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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Feynman Rules and Feynman Diagrams in QFT by Srednicki [duplicate]

I'm reading Srednicki's Quantum Field Theory. I 'm trying to read Srednicki's presentation of Feynman Diagrams in the chapter Path Integral for the Interacting Field Theory. Link to the textbook: http:...
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44 views

Why is the infinitesimal SUSY variation generated by the sum of a left- and right-chiral generator

I was wondering why in many (all? e.g.https://arxiv.org/abs/hep-ph/9709356) resources on N=1 SUSY the variation of a field in the simplest free susy model is defined as $$\delta_\epsilon \phi = (\...
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41 views

How to understand CP-violation in kaon systems with Feynman diagrams and matrix elements?

I am trying to understand CP-Violation in the Kaon system using feynman diagrams and matrix element. Here is a slide from Mark Thomson corresponding exactly to what I am looking for (http://www.hep....
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1answer
69 views

Problem with figuring out sign conventions in QFT

I have a problem with sign conventions in QFT which I have trouble dealing with myself. I self-study and mainly use Weinberg and Peskin. I will present the reasoning following conventions adapted by ...
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35 views

Translational symmetry and generalized Heisenberg equation of motion [on hold]

Suppose, there are 2 plates; one at x=0 and another at x=L such that the area vector of the plate surface is parallel to the x axis and electromagnetic field is confined between this plates. I am ...
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3answers
287 views

Dummy variables in Dyson series

In the Dyson series, it is known that: \begin{align} {\cal T}\exp\left[-\frac{i}{\hbar}\int_0^tH(t')dt'\right] &= I - \frac{i}{\hbar} \int_{0}^{t} dt' H(t') + \left(-\frac{i}{\hbar}\right)^2 \...
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1answer
58 views

Integral form of solution of Dyson series and differentiation of the exponential form

The solution to time dependent hamiltonian equation is: $$\frac{\partial}{\partial t}U(t) = -\frac{i}{\hbar}H(t)U(t)$$ The immediate integral form solution is $U(t) = I - \frac{i}{\hbar}\int_{0}^{...
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1answer
46 views

Gauge Theory of Superconductors

I'm trying to understand better the nature of the gauge redundancy and the Higgs mechanism in superconductors. Specifically, I'm looking for a good reference that explains monopoles, vortices, and ...
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0answers
66 views

Srednicki's QFT: Feynman Rules and Feynman Diagrams

I'm reading Srednicki's Quantum Field Theory. I 'm trying to read Srednicki's presentation of Feynman Diagrams in the chapter Path Integral for the Interacting Field Theory. The path integral for the ...
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35 views

A question about the Ward-Takahashi identity

I am studying Peskin and Schroeder's textbook of quantum field theory. I have proceeded to Ward-Takahashi identity and have one question. Eq.(7.66) and Eq.(7.67) are the two cases involved. Then ...
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32 views

What is the recursive relation for three-particle Green's functions?

In condensed matter physics, one often choose to study the many-body Green's functions (GF) with the diagram (perturbation) expansion technique. In what follows only two-body interaction is concerned. ...
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43 views

Time ordered product of operator and Heisenberg equation of motion

Can we use time ordered product of operators in Heisenberg equation of motion? Please give me an example.
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33 views

Fermi's golden rule and S-matrix

As I understand, Fermi's golden rule is a result from first order perturbation, which says that the transition rate of an initial state $|i\rangle$ to a final state $|f\rangle$ is $$ \Gamma_{i\...
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3answers
39 views

Notation about basis of gamma matrices in $4d$

In Quantum Field theories, we encounter gamma matrices a lot. Reading from various textbook, i encountered some textbook use different basis for their gamma matrices. Gamma matrices are defined such ...
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40 views

Hermiticity of the Lagrangian density [duplicate]

In quantum mechanics, the dynamical variables are replaced by hermitian operators. However, the Lagrangian density in quantum field theory is not an observable but we also make sure that it is ...
3
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0answers
55 views

Renormalization group equation: physical meaning of energy scale [duplicate]

I'd like to understand the physical meaning of the energy scale $\mu$ that emerges in the renormalization group equation (RGE). In particular I don't understand in what way a running coupling constant ...
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1answer
50 views

