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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Anomalies for not-on-site discrete gauge symmetries

If a symmetry group $G$ (let's say finite for simplicity) acts on a lattice theory by acting only on the vertex variables, I will call it ultralocal. Any ultralocal symmetry can be gauged. However, in ...
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129 views

Calculating Forces via Feynman diagrams?

How would one go about calculating forces that test objects feel using Feynman diagram methods? For example, say we have a massive object in GR so that the metric takes on the standard ...
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83 views

Half-integer Spin and “natural conformal dimension”

If we consider a classical field theory for a massless particle of integer spin $s$, in a curved space-time, one finds that it is "naturally" conformal in a space-time of dimension $2+2s$ For ...
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168 views

Stress-energy Trace of Massless Klein Gordon Field

I've calculated the trace of the stress-energy for a massless KG field and I keep getting $T = - (\partial \phi)^2$ in 3+1 dimensions. I'm using $$T_{\mu\nu} = \partial_\mu \phi \partial_\nu \phi - ...
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171 views

How do non-transverse photon polarizations cancel in Euclidean QED?

First, recall how to write scattering amplitudes in covariant fashion in Minkowskian QED. One starts by considering some process with an external photon whose momentum is chosen to be ...
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201 views

$2\pi$ and Feynman Rules

I notice a $2\pi$ term in the $\delta$-function when trying to construct an amplitude using the Feynman Rules. The $2\pi$ also appears as an integration measure to enforce normalisation in the phase ...
6
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211 views

Basic question about the S-Matrix, Unitarity and Effective Field Theory

Consider scattering some particles in a state collectively denoted by $i$ to a final state denote by $f$. The scattering amplitude, S-matrix is then defined by: $S_{fi}\equiv \langle ...
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682 views

Why is there a minus sign in this wave equation derivation?

My book on quantum mechanics suggests a derivation of the wave equation $$\left(\Delta - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} \right) \psi(\bar{r},t) = 0$$ from the photon energy-impulse ...
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1answer
82 views

are there any “known unknowns” that could affect the possibility of a false vacuum?

(Although Donald Rumsfeld was mocked for talking about "known unknowns" and "unknown unknowns", I think it's an truly important distinction.) Periodically, I hear about how the universe might be in a ...
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93 views

Peskin's book page 334 proof of $Z_1=Z_2$ to all orders in QED perturbation theory

Peskin in his QFT page 334 argued that $Z_1=Z_2$ to all orders in QED perturbation theory, but I couldn't understand his argument: ... With a generalization of the argument given there (section ...
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2answers
222 views

If photons don't interact directly, how can electromagnetic waves interfere?

If photons don't interact directly, how can electromagnetic waves interfere? I know that photons can scatter via higher order mechanisms, but not directly. Does those mechanisms explain the classical ...
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60 views

Matrix integral in multi-matrix model

Though it is a mathematical problem, maybe more physicists know it well. In quiver matrix model which is reviewed DV or CKR, the path integral reduce to the matrix integral $$Z \sim \int ...
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2k views

What are the calculations for Vacuum Energy?

In wiki the Vacuum Energy in a cubic meter of free space ranges from $10^{-9}$ from the cosmological constant to $10^{113}$ due to calculations in Quantum Electrodynamics (QED) and Stochastic ...
2
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1answer
97 views

Transferring CFT correlations from $\mathbb{R}^3$ to $S^3$

There seems to be a simple method to transfer a CFT's correlations from $\mathbb{R}^3$ to $S^3$ but I am not understanding why it is supposed to work. The idea is that somehow because, $ds^2_{S^3} = ...
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71 views

QFT Literature recommendation [duplicate]

Before answering, please see our policy on resource recommendation questions. Please try to give substantial answers that detail the style, content, and prerequisites of the book or paper (or ...
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110 views

Are composite bosons always bosonic (e.g. the pion-cloud surrounding the nuclei)?

The $\pi$-meson is a boson, but consists of quark-antiquark (fermions). It seems to me that at some energy level (equivalently distance) the inner structure (fermionic nature of the quarks) of the ...
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4answers
2k views

What does spin 0 mean exactly?

I heard two definitions: (1) Spin 0 means that the particle has spherical symmetry, without any preferred axis. (2) The spin value tells after which angle of rotation the wave function returns to ...
2
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1answer
142 views

Does a Lagrangian imply a well-defined quantum Hamiltonianian with a Hilbert space?

