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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Outside of string theory, can exchange particles be understood as being one-dimensional?

I'm pretty new to quantum, without any formal education therein, so forgive my general layman ignorance when I ask how it is that point-like exchange particles can be modeled in Feynman diagrams as ...
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36 views

Quantizing field with anti-periodic boundary condition

This is a naive question about a possible toy model in QFT. In particular, I am trying to find a simple model where spin-statistics theorem holds. One can construct a 1+1 dimensional classical ...
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52 views

Feynman diagrams with classical apparatus on the perturbative region

on QFT, one usually simplifies the interaction between fields and classical apparatus (sources, detectors, etc.) by assuming the classical devices only interact with the asymptotic on-shell states ...
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49 views

Every Relativistic Field Satifies the Klein-Gordon Equation?

I've read that every relativistic scalar field (and in some sense, any field) satisfies the Klein-Gordon equation. Is the reasoning for this just based on the quantum mechanical substitution of $E\to ...
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32 views

Fujikawa method for arbitrary transformations

When the Fujikawa method is presented in every book I've read so far, the transformation is initially written as $e^{i\chi (x) \gamma^{5}}$. The trace of $i\chi(x)\gamma^{5}$ is done by including a ...
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97 views

Does equality of operators on vacuum imply equality of operators on the whole space?

Consider a field operator $\Phi(x)$ which generates states from the vacuum such as $$ \tag 1 | x \rangle = \Phi(x) | 0 \rangle.$$ Consider also how a translation is implemented on such a state: $$ ...
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65 views

Does point group symmetry also act within “spin space” for a lattice spin system?

As an example, let's consider a quantum spin system on a 2D square lattice. The lattice point group symmetries include $C_4$ rotation, parities, etc.... And let's take $C_2$ symmetry (2-fold rotation) ...
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46 views

Delta functional in path integrals - reference needed

In a few articles dealing with path integral quantization I came across some calculations where apparently identities of the form \begin{equation} \int (\mathcal{D}\Phi)\, ...
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90 views

Quick question regarding Wick's theorem

Let $T\{...\}$ denote time-ordering, $N\{...\}$ normal-ordering and $\left<ab\right>$ be the propagator. Wick's theorem states that $$ T\{ab\} = N\{ab\} + \left<ab\right>. $$ I now ...
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96 views

Questions regarding $D=4 $ ${\cal N}=4$ supersymmetric Yang-Mills

I have some questions regarding the $D=4 $ ${\cal N}=4$ super-Yang-Mills theory (the one with a really long action which can be acquired by compactifying the 10-dimensional ${\cal N}=1$ theory). I ...
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53 views

Need help understanding the quantization procedure in QFT for the Klein-Gordon equation

I am having some conceptual issues with the quantization process in QFT. So we define a particle as a collection of functions $\mathcal{H}$ that satisfy some differential equation (more specifically a ...
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533 views

Why is the Klein Gordon equation of second order in time?

I was wondering if there is any way to interpret the fact that the Klein Gordon equation is a 2nd order PDE in time. I mean, normally you would expect that as soon as you fix the initial wavefunction, ...
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42 views

Ladder operators evolution for fermions

For the free Dirac field we have $$ \psi(x) = \sum_s\int d\Omega_{m}\frac{1}{\sqrt{2}k_0}\left(b(\mathbf{k},s)u(\mathbf{k},s)e^{-ik\cdot x}+d^\dagger(\mathbf{k},s)v(\mathbf{k},s)e^{+ik\cdot ...
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52 views

Transformation of the scalar field under Lorentz Boost [closed]

Assume a Lorentz transformation $\Lambda$ is to be implemented as the unitary operator $U(\Lambda)$ in the Hilbert space of quantum states of the Fock representation upon which the scalar Klein-Gordon ...
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37 views

If 2 photons collided head on, what would happen? [duplicate]

If 2 photons, in perfect synch (frequency, amplitude, etc. were all equal) and they collided head on, what would happen? Would they pass right through each other? Would they interfere, then go back to ...
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105 views

How do you build a Lagrangian in particle/nuclear physics? (A specific example)

I know that the terms in the Lagrangian needs to be scalars (with respect to Lorentz symmetry etc.). Also I know that [see C. G. Tully (EPP) p. 85] in general, for $\psi$ in the fundamental ...
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204 views

Mølller scattering

I came across Mølller scattering today (which is just a fancy name for electron-electron scattering. I'm confused as to why there are two tree level Feynman diagrams for this process: Check out the ...
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1answer
62 views

The contraction of fermion field in 1+1-dimensional massless QED

My question comes from the textbook by Peskin & Schroeder, the integral (19.26): $$\begin{align} \int \frac{d^2 k}{(2\pi)^2}\! e^{- i k\cdot (y-z)}\frac{i \not{k}}{k^2} = -\not\partial ...
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34 views

Example of critical (non-relativistic) quantum field theory in 1D?

