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 ...

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anomalous chiral symmetry and the $\bar\theta$ parameter

I am studying anomalous U(1)'s, related to the strong CP problem, and I have some trouble with the origin of the parameter $\bar{\theta}$. We start with the QCD Lagrangian with the topological term: ...
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0+0 self interacting QFT - $ e^{-\sin^2 x}$ type integral — Bessel function expansion around infinity

In a physics paper (here) I found this variant of the Bessel function of the first kind. $$ Z(g) = \frac{1}{\sqrt{g}} \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} e^{-\frac{1}{2g} \sin^2 x} \, dx = ...
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15 views

Why does non-abelianity implies a single coupling constant?

Why does a theory described by a non-abelian group has only a single coupling constant $g$? While on the other hand in an abelian theory, as Electromagnetism, each charged particle has its own charge ...
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17 views

What's the physical or mathematical meaning of considering non-minimal coupling?

Why we still consider the case of non-minimal coupling? And I don't really understand the motivation of coupling. In general relativity, the non-minimal coupling violates the principle of ...
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5 views

Chrial multiplet's fundamental and anti-fundamental representation

Here i follow the notation in arXiv 9312104v1 (Witten's Verlinder algebra ~ paper) The usual kinetic energy for a chiral multiplet is given as (In 2 dimensional $N=(2,2)$ supersymmetry theory) ...
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36 views

Is there a well-defined partition function of 4d Yang-Mills?

So I've looked everywhere to find a resource on 4 dimensional Yang-Mills partition functions, but have only managed to find examples using supersymmetry. Is there a resource describing the partition ...
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29 views

Weinberg Chapter 19.5, pion scattering amplitude derivations

I've been reading through Weinberg's Chapter 19, and am somewhat confused about how he manages to derive equations 19.5.25 and 19.5.29, which read: ...
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34 views

Explicit demonstration of the relativistic invariance of the Weyl equation

It can be demonstrated explicitly that the Dirac equation is relativistically invariant. This is a proof (borrowed from Peskin & Schroder, see the unnumbered equation after the eqn. 3.31): ...
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95 views

QEC and QED with unlimited computational power - how precise they are going to be?

My question is about quantum algorithms for QED (quantum electrodynamics) computations related to the fine structure constants. Such computations (as explained to me) amounts to computing Taylor-like ...
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1answer
54 views

Can the Higgs condensate be described in terms of creation operators?

In superconductivity, the BCS condensate can be described in terms of 2 creation operators (the 2 electrons of the pair) acting on the vacuum. I'm wondering whether a similar description can be given ...
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39 views

Scattering amplitude with on-shell virtual photon

Let's assume electron-electron scattering in QED in second order of perturbation theory. Then in the corresponding scattering amplitude there will appear photon propagator $$ D_{\mu \nu}(q = p_{i} - ...
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26 views

What are some most advanced theories explaining why same charge repel, opposite charge attract? [duplicate]

It is the holidays with a lot to think about. One of the thing that I couldn't get out of my mind was something I read in Stephen Hawking's "Brief History of Time". In it, he described the repelling ...
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199 views

Are all fermions massless at high temperatures?

According to the standard model, the electroweak symmetry is unbroken at high temperatures, and therefore all gauge bosons are massless then. But since fermions are said to acquire mass by a different ...
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1answer
100 views

Lorentz transformations for scalar fields in QFT — Peskin and Schroder

I'm struggling to understand the following logic from Peskin and Schroeder, page 23: The book defines $$ |\vec{p} \rangle = \sqrt{2E_p} a^\dagger_p |0 \rangle $$ so that the inner product $\langle ...
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2answers
200 views

How does the Hawking Radiation mechanism cause a black hole to lose its mass? [duplicate]

Correct me if I am wrong: in the Hawking Radiation mechanism, when a virtual particle-antiparticle pair gets created at the edge of the black hole, a black hole could sometimes eat up one of the ...
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99 views

Why is it important that the vector current should be conserved in QED?

