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 ...

learn more… | top users | synonyms (1)

1
vote
3answers
134 views

Can virtual particles, in particular gravitons, interfere?

Question 1. Can virtual particles, in particular gravitons, interfere? Virtual particles are created and annihilated in a distance too small and a time too short to be measured. Their existence is ...
1
vote
1answer
82 views

Spin-statistics theorem proof details

Recently I have read one book where there was some incomprehensible proof of the Pauli's spin-statistics theorem. I want to ask about a few details of the proof. First, the author derives ...
3
votes
2answers
139 views

The Fifth Gamma Matrix

This is regarding $\gamma^5$, the fifth gamma matrix in quantum field theory. I know its defining properties, namely, $$\gamma^5= -i\gamma^0 \gamma^1 \gamma^2 \gamma^3 $$ with ...
2
votes
2answers
114 views

electron in the nucleus

In the event that the electron is in nucleus of the atom (via tunneling effects and other things I don't understand), How does QED deal with this situation?
2
votes
2answers
49 views

Electron Electric Field Mass?

I am confused of whether or not the expected electromagnetic field generated by the point-like electric charge of the electron distributed smoothly across space as a probability distribution creates ...
2
votes
0answers
72 views

Entanglement entropy and area law

I am currently reading a review "Area law for the entanglement entropy" by Eisert, Cramer and Plenio (2010). From what I understand: In one dimension, for local gapped models, we have an area law ...
6
votes
0answers
32 views

Normalization of Source Terms in Large-N Gauge Theory

Typically when you do the counting for large N gauge theory, you rescale fields so that the Lagrangian takes the form \begin{equation} \mathcal{L}=N[-\frac{1}{2g^2}TrF^2+\bar{\psi}_i\gamma^\mu D_\mu ...
7
votes
2answers
737 views

Is Zitterbewegung an artefact of single-particle theory?

I have seen a number of articles on Zitterbewegung claiming searches for it such as this one: http://arxiv.org/abs/0810.2186. Others such as the so-called ZBW interpretation by Hestenes seemingly ...
5
votes
2answers
199 views

One Loop Higgs Mass Correction

I am attempting to compute the one loop correction to the Higgs mass, which requires the evaluation of a scattering amplitude, namely $$\require{cancel} \mathcal{M} = (-)N_f \int \frac{\mathrm{d}^4 ...
3
votes
1answer
123 views

Paths in the path integral

In the path integral approach one defines in some heuristic way the functional path integral \begin{equation} Z=\int{\cal{D}}\phi e^{iS(\phi)} \end{equation} and the one claims that one must ...
4
votes
1answer
139 views

CP violation from the Electroweak SU(2)$_{weak,flavor}$ by $\int \theta F \wedge F $

Question: Why there is NO Charge-Parity (CP) violation from a potential Theta term in the electroweak SU(2)$_{weak,flavor}$ sector by $\theta_{electroweak} \int F \wedge F$? (ps. an explicit ...
1
vote
0answers
53 views

Why Green's function will diverge at the same spacetime point?

In $d+1$ dimensional quantum field theory, the 2-point Green's function will diverge at the same spacetime point when $d\geq1$. When $d=0$, $\phi(t)=q(t)$, that is the case of QM, and 2-point Green's ...
2
votes
1answer
117 views

Weinberg dimension 5 operator

How to prove that the $\Delta L=2,$ dimension=5 Weinberg operator $LLHH$ is the unique operator which violates lepton number by two units, without derivative couplings, etc.??
6
votes
1answer
79 views

Anomalous Dimensions of Gauge Interactions

Peskin and Schroeder mention a few times that the anomalous dimension of a gauge interaction operator is zero. The justification for this is that the charge operator shouldn't get modified under ...
10
votes
2answers
365 views

What does a $SU(2)$ doublet really mean?

What do we really mean when we say that the neutron and proton wavefunctions together form an $SU(2)$ doublet? What is the significance of this? What does this transformation really doing to the ...
11
votes
5answers
2k views

“Velvet way” to Grassmann numbers

In my opinion, the Grassmann number "apparatus" is one of the least intuitive things in modern physics. I remember that it took a lot of effort when I was studying this. The problem was not in the ...
4
votes
2answers
94 views

How to conclude that an interaction is attractive from its Fourier transform (momentum space representation)?

