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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Gradient involved commutator in $\phi^4$ theory

In a phi fourth theory, the Hamiltonian density is: $$\mathcal{H}=\frac{1}{2}\pi^2+\frac{1}{2}(\nabla \phi)^2+\frac{1}{2}m^2\phi^2+\frac{\lambda}{4!}\phi^4$$ Now I impose the usual equal time ...
3
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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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1answer
630 views

How do instantons cause vacuum decay?

From what I read about on instantons (Zee, QFT in a Nutshell, pg 309-310), an instanton is a vacuum solution that maps $S^3 \rightarrow S^3$ (the boundary of Euclideanized spacetime), which comes from ...
3
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1answer
59 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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21 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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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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45 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
236 views

Intuition for S-duality

first of all, I need to confess my ignorance with respect to any physics since I'm a mathematician. I'm interested in the physical intuition of the Langlands program, therefore I need to understand ...
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3answers
135 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 ...
2
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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 ...
3
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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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1answer
307 views

effective field theory of the projective semion model

The "projective semion" model was considered in http://arxiv.org/abs/1403.6491 (page 2). It is a symmetry enriched topological (SET) phase. There is one non-trivial anyon, a semion $s$ which induces a ...
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4answers
7k views

Why you need a graviton when you have the higgs boson?

Since I studied General Relativity I had this question running on my mind. As I see it (just taking lectures of Quantum Field Theory right now) "Why you need a gauge boson for gravity when the higgs ...
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1answer
134 views

Gaussian path integrals and convergence

The Hamiltonian path integral in quantum mechanics, for a particle with coordinate $q$ and momentum $p$ and Hamiltonian $H=p^2/2m+V(q)$, is $\int \mathcal{D}q(t)\mathcal{D}p(t)e^{i\int_0^T(p\dot{q}-\...
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1answer
146 views

Representations of SO(3) and the classification of relativistic massive particles as in Weinberg's “The Quantum Theory of Fields”

I'm reading about the classification of relativistic massive particles in Weinberg's "The Quantum Theory of Fields", and I found something that doesn't convince me. In Chapter 2, paragraph 5, having ...
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39 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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2answers
757 views

About Boltzmann H-theorem

What is the assumption for Boltzmann H-theorem? One can derive it just from the unitarity of quantum mechanics, so this should be generally true, does it imply a closed system will always thermalize ...
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1answer
66 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\...
2
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1answer
136 views

Calculating the boundary modes in Kitaev Chain

In section 2 of the paper, 'Unpaired Majorana Fermions in Quantum Wires', equation (14), the following transformation: \begin{equation} b^{'} = \sum_{j} (\alpha_+ ^{'} x_+ ^{j} + \alpha_- ^{'} x_- ^{...
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0answers
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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4answers
121 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
2k views

What does it mean that there is no mathematical proof for confinement?

I see this all the time* that there still doesn't exist a mathematical proof for confinement. What does this really mean and how would a sketch of a proof look like? What I mean by that second ...
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3answers
102 views

In, QFT, do the excitations in the quantum fields exist physically? [closed]

In QFT, all particles are really just excitations in their quantum fields, and we know that these fields are just mathematical.For example, an electron is an excitation of the electron field. But my ...
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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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1answer
123 views

What is the physical relevance of the classical limit to a quantum field theory?

We know the physical relevance of the classical limit of quantum mechanics quite well. However, if I take the classical limit of a quantum field theory, the answer is not so clear. Suppose I take the ...
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1answer
53 views

How do I extract the groundstate of a quadratic field theory?

I have successfully solved a field theory quadratic in fermonic creation and annihilation operators via Bogolyubov transformation to a diagonal field theory. I now want to extract the groundstate of ...
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68 views

Some subtleties in quantizing a fermi field

Consider the quantization conditions for a complex Fermi field $\Psi=\Phi_1+i\Phi_2$: $$\{\Psi(x),\Psi(y)\}=\{\Psi^\dagger(x)\Psi^\dagger(y)\}=0,~~~~ \{\Psi^\dagger(x),\Psi(y)\}=\delta(x-y)$$ Compare ...
6
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1answer
93 views

Which inverse of $-(\partial^2 + m^2)$ should be used in the path integral?

The partition functional for free scalar field is $$Z=\int D\varphi e^{i\int d^4x[-\frac{1}{2}\varphi (\partial^2+m^2)\varphi+J\varphi]}.\tag{1}$$ To evaluate this functional integral, we usually ...
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0answers
42 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 ...
2
votes
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
40 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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9answers
5k views

Rigor in quantum field theory

Quantum field theory is a broad subject and has the reputation of using methods which are mathematically desiring. For example working with and subtracting infinities or the use of path integrals, ...
5
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1answer
167 views

When particle number can change in quantum physics?

Let me write a paragraph from D.Tong lecture notes on QFT-chapter2 when he is talking about non-relativistic limit of scalar quantum field theory : A related fact is that the conserved charge $Q=\...
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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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 ...
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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 ...
26
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3answers
729 views

Renormalization Group for non-equilibrium

For equilibrium/ground state systems, a (Wilson) renormalization group transformation produces a series of systems (flow of Hamiltonians/couplings $H_{\Lambda}$ where $\Lambda$ is the cut-off) such ...
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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}....
1
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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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1answer
153 views

Invariance in Euclidean and Minkowski spaces

Consider Wick's rotation from Minkowski to Euclidean space in QFT. What is the connection between O(4) invariance in Euclidean space and Lorentz invariance in Minkowski space? If we define a quantity ...
19
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2answers
711 views

S-Matrix in $\mathcal{N}=4$ Super-Yang Mills

This is a general question, but what is meant when people refer to the S-Matrix of $\mathcal{N}=4$ Super Yang Mills? The way I understood it is the S-Matrix is only well defined for theories with a ...
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0answers
101 views

Hawking radiation at the mouth of Schwarzschild wormholes

I was researching a question for another post and it occurred to me that you might expect to see Hawking radiation at the mouth of wormholes. Given the mechanism of Hawking radiation at the event ...
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0answers
42 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 ...
2
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1answer
111 views

Angular Momentum of the Dirac field

I'm going through the Peskin & Shroeder's discussion on the Dirac field, and I am struggling with a couple of claims they make about angular momentum. First of all, the angular momentum operator ...
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1answer
55 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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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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0answers
57 views

Some questions about QCD [closed]

About QCD, I have two questions. I know I should propose one question one time, but they are actually two steps of the same question: Non-perturbative aspects of QCD. 1, Why do we need to solve QCD ...
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2answers
35 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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1answer
47 views

Feynman diagram elementary vertex with 4 lines?

Are there processes that require vertices with 4 lines in a Feynman diagram? (And cannot be written as composition of 3-line vertices?) If not, is it matter of models we use (where there are no ...