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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 particle physics. Don’t combine with the [quantum-mechanics] tag.

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Triangle diagrams with axial currents at all vertices [closed]

I have problem with this exercise. We are considering Abelian anomaly and in particular axial currents anomalies. Consider the amplitude $ \langle 0 |T{j^\lambda_5(0)j^\mu_5(x_1)j^\nu_5(x_2)}| 0 \...
Franca's user avatar
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How to avoid the ordinary Coulomb solution in QCD?

To see where QCD starts to differ from the behavior of EM fields, we might begin by looking at the classical field. A search brings up [question 339978] and [question 360061] but no answer is found ...
Jos Bergervoet's user avatar
2 votes
1 answer
64 views

Loop Effect of $\phi$ Propagator in $t$-channel of scalar $\phi^3$ theory [closed]

In Schwartz's QFT chapter 16, he calculates the loop effect (vaccum polarization) of $\phi$ propagator in $\phi^3$ theory, with the choice of Pauli-Villars regulator, the scattering amplitude would be ...
Ting-Kai Hsu's user avatar
-1 votes
2 answers
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Can the Strong CP problem be explained by the cancellation of quark electric dipoles by dipoles from some as yet undetected matter surrounding quarks?

I am not a mathematical physicist but from popular science articles I get the impression that CP violation occurs because quarks unexpectedly don't produce an electric dipole. If this is correct could ...
DaveTheWave's user avatar
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1 answer
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Square of the Feynman amplitude for $a +b\to c+d$ and its reverse

In quantum field theory, if a process $a +b\to c+d$ is allowed by a certain interaction Lagrangian (hermitian), the reverse process, $c+d\to a+b$, must also be allowed (as far as I understand) by the ...
Solidification's user avatar
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70 views

Mandelstam variables sign

I am self-studying the book "Quantum Field Theory and the Standard Model" by Schwartz, on page 99 (paragraph "Mandelstam variables"), the context is the $2\rightarrow 2$ scattering ...
Andrea's user avatar
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A reference for the fact that the second cohomology of the full Poincare algebra is zero

S. Weinberg in his book "The quantum theory of fields" vol. I says in page 86 that the full Poincare algebra is not semi-simple but its central charges can be eliminated (as he showed in the ...
Mahtab's user avatar
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$ \pi^0\to \gamma\gamma$ parity conservation

Let's consider the decay process $\pi^0\to \gamma \gamma$. After we spontaneously broke the chiral symmetry of QCD coupled to an abelian gauge field $A^\mu$, we end up with the Goldstone boson ...
Alex's user avatar
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About momentum states covariant normalization

I'm following QFT of Schwrtz and I have a doubt about Eq. (2.72). In particular, from Eq. (2.69): $$[a_k,a_p^\dagger]=(2\pi)^3\delta^3(\vec{p}-\vec{k}),\tag{2.69}$$ and Eq. (2.70): $$a_p^\dagger|0\...
Albus Black's user avatar
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Phase Coherence in the BCS wavefunction and the Cooper Pair Wavefunction

I have a couple question regarding the following BCS wavefunction ($|0\rangle$ is the vacuum state): $$|\psi\rangle = \Pi_k \big(|u_k|+|v_k|e^{i\varphi}c^\dagger_{k\uparrow} c_{-k\downarrow}\big)|0\...
scruby's user avatar
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Some calculation in Schwartz's Quantum field theory eq. (16.39)

In Schwartz's Quantum field theory and the standard model, p.307 he derives a formula: $$ \Pi_2^{\mu \nu} = \frac{-2 e^2}{(4 \pi )^{d/2}}(p^2g^{\mu\nu}-p^{\mu}p^{\nu})\Gamma(2- \frac{d}{2}) \mu^{4-d} \...
Plantation's user avatar
3 votes
3 answers
640 views

Where are quantised states in QFT?

