like hyperplane, usually chosen as $t = 0$. What would happen if we chose a mixed-...
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observing the conserved canonical momenta

Suppose I have a Lagrangian $\mathcal{L}[\phi]$ with $\phi$ a cyclic variable, which means that the Lagrangian is symmetric under shift of $\phi\rightarrow\phi+c\quad$. The equation of motion will be ...
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Detail on C vs. CP violation

In the answer given by knzhou to the post What distinguishes the behaviour of particle from its antiparticle: C violation or CP violation? it is said that "but the reaction $i \rightarrow f$ will ...
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Question related to electric dipole moment via QFT

My question is related to the following post: Extracting Electric Dipole Moment from Matrix Element via Form Factor There, it is said that the electric dipole moment (EDM) is giving by a term that ...
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Canonical commutation relations for a real scalar field

I am taking my first course in QFT and have come across this problem From the canonical commutation relations for a real scalar field $\hat{\phi}$ show that $$[\partial_i \hat{\phi} , \hat{\phi}...
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1answer
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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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1answer
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Driving force and mean of a particle wave function [duplicate]

I am currently undergoing a course on introduction to quantum mechanics and we took the historical approach. I'm currently at DeBroglie wavelength. He introduces the wave particle duality in matter, ...
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How to break softly a symmetry

If you start from a theory (non-SUSY) with whatever symmetry and you break it by adding a soft term. Do you have to add to your Lagrangian all possible soft terms that break the symmetry? If so, why? ...
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Fermi golden rule: occupation factor

Fermi's golden rule for transitions between single-particle states $a$ and $b$ is $$ \Gamma_{ a \to b} = \frac{2\pi}{\hbar}\vert M_{ab} \vert^2\delta(\epsilon_a - \epsilon_b) \, .\tag{1} $$ Here $\...
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Size of quantum corrections at infinity

Suppose we have a one dimensional field theory for the field $\phi(r)\;r\in[0,\infty]$ and that the solution for the background (Euler Lagrange equations) give a function $\phi_0$ that goes to a ...
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Piecewise solution to Euler-Lagrange equations

I would like to consider a background for a quantum field theory made up by connecting continuously two different solutions of the Euler Lagrange equations. The problem is one dimensional (let's call ...
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Do Lorentz invariance and General covariance always hold at low energies, or are they sometimes violated?

This is motivated by Weinberg’s folk theorem, where the construction of our perturbative expansion (and choice of theory space) is mostly safe given that we only have to enforce very general symmetry ...
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Peskin equation on the treatment of chiral anomaly

In page 666 (it couldn't be other way - bad joke), chapter 19, the Eq. (19.73) claims (see properties of the $\phi_n(x)$ functions in this post: Change of variables in path integral measure): $$ \...
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Gordon decomposition in Cheng and Li p. 422

In the $\mu \rightarrow e+\gamma$ calculation in Cheng and Li "Gauge theory of elementary particle physics" p.422 they have $$ T=A\bar{u}_e(p-q)(1+\gamma_5)i\sigma_{\lambda\nu}q^\nu\epsilon^\lambda ...
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Virtual pair of particle-antiparticles trajectory [duplicate]

Is it possible to do heuristic calculations on virtual pair of particle-antiparticle trajectories that appear in a vacuum? For example, what is the maximum distance between them during virtual process?...
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Change of variables in path integral measure

In fermion's path integral we have a measure that you can write, in terms of the Grassmann variables $\psi, \bar{\psi}$ as $$ D\bar{\psi}D\psi, \quad \psi(x) = \sum_n a_n\phi_n(x), \quad \bar{\psi}(x)...
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Simplest model in field theory which leads to a pseudo-Goldstone boson

What can be a simple (if not simplest) continuum field theory model that gives rise to a pseudo Goldstone boson (doesn't matter if it is a toy model)? For example, I would be very happy if one can ...
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Derivation of the QFT Propagator

I don't understand how we get from the RHS to the last line. \begin{eqnarray} \left[ \hat{H}_x - i \frac{\partial}{\partial t_x} \right] G^+(x,t_x,y,t_y) &=& -i \delta (t_x - t_y) \sum_n{\...
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Symmetry and symmetric vacuum in Quantum Field theory

In the start of section 28.2 of Schwartz's Quantum Field theory and the Standard Model, Schwartz states that for a conserved charge, $\hat{Q}$, which generates the corresponding symmetry ...
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References to understand BRST Quantization

I'm looking for good, rigorous references that discuss BRST quantization in relation to how it leads to dealing with anomalies and ghost fields. I'm looking at high level references (i.e., assume ...
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Why a field theory containing only fermions does not show spontaneous symmetry breaking?

For a real scalar field $\phi$, a theory as simple as the $\phi^4$ theory, can exhibit the phenomenon of Spontaneous Symmetry Breaking (SSB). For a complex scalar field $\phi$, a theory as simple as ...
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Why is the approximate $\rm U(2)\times U(2)$ global symmetry of QCD that has a special importance?

I was looking at Peskin and Schroeder (Section 19.3, page $667-668$). They talk about $\rm U(2)\times U(2)$ symmetry for the QCD Lagrangian in the limit of massless $u$ and $d$ quarks. However, this ...
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Corrections from (to?) the Quantum Action Principle

In expositions of the Quantum Action Principle (sometimes the Quantum Dynamical Principle) it is shown that information may be derived from the vacuum transition amplitude. Specifically, $\langle \psi ...
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Gauge and global symmetries in Chern-Simons/WZW correspondence

I am trying to understand how bulk gauge symmetry in 3d Chern-Simons theory becomes a global symmetry in the boundary 2d WZW theory. In particular, I am trying to understand the papers by Elitzur et ...
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Is it true that in practice quantum fields are *always* measured by means of coupling to particle detectors?

I'm watching some lectures on Relativistic Quantum Information and in one of them - available here - the instructor is talking about measuring quantum fields. He then says basically that in real ...
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rigorous definition of coherence length at mean field theory

so as far as I know, when we are doing mean field theory, in qft, we expand a action of a theory around a classical solution. so we find a classical solution, than we add quantum mechanical ...
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Matsubara Sums and Multiple Poles

In Mahan's book, equation (4.127), he claims that \begin{align} &\frac{1}{\beta}\sum_{ik_n} \frac{1}{ik_n-\xi_1}\frac{1}{ik_n-\xi_2}\frac{1}{ik_n-\xi_3} \\ =& \frac{n_F(\xi_1)}{(\xi_1-\xi_2)(\...