Is there an example of a critical non-relativistic bosonic quantum field theory in 1D (no time)? So, the field theory can be describe by annihilation, $\psi(x)$, and creation operators, ...
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56 views

Field transformations

I'm reading Maggiore's book "A modern introduction to quantum field theory" and I'm very confused by what he did in chapter 2.6 page 31 eq. (2.80). He basically wants to find the generators of the ...
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1answer
58 views

Why are Green Functions/(Correlation Functions) not on the mass shell?

The difference between Green Functions and the S-matrix in Quantum Field Theory is whether the momentum is on the mass shell. Why are the Green Functions/(Correlation Functions) not on the mass shell? ...
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33 views

Trilinear term in SUSY soft-breaking

In MSSM soft-SUSY breaking, there are such term called 'A-triliear term'. But, some papers, e.g Riva-Biggio-Pomarol, do not have trilinear term. What is the use of introducing trilinear term?
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116 views

How does the notion of topological order relate to the Landau-Ginzburg theory of phase transitions?

As per Landau-Ginzburg (LG) theory, we write down a theory (Hamiltonian) with all possible interactions/operators (in terms of some order parameter) that respects certain symmetries. The ground state ...
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69 views

How can we measure chirality in experiments?

Chirality is a concept quite different from helicity. These two concepts only happen to have the same numerical value for massless particles. I understand that we can measure helicity, but how can we ...
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472 views

Width of a photon. And its length

Everyone is always talking about photon's wavelength. But what about its dimensions? What is length and width of it? And does it even have a point to think about such things? Or those dimensions are ...
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290 views

How do I solve this Gaussian path integral?

Suppose $$ Z = \int \mathcal D[\phi^*] \mathcal D[\phi] \exp(\phi^*A\phi + \phi B\phi) $$ where $A$ and $B$ are operators. I know how to solve a Gaussian path integral involving only $\phi^* A \phi$ ...
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132 views

Why do we require quantum fields to vanish at infinity?

Classical fields, like the electrical field must vanish at infinity, because otherwise their energy would be infinite. This can be used in computations to exclude certain solutions. In quantum ...
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104 views

Fock representation of a electromagnetic wave

Suppose an arbitrary classical (electromagnetic) wave package $E(x)$. What is its Fock space representation? I.e. I am looking for a state $| \psi \rangle$ such that $\langle \psi | \hat E(x) | \psi ...
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65 views

Matter antimatter fundamental and adjoint representation (Hermitian Anti-Hermitian)

I’m struggling with the following. I read in “The Standard Model: A Primer by Cliff Burgess”, page 493, that fermion fields in the fundamental representation can be thought of as column vector(s) ...
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2answers
141 views

Why is the $(\frac{1}{2},\frac{1}{2})$ representation of the Lorentz group realized as the vector space of complex $2\times 2$ matrices?

Why can we write an arbitrary object $v_{a \dot{b} }$ our transformations in this basis act on as $$ v_{a \dot{b} } = v_{\nu} \sigma^{ \nu}_{a \dot{b} } = v^0 \begin{pmatrix} 1&0 \\ 0&1 ...
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151 views

What is the quantum state of a static electric field?

This is something that I've been curious about for some time. A coherent, monochromatic electromagnetic wave is well described by a coherent state $|\alpha\rangle$. The quantum treatment of the ...
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1answer
44 views

Trace of derivatives of unitary operators [closed]

I have been studying some lecture notes on the non-linear sigma model and I came up with some difficulties involving a trace. I have the following unitary operator $$ U=\exp\left( ...
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50 views

How to deal with coupled fermion boson operators?

I am a beginner in field theory and I have an exercise where I have a product of coupled fermion boson operators? $$ \hat{b_{l} }^{\dagger}\hat{c_{l^{'}} }^{\dagger}\hat{a_{q} }\hat{b_{l} ...
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145 views

What exactly do we mean by symmetry in physics?