In Quantum Field Theory and the Standard Model by MD Schwartz in the chapter about the anomalies, he derives from the equation of motions and the Noether currents of a effective massless QED ...
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181 views
+500

Wave/particle-duality as result of taking different limits of a QFT

There is an account on dualities in quantum field theories and string theories by Polchinski from last week http://arxiv.org/abs/1412.5704 At the end of page 4, he writes the wave/particle ...
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63 views

Why $D^{\mu} D^{\nu} F_{\mu \nu}=0$ ? (Noether Identity) [closed]

I have to show that: $$D^{\mu} D^{\nu} F^A_{\mu \nu}=0$$ vanish identically. This is the generalization to non Abelian groups of $\partial^{\mu} \partial^{\nu} F_{\mu \nu}=0$, apparently called ...
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180 views

Making precise the statement “particles are excitations in a quantum field”

I've been trying to self teach QFT lately. I find that the basic physical idea makes sense, and I can keep up with the mathematical formalism without too much trouble, but I'm having trouble ...
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40 views

What is a nucleon field?

A nucleon is either a proton or a neutron. A field is, as John Gribbin says, a physical quantity that has a value for each point in space and time. But what is meant by a nucleon field? Can anybody ...
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109 views

If a symmetry operator S in a QFT annihilates the vacuum, why does S preserve the space of 1-particle states?

In the paper "Supersymmetry and Morse Theory", on the third page (p. 663 in the journal version), Witten says: "Now in any quantum field theory if a symmetry operator (an operator which commutes ...
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2answers
67 views

Higher rank $\gamma$-matrix question

I read that the higher rank $\gamma$ matrices can be written as alternate commutators and anti-commutators. For example, the rank 3 gamma matrix can be written as $$\gamma^{123} = ...
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58 views

Lorentz transformation - Bjorken & Drell

I'm trying to derive (14.25) in Bjorken & Drell (B&D) QFT. This is $$\tag{14.25}U(\epsilon)A^\mu(x)U^{-1}(\epsilon) = A^\mu(x') - \epsilon^{\mu\nu}A_\nu(x') + \frac{\partial ...
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57 views

Time ordering, interaction Lagrangian calculation, QED

I am trying to compute $$ \langle 0| \, T\left\{\phi^\dagger(x_1) \phi(x_2) \exp \left[i \! \int{L_1(x) \, \mathrm{d}x} \right] \right\}|0 \rangle $$ for $$ L_1(x) = ...
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111 views

What does Weinberg–Witten theorem want to express?

Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin $j > 1/2$ cannot carry a Lorentz-covariant current, while massless particles with spin $j > 1$ ...
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26 views

Fast and slow modes in renormalization group of nonlinear sigma model

A general nonlinear sigma model can be expressed as \begin{equation} S[g] = \frac{1}{\lambda} \int d^dr\ \text{tr}[\triangledown g\triangledown g^{-1}] \end{equation} where $g$ takes value in a matrix ...
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42 views

Can asymmetrical Lorentz forces account for Relativistic affects near the speed of light?

The underlying thought here is that at low relativistic speeds all objects are subjected to emf radiation from all directions. This is basically the sum of all the radiation (light, infra-red, ...
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22 views

Real representations of chiral fields

Why we can´t have real representations of chiral fields, i.e. why does a multiplet of chiral field (Weyl spinors) under a real representaiton of a Lie Group transforms as a "vector". It is easy to see ...
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93 views

Is gravitational Chern-Simons action “topological” or not?

Here are the 2+1D gravitational Chern-Simons action of the connection $\Gamma$ or spin-connection: $$ S=\int\Gamma\wedge\mathrm{d}\Gamma + \frac{2}{3}\Gamma\wedge\Gamma\wedge\Gamma \tag{a} $$ $$ ...
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2answers
79 views

Heisenberg picture with creation annihilation operators

In the Schrodinger picture, states are time dependent and operators time-independent. So expected values look like: $\langle s_1,t|\hat{A}|s_1,t\rangle$. If we go over to the Heisenberg picture the ...
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27 views

Connected diagrams in Sine-Gordon action

I consider a bosonic action of the type $$\int dx d\tau\left( \underbrace{a(\nabla\theta)^2+b(\nabla\phi)^2}_{free} +\underbrace{c\cos{4\phi}}_{interaction}\right),$$ and want to treat the cosine term ...
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79 views

Total divergence term and corresponding Feynman Diagram

A total divergence term added to the Lagrangian doesn’t affect the action because the integral of a total divergence vanishes. But if one attempts to derive the Feynman rules from the Lagrangian with ...
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53 views

Getting the electric field using Green's function [closed]

Let the Green's function for the gauge field be given (after gauge fixing) as $$G_{\mu \nu}(x,y) = \delta_{\mu \nu}G(x-y) \tag{1}$$ where $$G(x-y)= \int \frac{d^dk}{(2\pi)^d} \frac{e^{ik \cdot ...
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1answer
40 views

Understaning Euclidean Green's function

Consider a scalar field coupled to a source $$(\Box - m^2)\phi(x) = -J(x)\tag{1}.$$ Then, the response of the source is determined by the Green's function $G(x-y)$, which satisfies $$(\Box - ...
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70 views

Symmetries in QM and QFT — operator transformation laws

In quantum mechanics, we implement transformations by operators $U$ that map the state $|\psi\rangle$ to the state $U|\psi\rangle$. Alternatively, we could transfer the action of $U$ onto our ...
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1answer
39 views

Is the weak interaction Lagrangian invariant under parity transformations?