The question is about: (1) whether giving a Lagrangian is sufficient enough to (uniquely) well-define a Hamiltonianian quantum theory with a Hilbert space? The answer should be Yes, or No. If ...
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353 views

Ward Identity makes QED logarithmic divergent?

Quick question regarding superficial degrees of freedom and Ward identities. For instance in Peskin and Schroeder it is stated that the photon-self energy is superficially quadratically UV divergent ...
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44 views

What is the importance of the Odderon?

From hep-ph/0001149v1: (1) an Odderon contribution is absolutely necessary to reproduce quantitatively well the data; while its presence is not explicitly needed at $t = 0$, its inclusion is ...
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3answers
2k views

Would a spin-2 particle necessarily have to be a graviton?

I'm reading often that a possible reason to explain why the Nobel committee is coping out from making the physics Nobel related to the higgs could be among other things the fact that the spin of the ...
6
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2answers
160 views

Gauge fields and strings: Loop equations

I am trying to derive Eq. (7.25) (p. 117) of Polyakov's book: $$ \delta \Psi (C) = \int_{0}^{2\pi} {\rm P} \left(F_{\mu\nu}(x(s)) \exp \oint_C A_\mu dx^\mu \right)\dot{x}_\nu \delta x_\mu(x) \, {\rm ...
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1answer
118 views

Photon propagator in terms of creation/annihilation?

As far as I understand it the photon propagator, $P(A\rightarrow B)$, described in Feynman's QED book, gives the amplitude that a photon moves from spacetime point A to spacetime point B. I was ...
4
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1answer
318 views

How can we derive the Feynman rule for the ordinary QED 3-vertex?

I have checked some Quantum Field Theory texts that include basic QED and they all include the Feynman rule that each vertex bring with it a factor of $$\pm i e \gamma^\mu$$ but I have yet to find a ...
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77 views

$E$ and $B$ fields in Axial Gauge

I am trying to compute the $\vec{E}$ and $\vec{B}$ fields in the Axial gauge ($n \cdot \vec{A}=0$) where $n^2=1$, but I'm having trouble seeing the usefulness/how it simplifies the equations.
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1answer
110 views

Observables still commute even if fields only anti-commute

In Peskin & Schroeder page 56, after introducing anti commutation relations for the fields instead of commutation relations (in order to fix the negative energy problem as well as to have proper ...
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273 views

Causality for the Dirac Field

In Peskin & Schroeder page 54, they are trying to show how far they can take the idea of a commutator for the Dirac field instead of anti-commutator. To this end they are examining causality, ...
5
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1answer
103 views

The amplitude for a particle to be created/annihilated

In A. Zee's "QFT in a nutshell", there is such a statement about massive spin-1 particles (Chap I.5). The three polarization vectors $\xi^{(a)}_\mu(k)$ are simply the three unit vectors pointing ...
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1answer
589 views

Quantization of Gravitational Field: Quantization conditions

I'm begining to study Quantization of field with the second quantization formalism. I've studied phononic field, electromagnetic field in the vacuum and a generic relativistical scalar field. I ...
6
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1answer
264 views

Using $\frac{1}{A+i\epsilon} = PV\frac{1}{A}-i\pi\delta(A)$ in Feynman Integrals

Are the following operations O.K.? This is related to the Feynman parameter trick. $$F:= \int_0^1 \mathrm{d}x\int_0^{1-x}\mathrm{d}y \frac{1}{f(x,y)+\mathrm{i}\epsilon}.$$ Now using ...
2
votes
1answer
148 views

When it is said that the Higgs field is a scalar, do they mean Lorentz scalar?

We often hear that Higgs boson is a scalar boson, and that Higgs field is a scalar field. I was always thinking that this means "4-scalar". In other words, it is space-time invariant, .i.e. it's ...
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2answers
351 views

QFT Dyson series: why are we solving the Schrodinger equation?

In quantum field theory, the solution of the time evolution operator of the Schrodinger equation (in the interaction picture) is given by Dyson's series, which is used to calculate the S-matrix. Why ...
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1answer
76 views

What is quark transverse momentum?

When you google my question you get something on the order of 400 000 results but none of them explains how it is defined (No I didn't check them all). I know what the words quarks, transverse and ...
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1answer
155 views

What to do with a $\phi$ term in a Lagrangian?