I'm referring here to invariance of the Lagrangian under Lorentz transformations. There are two possibilities: Physics does not depend on the way we describe it (passive symmetry). We can choose ...
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67 views

Field renormalization of scalar Yang-Mills

In most books, one can find the field renormalization $Z_3$ in Yang-Mills with fermionic matter in the fundamental. In the $\overline{MS}$ scheme, tt is given by $$ Z_3 = 1 + \frac{g^2}{16\pi^2 ...
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126 views

Global symmetry and particle multiplets

In chapter 20, of Peskin and Schroeder's quantum field theory book, they start with a comment that a global symmetry that is manifest lead to particle multiplets with restricted interactions. Can ...
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1answer
72 views

Question about surface term in QFT problem

I am trying to follow the solution of the following problem (Srednicki 39.2): To show that: $$J_z b_s^\dagger(p\hat z)|0\rangle=\frac{1}{2}\ s\ b_s^\dagger(p\hat z)\ |0\rangle, $$ where $J_z$ ...
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1answer
82 views

One loop tadpole diagram $\phi \to \phi$ in $g\phi^3$ theory

I am trying to evaluate the tadpole diagram of $\phi^3$ theory to practice one loop amplitudes, but I am stuck at a certain point. The amplitude is given by the integral, $$\mathcal{M} = ...
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21 views

Why third Pauli $\tau_3$ becomes third Isospin component $\tau_3^{<\Phi>}$?

When considering the higgs coupling to the neutral gauge boson of EW theory (see e.g. C. G. Tully (EPP nutshell) page 102): $$\tag{1}\mathcal{L} = \frac{1}{4}\left\{\left(g' B_\mu Y_\Phi+gW_\mu^3 ...
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1answer
211 views

How does QFT interpret the Negative probability problem of the real scalar fields' Klein-Gordon equation?

I am totally a beginner in QFT, here's the problem that I got: for the real scalar fields, are there any elementary particles descriped by them. If so, how to understand the negative probability ...
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38 views

Why scattering of red and blue quark only involves $G_8^\mu$?

According to the author C. G. Tully (Particle physics in a nutshell), the scattering of a red and blue quark only involves $G_8^\mu$. How come this is so? I thought $G_3^\mu$ and $G_8$ only mediate ...
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1answer
67 views

What would be the most general effective Lagrangian involving one Higgs and two gluons?

Two different possibilities come into my mind $\mathcal{L}\sim{}HG_{\mu}G^{\mu}$ where $G^{\mu}$ is the gluon field and $H$ the Higgs, or either $\mathcal{L}\sim{}HG_{\mu\nu}G^{\mu\nu}$ Where ...
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1answer
47 views

Evaluation Feynman parameters from denominator

I try to evaluate Feynman parameters but got stuck at some point. $$ \int_0^1 \frac{1}{(Ax+(1-x)B)^2}\,dx=\frac{-1}{(Ax+B(1-x))}\frac{1}{A-B}=\frac{1}{AB} $$ $$ \frac{1}{AB}=\int_0^1 \int_0^1 ...
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't Hooft many instanton solutions

I'm study 't Hooft many instanton solutions of self-duality equation. In this method $A^a_\mu=-\bar{\eta}^{a}_{\mu\nu}\partial^\nu \ln{\Phi}$. After substitution in self-duality equation I've proven ...
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83 views

QCD color factors from quark gluon vertices

The color factors in QCD tell us the relative strength of the coupling of a quark emitting a gluon, a gluon emitting a quark-antiquark pair or a gluon emitting two gluons. To calculate let them we ...
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33 views

Sphaleron interactions erase baryon asymmetry?

The sphaleron interactions in the standard model is $(B-L)$ conserving and $(B+L)$ violating. Each sphaleron transition causes $\Delta B$ and $\Delta L$ to change by the same amount so that ...
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61 views

Variation of the kinetic quark term of the QCD Lagrangian under gauge transformation

A simple kinetic quark term would look like $$\bar{\psi}(\gamma^{\mu}\partial_{\mu} - m){\psi}.$$ Imposing SU(3) symmetry the Dirac spinor transforms like $$\psi(x) \rightarrow \psi'(x) = e^{ig_s ...
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91 views

Klein-Gordon field commutator integral identity [closed]

Consider a Klein-Gordon field $\phi$ on points $x,y$ of $\mathbb R^4$ Minkowski-spacetime. Here I'm writing $x=(x^0, \stackrel \rightarrow x)$ so that $\stackrel \rightarrow x$ gives the spatial ...
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3answers
101 views

Klein Gordon for spin-1 particle photon

If Klein Gordon equation is for spin-0 particles, I write massless fields as $\square A=0$, how can I say $A_\mu=\epsilon^\mu e^{-ikx}$ as a wave function of polarized photon (spin-1) ?
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28 views

A question about the interchanges of particles belonging to species in Weinberg's QFT book 1

Weinberg put this in page 171 that I can't quite understand: If we like, we can avoid this question by simply agreeing from the beginning to label the state-vector by listing all photon momenta and ...