The relation between critical surface and the (renormalization) fixed point

In the book, I read some remarks about the criticality: Iterations of the renormalization (group) map generate a sequence of points in the space of couplings, which we call a renormalization ...
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0answers
18 views

Local Effective actions

While studying partition functions in general, i came across a statement which says that "the partition function of a theory without gapless excitations must be a local functional of the background ...
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43 views

Running of $\alpha$ and scattering amplitudes

Consider a QED scattering process $e^-+e^-\rightarrow e^-+e^-$. The scattering crosssection at the tree-level depends on the square of the fine-structure constant $\alpha$ (apart from the electron ...
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1answer
58 views

Srednicki's Path Integrals: Ground-State to Ground-State Transition Amplitude in the Presence of a Perturbation

Srednicki's Quantum Field Theory mentions the following at the end of the unit on path integrals in non-relativistic quantum mechanics: Assume that the total Hamiltonian is of the form, $$ H = ...
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1answer
64 views

Does Microcausality follow from Lorentz Invariance?

In a Lorentz Invariant theory, does microcausality automatically hold? In a free theory this is obvious. In an interacting theory I found some 'proof's in this paper: http://arxiv.org/abs/0709.1483 ...
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1answer
41 views

Distributive property of the time-ordering symbol

Most derivations of the LSZ reduction formula, e.g. Srednicki (equations 5.13, 5.14, 5.15), Schwartz (equations 6.17, 6.18, 6.19), Wikipedia use a property of the time-ordering symbol that looks like ...
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3answers
134 views

Electron-positron annihilation: Feynman diagram

Maybe my question is just a blunder. Consider Compton interaction: $e^{-}+\gamma \rightarrow e^{-}+\gamma$. There are two Feynman diagrams related to this process to the lowest order of $\alpha$. Now ...
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29 views

Why is the spacelike conserved charge due to spacetime translations the momentum?

Whilst reading several books on QFT, I have come across the derivation of the conserved charges due to the symmetry under spacetime-translations. I can follow the derivations, and have that the ...
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1answer
42 views

Using Dyson formula in Schrodinger picture

From Time-ordering and Dyson series and what I learnt, Dyson formula is used in the situation of interaction picture: $$i\frac{dU_I}{dt} = H_{I}(t)U_I$$ where $H_I(t)$ is interaction Hamiltonian ...
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How do Physicists picture an Electron in their minds? [closed]

What is the first image that appears in your heads when I say the word "Electron"?
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43 views

Intuition for why there are quantum beats in $V$-type but not in $\Lambda$-type atoms

When calculating the emitted intensity of an excited $\Lambda$-type or $V$-type atom with a quantized field (instead of a semiclassical approach with only quantized energy levels) one finds that there ...
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37 views

Confusion about symmetry factor

I have some questions about symmetry factor. When we count symmetry factor, we count something like how to permute propagators in Feynman diagram, but I think this counting is already taken care of by ...
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1answer
62 views

Kallen-Lehmann representation versus perturbation theory

According to the Kallen-Lehmann representation of the propagator, the propagator has a branch cut beginning around $p^2\approx4m^2$. This appears to invalidate the use of the usual $\frac{i}{p^2-m^2+i\...
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30 views

Influence of matter of a star on masses of neutrinos

It is well known that if neutrinos has masses then from Dirac equation it follows that they propagate (in vacuum) as a eigenstates of mass (not as eigenstates of interaction). It's wave function is of ...
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191 views

Interpreting the Klein-Gordon Annihilation Operator Expression

I can derive $$a(k) = \int d^3 x e^{ik_{\mu} x^{\mu}} (\omega_{\vec{k}} \psi + i \pi)$$ for a free real scalar Klein-Gordon field in three ways mathematically: the usual Fourier transform way in ...
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4answers
119 views

What actually happens when a photon is absorbed by matter?

In my physics courses so far we've only discussed the before and after of a photon being absorbed by matter. But what actually happens here? How does the light "meld" with the atom that it is incident ...
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1answer
55 views

Collapse of Wavefunction after space-like Seperated Measurements

Suppose I have a pair of entangled particles, each one goes in a different direction. Now I measure the momentum of one particle and the position of the other at the same time. Because the ...
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41 views

Is the vacuum state of a quantum field necessarily zero temperature?