Background: In the book by Altland and Simons, Condensed matter field theory, in exercise 4.5.7, one is supposed to use the effective field theory method to integrate out the phonon field in an ...
3
votes
0answers
75 views

Why do we use functional integration in QFT?

Recently I learned functional integral's formalism in QFT. I have realized that I don't understand why exactly do we introduce it. We have the expression for $S$-matrix, then we may rewrite it in ...
56
votes
4answers
4k views

Gauge symmetry is not a symmetry?

I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate ...
3
votes
0answers
58 views

1+1D Bosonization on a line segment or a compact ring

I have been informed that 1+1D Bosonization/Fermionization on a line segment or 1+1D Bosonization/Fermionization a compact ring are different - Although I know that Bosonization can rewrite fermions ...
68
votes
5answers
21k views

What is the actual significance of the amplituhedron?

A news has recently became viral that physicists have discovered a geometrical object that simplifies a lot our models quantum physics. For an outsider like me, it is difficult to actually understand ...
1
vote
0answers
32 views

Is the reduction map completely positive? [duplicate]

I am struggling with proving the complete positivity of a general map ( granted it is CP ). The reduction map is defined as $$ \rho \rightarrow \mathrm{Tr}(\rho)I - \rho $$ It is a trivial job to ...
2
votes
3answers
467 views

Scalar Field Redefinition and Scattering Amplitude

Consider a field redefinition $$ \phi \rightarrow \phi' = \phi+\lambda \phi^2 $$ Find the Feynman rules for this theory and work out the $2\rightarrow 2$ scattering amplitude at tree level (The result ...
0
votes
1answer
74 views

Amplitudes involving Goldstone bosons

Does anyone know some theorem or statement about amplitudes involving only Goldstone bosons in theories with spontaneous symmetry breaking in the limit of low energies?
59
votes
0answers
3k views

Superfields and the Inconsistency of regularization by dimensional reduction

Question: How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)? Background and some references: ...
3
votes
0answers
48 views

Is it necessary to use decay width calculated at the same order as the scattering process?

I would like to calculate higher order corrections to a process for which there is an intermediate resonance which subsequently decays into lighter states. I am confused about how to treat the width ...
9
votes
7answers
1k views

Can energy be taken out of the QFT vacuum?

There have been recent questions about the vacuum. In my simplified knowledge the vacuum is like a ground state energy level, and also that there might even exist other lower energy levels than the ...
7
votes
1answer
103 views

Assumptions of the Coleman-Mandula Theorem

In the original paper All Possible Symmetries of the S-Matrix, by S. Coleman and J. Mandula, they prove their famous 'no go' theorem regarding the possible extensions of Poincaré symmetry. The ...
4
votes
1answer
192 views

How to derive the form of the parity operator acting on Lorentz spinors?

I'm reading Berestetskii (Volume 4 of Landau & Lifshitz) section 19 on inversion of spinors. Berestetskii says parity $P$ maps undotted spinors into dotted spinors and vice-versa as ...
2
votes
1answer
61 views

Materials about S-matrix and S-matrix theory

What is the best book or paper to learn about analytical structures of S-matrix and S-matrix theory? I already know books as The Analytic S-matrix by RJ Eden, PV Landshoff, DI Olive, JC P and Quantum ...
0
votes
1answer
219 views

What happens to the wave function after applying the D'Alembert operator?

Is the result of applying the D'Alembert operator on a wave function always zero? Or are there exceptions?
4
votes
1answer
125 views

The BRST construction for YM with or without auxiliary field

I'm learning BRST symmetry for Yang-Mills theory and I see that there are two ways of writing BRST differential. In some books (for example Ryder's and Ramond's textbooks) BRST differential acts as ...
2
votes
2answers
122 views

Angular Momentum Operator in Quantum Field Theory

I'm following along with David Tong's QFT course and am trying to derive the result shown in question 6 on his 2nd problem sheet, but am running into problems when applying it to the free real scalar ...
2
votes
0answers
34 views

Energy interpretation of 1PI effective potential in Weinberg 16.3: is adiabatic turning on the current necessary?

In section 16.3 of Weinberg, he interprets the 1PI effective potential as the minimum of expectation value of the energy density under some constraint. The essential argument is \begin{equation} ...
1
vote
0answers
58 views

What if UV behaviour of gravity was perturbative?