Perhaps the most striking fact of quantum mechanics, and where the name comes from, is the fact that the energy of a quantum system is generally quantized (for bound states), i.e. it can only take ...
Gabriel Ybarra Marcaida's user avatar
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Gauge invariance of Hadamard point-splitting renormalization procedure

The current density of a charged complex scalar field in a background electromagnetic field $A_\mu$ is given by $$ j^\mu = ie( (D^\mu \phi)^*\phi - \phi^*D^\mu \phi)$$ with $D_\mu = \partial_\mu + ...
dolefeast's user avatar
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2 answers
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Understanding Feynman Diagrams in Loop Corrections to the propagator $\phi ^3 $ theory [closed]

I found other posts talking about the same chapter in the same book, but none of them were exactly about what I am asking here. In Srednicki's chapter 14 (Loop corrections to the propagator), we are ...
Fernando Garcia Cortez's user avatar
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1 answer
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What happens to the fermion spin when I move around it in a full circle

I would like to understand the actual meaning of the description of a fermion as a spinor. I have a background in QFT and understand the calculations, but there is a leap to the actual experiment ...
ziv's user avatar
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Retarded Green's function in Peskin & Schroeder

In an Introduction to Quantum Field Theory by M. E. Peskin & D. V. Schroeder (eq. 2.56 on page 30) the following relation for the retarded Green's function was established: $$(\partial^2 + m^2) ...
Volodymyr's user avatar
2 votes
0 answers
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Quantum field expansion and bogoliubov coefficients in the interior of a rotating black hole

I am trying to quantize a real scalar field in the interior of a rotating black hole (3+1 D, asymptotically flat). My question is regarding the modes of the radial part of the equation (obtained after ...
Ratul Thakur's user avatar
1 vote
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120 views

On which bundle do QFT fields live?

In QFT, there is a vector field of electromagnetism, usually notated by $A$, which transforms as a 1-form under coordinate changes. Since quantum fields are operator-valued, I thought it is a section ...
Sung Kan's user avatar
2 votes
2 answers
79 views

How does inserting an operator in the path integral change the equation of motion?

I am reading this review paper "Introduction to Generalized Global Symmetries in QFT and Particle Physics". In equation (2.43)-(2.47), the paper tried to prove that when $$U_g(\Sigma_2)=\exp\...
gshxd's user avatar
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Asymptotic states and physical states in QFT scattering theory

Context In the scattering theory of QFT, one may impose the asymptotic conditions on the field: \begin{align} \lim_{t\to\pm\infty} \langle \alpha | \hat{\phi}(t,\mathbf{x}) | \beta \rangle = \sqrt{Z} \...
Steven Chang's user avatar
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1 answer
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$2\pi$-rotation of fermionic states vs. fermionic operators

Given a fermionic state $|\Psi\rangle$, a $2\pi$ rotation should transform it as \begin{equation} |\Psi\rangle \quad\to\quad -|\Psi\rangle \,, \end{equation} On the other hand, given a fermionic ...
Mateo's user avatar
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1 answer
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Vacuum flucutuations = local entanglement between quantum fields?

I'm puzzled by this statement by Dieter Zeh: "Various types of quantum fluctuations (in particular vacuum fluctuations, often visualized in terms of 'virtual particles') are used to describe ...
Husserliana's user avatar
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0 answers
71 views

Questions about fundamental solutions and propagators for the Dirac operator

I thought that propagator is a synonym for fundamental solution. But that seems not to be the case since in this answer it is said that an expression with delta function on a surface has to be ...
Andrew's user avatar
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2 votes
0 answers
102 views

Instantons in the Global $O(2)$ Model (Compact scalar field) - Polyakov textbook

This question is related with Polyakov, "Gauge Fields and Strings" section 4.2 In section 4.2, partition function is \begin{equation} Z=\sum_{n_{x,\delta}}\int_{-\pi}^{\pi}\prod_x\frac{d\...
zahra's user avatar
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3 votes
3 answers
604 views

Path integral at large time

From the path integral of a QFT: $$Z=\int D\phi e^{-S[\phi]}$$ What is a nice argument to say that when we study the theory at large time $T$, this behaves as: $$ Z \to e^{-TE_0} $$ where $E_0$ is the ...
BVquantization's user avatar
2 votes
1 answer
112 views

What does it mean to "resum" the large logarithms?