The weak interaction term in the Lagrangian reads $$ \bar \Psi \gamma_\mu P_L \Psi W^\mu. $$ Under parity transformations, because of $\Psi \rightarrow \gamma_0 \Psi$ and $\gamma_5 \rightarrow ...
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18 views

Charge dependence of operators in QED renormalization

Consider a UV cutoff regulator $\Lambda$ with an effective QED lagrangian: $\mathcal{L}_{\Lambda} = \bar{\psi}_{\Lambda}(i\not \partial - m_{\Lambda})\psi_{\Lambda} - ...
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3answers
139 views

QFT and violation of Heisenberg uncertainty principle

In some QFT books is said that a free electron can emit a virtual photon as long as it reabsorbs the photon and returns to its original state within a time: $$\Delta t<\dfrac{\hbar}{2\Delta E}$$ ...
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2answers
77 views

Can a quantum field be understood as a superposition of all particles' wave functions?

Many text books emphasize that the quantum field is not wavefunction. But because of the similarity in the format, I could not stop from wondering whether they are actually the same thing.
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49 views

$d=2$ pole argument of quadratic divergences in Peskin & Schroeder's book

Q1: My question is, in the context of dimensional regularisation(DREG, in dimension $d$), why do they mention the absence of $d=2$ pole in the gauge theory cases[1], whereas the $d=2$ pole is not ...
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89 views

Reconciling two interpretations of renormalization

I know of two fascinating and perfectly reasonable explanations of renormalization. However, I'm having difficulty reconciling the two. The first is to say that when we initially write down a ...
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1answer
143 views

How do creation operators change with time in an interacting theory?

When studying the quantization of a field theory with free fields, the creation operators $a^\dagger(k)$ are independent of time. In an interacting theory, they are time-dependant, and therefore ...
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26 views

Wavefunction renormalisation in first order perturbation theory

I just read the following in the context of scattering amplitudes in QFT: Note that the wavefunction renormalisation factor $Z$ itself is of the form $1 + \mathcal{O}(\lambda)$ in perturbation ...
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1answer
58 views

Is there a field for which neutral particle and antiparticle, can be considered as positive and negative charge?

I apologize, but QFT is not my domain. What I ask is connected with the question Do the fields exist without charges? . By analogy with the electron and proton, that carry the electric charges of the ...
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An annoying question about perturbative quantum field theory

I am so sorry for posting this long question. But I've been confused and frustrated by perturbation series in Quantum Field Theory for years. I hope someone can help me. Thank you so much! In the ...
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Gordon decomposition of Dirac current for massless electron?

We know Gordon decomposition of Dirac current is applicable only for massive (nonzero mass) Dirac particles. Is there an analog for massless Dirac particles? (I have made an attempt to answer ...
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3answers
126 views

Is Parity really violated? (Even though neutrinos are massive)

The weak force couples only to left-chiral fields, which is expressed mathematically by a chiral projection operator $P_L = \frac{1-\gamma_5}{2}$ in the corresponding coupling terms in the Lagrangian. ...
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1answer
80 views

Feynman diagrams for scalar field: which particle are we drawing?

Chapter I.7 of Zee's Quantum Field Theory in a Nutshell is an introduction for Feynman diagrams in the context of a scalar field $\varphi$, with Lagrangian $\mathcal{L} = \frac12[(\partial ...
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1answer
67 views

Do Dirac field states belong to a Hilbert space with spinor coefficients?

The quantized Dirac field at a certain space-time point can be written (roughly) as a linear combination of creation operators acting on the Hilbert space of physical states, with coefficient that are ...
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1answer
52 views

Terminology of Higgs boson and Goldstone boson

I know, the from the Higgs Mechanism, or Spontaneous symmetry breaking, the massless Goldstone boson becomes massive. So in some sense Goldstone bosons are eaten by gauge "boson". Here I got ...