I understand that the UV behaviour of gravity ought to be dominated by black hole production and that graviton-graviton scattering ought to blow up above the Planck scale. Suppose, however, that ...
4
votes
1answer
116 views

Non-relativistic limit in a Lagrangian density

What criteria should I consider when determining the non-relativistic limit of a Lagrangian density? For example, how would I take the non-relativistic limit of the following Lagrangian density: ...
0
votes
2answers
141 views

S. Weinberg, “The Quantum theory of fields: Foundations” (1995), Eq. 9.2.15

In Weinberg's book The Quantum Theory of Fields, Volume 1 on p.388 (Chapter 9), the following identity is used (with f being any "reasonable" function): $$f(+\infty) + f(-\infty) = \lim_{\epsilon ...
6
votes
2answers
151 views

Physical consequences of non-abelian non-trivial holonomy

The Aharonov-Bohm effect (http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect#Significance) can be well described and explained in terms of holonomy of the $U(1)$ connection of the ...
2
votes
1answer
84 views

What's the relation or difference between Lippmann-Schwinger equation and Dyson equation?

In quantum scattering theory, Green's Function is defined as [1] $$G_0(z)=(z-H_0)^{-1},$$ $$G(z)=(z-H)^{-1},$$ where $H_0$ and $H=H_0+V$ are separately non-interacting and interacting Hamiltonian. $V$ ...
2
votes
0answers
83 views

How should I regularize this integral?

I need to calculate the following integral (which is divergent): \begin{equation} I(m,C)=\int_{-\infty}^\infty {\rm d}\omega\int_{\rm space}{\rm d^3 ...
10
votes
1answer
170 views

Phase Structure of (Quantum) Gauge Theory

Question: How to classify/characterize the phase structure of (quantum) gauge theory? Gauge Theory (say with a gauge group $G_g$) is a powerful quantum field theoretic(QFT) tool to describe ...
2
votes
0answers
37 views

Conversion of QCD cross section formula

I'm writing a program to calculate NLO cross sections for semi-inclusive high-$p_T$ pion production in proton-proton-collisions for my bachelor thesis. I've got a paper describing the production ...
2
votes
1answer
72 views

Increased likelihood of photon emission due to “nearby” absorber?

Is an excited atom more likely to emit a photon if there is a similar atom in the ground state nearby ready to absorb it? When I say "nearby" I guess I mean that the absorber has an approximately ...
8
votes
1answer
164 views

There are two definitions of S operator (or S matrix) in quantum field theory. Are they equivalent?

I read several textbooks of QFT and found that there are two kinds of definition of $S$ operator (or S matrix). First kind: Define $\hat{S}$ is map from out space to in space ...
4
votes
1answer
74 views

3 to 3 scattering in massless $\phi^4$ theory

During my QFT study I faced a problem of calculating amplitude of 3 to 3 scattering in massless $\phi^4$ theory in zero momenta limit at tree level. One of topologically distinct diagrams ...
1
vote
0answers
44 views

Wave equation for de Sitter invariant Green's functions

In several papers on QFT in de Sitter space (curvature set to $1$) it is asserted that the Klein-Gordon equation obeyed by the two point function of the free fields: $$(\square-m^2)G(x_1,x_2)=0 $$ can ...
6
votes
1answer
162 views

SU(N) Yang-Mills $gg \to ggg$ scattering at tree level

When talking about the spinor-helicity formalism in his new textbook on quantum field theory, Matthew D. Schwartz claims as a highly nontrivial example, it is quite easy to use the Parke-Taylor ...
3
votes
1answer
164 views

Three integrals in Peskin's Textbook

Peskin's QFT textbook 1.page 14 $$\int_0 ^\infty \mathrm{d}p\ p \sin px \ e^{-it\sqrt{p^2 +m^2}}$$ when $x^2\gg t^2$, how do I apply the method of stationary phase to get the book's answer. ...
7
votes
1answer
86 views

Some conceptual questions on the renormalization group

I recently followed courses on QFT and the subject of renormalization was discussed in some detail, largely following Peskin and Schroeder's book. However, the chapter on the renomalization group is ...
1
vote
0answers
61 views

How to calculate these integrals about propagator of QFT analytically?

How to get these three analytical solutions? Thanks very much! $$ G_{ret}(x,y) = \lim_{\epsilon \to 0} \frac{1}{(2 \pi)^4} \int d^4p \, \frac{e^{-ip(x-y)}}{(p_0+i\epsilon)^2 - \vec{p}^2 - m^2} = ...