I am struggling to understand the concept of resummation of large logarithms in QFT; from what I learnt so far the problem relies on the fact that if a full theory defined in the UV contains much ...
Filippo's user avatar
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1 answer
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Derivation of two-body Coulomb interaction in momentum space

$\newcommand{\vec}{\mathbf}$ In Condensed Matter Field Theory by Altland and Simons, they claim the two-body Coulomb interaction for the nearly-free electron model for a $d$-dimensional cube with side ...
zeroknowledgeprover's user avatar
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0 answers
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Static Patch Decomposition of Bunch Davies Vacuum

In the Jerusalem Lectures on Black Holes section 3.3 the author considers a QFT in Minkowski space. He then picks out a space coordiante, say $x$, and divides the Hilbert space $H$ of the QFT in two ...
Aralian's user avatar
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3 votes
0 answers
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Physical observables in the XY/sine-Gordon duality

My question is, during the duality map, real physical quantities seem to acquire a prefactor of $i$ and become purely imaginary. And I feel uncomfortable. Take bosonic current for example. Consider ...
T.P. Ho's user avatar
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On the symmetry of changing the sign of helicity of incoming and outgoing particles in the invariant matrix element

Let $\Psi_\Lambda^{\{\mu\}}\propto U_\Lambda^{\{\mu\}}$ and $\psi_\lambda^{\{\nu\}}\propto u_\lambda^{\{\nu\}}$ be spinors of spin $s$ fermions where $s \geq 1/2$ with respective helicites $\Lambda$ ...
infinitezero's user avatar
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-1 votes
1 answer
24 views

Deriving the equal time anti-commutator of the Dirac fields [closed]

I am trying to solve an exercise on deriving the equal-time anti-commutator of the Dirac fields. But I got stuck somewhere and couldn't get the desired result. I would like to show that $$ \{\psi(x), \...
user174967's user avatar
2 votes
1 answer
56 views

Causality for gauge dependent operators in quantum field theories

Suppose that $\mathcal{A}_{ij...}(x)$ and $\mathcal{B}_{ij...}( x')$ are two gauge dependent (so non-observable) operator in some theory. If they are spacelike, should I impose the causality ...
Ervand's user avatar
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-2 votes
1 answer
59 views

What is the energy of a photon in an electron-muon scattering?

Currently I am reading about this process in an Introduction to Quantum Field Theory by Peskin and Schroeder (pages 153-154). It should be mentioned that they are working in a center-of-mass (CM) ...
Volodymyr's user avatar
1 vote
0 answers
36 views

Goldstone Theorem in Schwartz, follow-up

This is somewhat of a related question to Goldstone theorem in Schwartz and is related to equation 28.16 in Schwartz's QFT book. One way to prove that $$ \langle \Omega | J^\mu(x) | \pi(p) \rangle = i ...
infinity's user avatar
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0 answers
30 views

Why the Slavnov operator is self-adjoint? [duplicate]

In the context of BRST we can define the Slavnov operator $\Delta_{BRST}$ which generates BRST transformations. My lecture notes claim that $\Delta_{BRST}$ is self-adjoint, but I don't see why.
Alex's user avatar
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1 vote
2 answers
106 views

Checks of anomaly cancellation

In a textbook I read that if $G$ is a global symmetry of the classical Lagrangian, then one has to check $G\times H^2$ anomalies, where $H$ is one of the SM gauge groups. For example, when $G$ refers ...
Fern's user avatar
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0 votes
2 answers
114 views

Do different bases of Fock space commute?

$\newcommand\dag\dagger$ Suppose we have a Fock space $\mathcal{F}$ with two different bases of creation and annihilation operators $\{a_\lambda, a^\dag_\lambda\}$ and $\{a_{\tilde \lambda}, a^\dag_{\...
zeroknowledgeprover's user avatar
1 vote
1 answer
59 views

Does electroweak theory have mass gap (not just Higgs mechanism)?