A statement in Quantum field theory: zero vs. finite temperature points to temperature as it relates to the vacuum as being a matter of definition. In that post, Will states By, "at zero ...
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25 views

Gauge invariance of non-Abelian theories under Pauli-Villars-Regularisation

Under the ordinary Pauli -Villars Regularisation one introduces a heavy mass ($\Lambda$) term $$\frac{1}{p^2-m^2+i\epsilon} \rightarrow \frac{1}{p^2-m^2+i\epsilon} - \frac{1}{p^2-\Lambda^2+i\epsilon}....
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1answer
46 views

Lagrangian of Yukawa Interaction and Quark Mixing

I'm trying to understand the original of quark and lepton mass. Here's a paragraph from the book: "Massive neutrinos in physics and astrophysics" by R. N. Mohapatra and P. B. Pal : The gauge ...
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12 views

Selection Rules in FCNC mediated diagrams

I am studying the flavour changing processes mediated by flavor changing neutral current (FCNC). Are there any selection rules involved in assigning the flavor to the outgoing quark? Can the ...
2
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1answer
41 views

Solar activity and radioactive decay rates [duplicate]

I recall hearing about this quite some time ago and thought it was very strange. I recently had it pop in my head again and was curious if anyone knew what was going on with this. Variable decay ...
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0answers
18 views

Amplitude at threshold

So I'm working through a problem in Peskin & Schroeder QFT textbook (This one, 4.3b http://www.physics.umd.edu/grt/taj/624a/LinearSigmaModel.pdf). I have to compute some scattering amplitudes and ...
2
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0answers
144 views

Gauge theory and lattice gauge theory [closed]

This is a question is a follow-up to the answer by @tparker about what in simple terms is gauge invariance. I want to know in detail the subtleties of the definitions for gauge theory (#3) and lattice ...
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0answers
39 views

Can energy go through higher dimensions?

It is hypothetically predicted that gravitons can escape from the 4th dimension or brane and "leak" or go through higher dimensions. I wonder if energy can do the same thing. Is there any explanation ...
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1answer
53 views

Position of indices in QFT

I have recently started studying quantum field theory from the book Quantum Field Theory and the Standard Model by Schwartz. In chapter 2 it is said that, contrary to GR, one can ignore the index ...
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0answers
26 views

Distinguishing Insulator, Metal, Superconductor by a flux insertion argument

I have the following argument to distinguish Insulator, Metal and Superconductor. For simplicity let's consider electrons on a circle and thread one quantum of flux (e$\Phi_0 = 2\pi$) through it (or ...
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1answer
46 views

Interpretation of the vector current in field theory

In field theory we write $$J^\mu=\bar{\Psi}\gamma^\mu\Psi$$ But I can't understand why it is so. Could anyone explain each of the terms in the multiplication?
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39 views

What are the differences (if any) between the Dyson's series definition and the “in/out” definition of the $S$-matrix

So long, in my QFT courses, I've seen two definitions of the $S$-matrix: The first, more elementary, definition is given in the interaction picture: $$S=\text T \lbrace \exp [-i\intop \text d ^4 x \,...
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2answers
34 views

Instantaneous transfer of information?

If suppose there is some charge which is not under influence of any other thing. Let us for observation surround this charge with circles of pointers pointing in the direction of its field. If I move ...
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42 views

Feynmann Propagtor and the Green's Function for a Free Field

I'm going through Mark Srednicki's Quantum Field Theory. Chapter 8 on The Path Integral for the Free Field Theory includes the following: In the presence of a classical source, $J$, the ground state-...
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1answer
103 views
+50

Why is this expression infrared divergent

On P.217 of Quantum Field Theory by Peskin and Schroeder, it is stated that the Eq.(7.16) is infrared divergent and therefore a small photon mass $\mu$ is added to the photon propagator. The equation ...
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1answer
36 views

Photon as a gauge boson for static fields

Excuse me if my question is naive, but I have never taken a proper QFT. I used to think of a photon as a quantum of EM field, quantum of light. But form QFT and particle physics prospective, photon ...
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12 views

Closed form expression for the partial decay widths of Higgs boson in massive vector bosons

Can anybody help me obtain a closed form expression for the Higgs partial decay width into massive vector bosons (off shell decays)? I am writing code for the partial decay widths of the Higgs and ...