I am considering a Lagrangian that is of the following form: $$\mathcal{L}=-{1\over 2}\partial_\mu\phi\partial^\mu\phi+2\mu^2\phi^2+2\sqrt{6}{\mu^3\over \lambda}\phi + {9\mu^4\over 2\lambda} + ...
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1answer
81 views

What is the nucleon axial charge?

Can someone point me to a short definition of what the nucleon axial charge is?
3
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1answer
106 views

Negative energy solutions Dirac equation without radation field

In the book "Relativistic Quantum Mechanics" by Bjorken and Drell in Chapter 5.1 page 64 there is the following statement about the problem of negative solutions to the Dirac equation: By their ...
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52 views

What is the definition of a charge-neutral operator?

What is the definition of a charge-neutral operator? I guess it means something like: it is invariant under charge conjugation. It that correct?
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0answers
136 views

Step in derivation of solution to Dirac equation for hydrogen

My text, when solving hydrogen in the Dirac equation, makes the claim $\varphi_{j m_j}^{(+)} = \frac{\mathbf{\sigma} \cdot \mathbf{x}}{r} \varphi_{j m_j}^{(-)}$ where $\varphi_{j m_j}^{(\pm)}$ are ...
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1answer
252 views

Non-linear Dirac equation in Einstein Cartan theory

Can someone explain this Wikipedia article, specifically the section on Einstein-Cartan theory? I have no idea how the equation ...
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3answers
247 views

Completing the square for Grassmann variables

When working with path integrals of both bosonic and fermionic field variables, I'm a bit unsure of how to do the usual complete the square trick when an interaction between the two is concerned. Say ...
6
votes
1answer
231 views

A Puzzle about $SO(3)$

Lie algebra of nonabelian group is $[T^a,T^b]=if^{abc}T^c$. For $SO(3)$ case, is the representation $T^a_{ij}=-i\epsilon^{aij}$ fundamental or adjoint? The fundamental representation is defined as ...
18
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1answer
589 views

Does local physics depend on global topology?

Motivating Example In standard treatments of AdS/CFT (MAGOO for example), one defines $\mathrm{AdS}_{p+2}$ as a particular embedded submanifold of $\mathbb R^{2,p+1}$ which gives it topology ...
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3answers
801 views

Grassmann paradox weirdness

I'm running into an annoying problem I am unable to resolve, although a friend has given me some guidance as to how the resolution might come about. Hopefully someone on here knows the answer. It is ...
5
votes
1answer
306 views

Derivation of a gamma matrices identity

While studying Srednicki's book on quantum field theory, I encountered a particular identity that is of interest to me (equation 36.40): $$\mathcal{C}^{-1}\gamma^\mu\mathcal{C}=-(\gamma^\mu)^T$$ where ...
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0answers
98 views

Moduli Space of $\mathcal{N}=4$ SYM on $\mathbb{R} \times S^3$

When we define $\mathcal{N}=4$ SYM on flat Minkowski space, the supersymmetric vacua are parametrized by scalars living in the cartan subalgebra of the gauge group. A generic point in the moduli space ...
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193 views

Why is the R-symmetry in $\mathcal{N}=4$ $SU(4)$ and not $U(4)$?

In $\mathcal{N}=4$ SYM we have 4 supercharges. Naively, I would have thought that the R-symmetry would be $U(4)$. I know that in theories with less SUSY the $U(1)$ can be anomalous. But ...
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220 views

For the $U(1)$ problem, is the Kugo and Ojima Goldstone quartet wrong?

On page 96 in "Local Covariant Operator Formalism of Non-Abelian Gauge Theories and Quark Confinement Problem", Prog. Theor. Phys. Suppl. 66 (1979) 1, KO state the following: Finally we should ...
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2answers
205 views

Local guage symmety implies causality

I read in a QFT book that local gauge symmetry implies causality. Could someone please explain that statement and why it's true? Thank you.
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321 views

Exact diagonalization by Bogoliubov transformation

I am developing a model of multiple gaps in a square lattice. I simplified the associated Hamiltonian to make it quadratic. In this approximation it is given by, $$ H = \begin{pmatrix} \xi_\mathbf{k} ...
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vote
1answer
72 views

Gauge fields in 2d spacetime

I believe it is only a technical question. However I cannot realize it. It is said in 2d spacetime the gauge fields $A_\mu$ can be rewritten in lightcone coordinates as $A_+=ig\partial_+g^{-1}$ and ...