I am extremely confused by seemingly contradictory statements. In this PE answer, the electroweak sector in the Standard Model does NOT have a mass gap (or at least not observed). In fact, the gauge ...
Keith's user avatar
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2 votes
0 answers
125 views

Prerequisites to learn/work on double copy theory and amplitude methods for gravity

I am a PhD student in classical gravity; specifically in BH perturbation and GW. I am interested in learning about the double copy and the use of scattering amplitudes in understanding GW physics. I ...
2 votes
1 answer
44 views

Precise relation between theromdynamic beta and coupling constant in Euclidean QFT

In statistical mechanics, the thermodynamic is inverse of the temperature: $\beta \propto T^{-1}$. In Euclidean QFT, I have often run into the expression like $\beta \propto g^{-2}$ where $g$ is the ...
Keith's user avatar
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1 vote
1 answer
144 views

2PI Effective Action from Double Legendre Transformation

This answer (https://physics.stackexchange.com/q/348673) provides good intuition for why Legendre transformation induces 1-particle irreducible graphs: It mainly tries to convey the idea that the ...
JinH's user avatar
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0 votes
1 answer
63 views

Understanding Virtual Particles and the Mediation of Forces

When trying to understand how the electromagnetic force works in a Quantum-Mechanic context (what mediates it), one concept you will quickly encounter is that of virtual photons (and more generally ...
Giorgos G's user avatar
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3 votes
0 answers
106 views

The commutation relations of photon and gluon?

In QED, the photon field has the following commutation relations: \begin{equation} [A^{\mu}(t,\vec{x}),A^{\nu}(t,\vec{y})]=0, \tag{1} \end{equation} where $A^{\mu}(t,\vec{x})$ is the photon filed. ...
Qin-Tao Song's user avatar
0 votes
1 answer
42 views

Bogoliubov transformation of Bunch-Davies vacuum

Let $\left|0\right>$ be the Bunch-Davies vacuum state of a QFT, for example a free scalar field, in de Sitter space. The creation and annihilation operators w.r.t. this state is a vacuum, i.e. $a^...
Aralian's user avatar
  • 505
0 votes
3 answers
219 views

2+1-dimensional $SU(N)$ Yang-Mills Theory

In recent years, there has been significant progress and growing interest in conducting quantum simulations of field theories using quantum devices. This typically involves formulating a Hamiltonian ...
Quantization's user avatar
3 votes
1 answer
285 views

Time-evolution operator in QFT

I am self studying QFT on the book "A modern introduction to quantum field theory" by Maggiore and I am reading the chapter about the Dyson series (chapter 5.3). It states the following ...
Andrea's user avatar
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-1 votes
0 answers
39 views

How to get $ H=\int\widetilde{dk} \ \omega a^\dagger(\mathbf{k})a(\mathbf{k})+(\mathcal{E}_0-\Omega_0)V $ in Srednicki 3.30 equation?

We have integration is \begin{align*} H =-\Omega_0V+\frac12\int\widetilde{dk} \ \omega\Big(a^\dagger(\mathbf{k})a(\mathbf{k})+a(\mathbf{k})a^\dagger(\mathbf{k})\Big)\tag{3.26} \end{align*} where \...
liZ's user avatar
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1 vote
1 answer
97 views

Feynman rule for scalar QED vertex

A popular problem in QFT textbooks and courses is to derive the Feynman rules for scalar QED. Usually, this theory is presented via the following Lagrangian density: $$\mathcal{L} = (D_\mu\phi)^\...
Rafael Grossi's user avatar
1 vote
3 answers
112 views

Has quantum measurement and particle appearance ever been modelled as a resonance effect created by the measuring device on the quantum wave?

Has anyone ever modelled quantum measurement as a resonance effect, that is created by introducing a measuring device into the quantum system? An analogy may explain what I mean: if you take the free ...
Ash90's user avatar
  • 141
1 vote
1 answer
35 views

Relative speed in unpolarized cross-section

In section 5.1 of Peskin and Schroeder, we are presented the computation of the amplitude for the $e^+e^-\to \mu^+\mu^-$ reaction and then the computation of the unpolarized cross section. After ...
Rafael Grossi's user avatar

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