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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Decay of massless particles

We don't normally consider the possibility that massless particles could undergo radioactive decay. There are elementary arguments that make it sound implausible. (A bunch of the following is ...
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Feynman diagrams in effective theories

I've been seeing many feynman diagrams lately that I can't quite interpret yet. I've heard a basic Quantum Field Theory lecture and so to me, a Feynman diagram is simply a mnemonic picture to quickly ...
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7answers
445 views

Where do the choice of basis in QFT come from?

Hi physics stack exchange. I am new and a mathematicians - so go easy on me. I have been trying to read up on QFT in the book Diagrammatica: The Path to Feynman Diagrams, and I have a question. The ...
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2answers
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Poincare group vs Galilean group

One can define the Poincare group as the group of isometries of the Minkowski space. Is its Lie algebra given either by the equations 2.4.12 to 2.4.14 (..as also given in this page - ...
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440 views

What's the definition of the time ordering operator for more than two particles?

For two particles, $\langle {\mathcal T} a(t_1) a^\dagger (t_2) \rangle = \langle a(t_1) a^\dagger (t_2)\rangle \theta (t_1-t_2) + \xi \langle a^\dagger (t_2)a(t_1) \rangle \theta (t_2-t_1)$ with ...
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What is the fundamental reason of the fermion doubling?

Recall that the fermion doubling is the problem in taking the $a \to 0$ limit of a naively discretized fermionic theory (defined on a lattice with lattice spacing $a$). After such a limit one finds ...
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616 views

Iterated dimensional regularization

Given a 2-loop divergent integral $\int F(q,p)\,\mathrm{d}p\mathrm{d}q$, can it be solved iteratively? I mean I integrate over $p$ keeping $q$ constant Then I integrate over $q$ In both iterated ...
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Lagrangians combining terms with 1 and 2 derivatives

How are field theory Langrangians treated when some terms have 2 derivatives but others have only 1? Because the number of derivatives in a Lagrangian term is more easily even than odd, the ...
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1answer
176 views

Quantum tunneling in Field theory with Time dependent potential

What should be the limits of integration for euclidean action $S(\phi)$ in 3d and 4d? This action is negatively exponentiated to calculate the decay rate. I suspect that it is variable limit problem. ...
11
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1answer
1k views

Cross-section in relativistic limit: Fermi's golden rule still valid?

In order to calculate the cross-section of an interaction process the following formula is often used for first approximations: $$ \sigma = \frac {2\pi} {\hbar\,v_i} \left| ...
2
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1answer
538 views

Equation of motion for explicit time dependent potential

What is the equation of motion for a single scalar field, which has a Lagrangian density in which the potential explicitly depends on time? For example: $$U(\phi,t)=\frac{1}{2}\phi^2 - \frac{1}{3} ...
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Why does the weak force distinguish left and right handedness?

I'm wondering why the weak interaction only affects left-handed particles (and right-handed antiparticles). Before someone says "because thats just the way nature is" :-), let me explain what I find ...
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A No-Nonsense Introduction to Quantum Field Theory

I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page here. pdf here), a 24-page overview of the topic, very helpful for beginning study. It all got me over the hump ...
6
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1answer
239 views

About unitarity and R-charge in 2+1 superconformal field theory

How does unitarity require that every scalar operator in a $2+1$ SCFT will have to have a scaling dimension $\geq \frac{1}{2}$ ? Why is an operator with scaling dimension exactly equal to ...
7
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2answers
378 views

What happens to a single quark in lattice QCD simulations?

I understand that if a pair quark/antiquark, out of the vacuum, tries to separate then the energy increases, another pair is produced, and we finish with two mesons or generically two hadron jets. But ...
7
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Representation of the Galileo Group and Central Charges

I've arrived at this question because I've been reading Weinberg's Quantum Theory of Fields Volume I, and I'm in the second chapter about relativistic quantum mechanics. Weinberg discusses the ...
3
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1answer
210 views

Why is the local field algebra $\mathfrak F(O)$ associated with a bounded non-empty open region $O$ of space-time not irreducible?

Let us consider a Wightman field theory for the free scalar neutral field $\phi$, and let $O\mapsto\mathfrak F(O)$ be the net of local von Neumann field algebras. If we take a non-empty bounded open ...
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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 ...
2
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0answers
138 views

Argument for quantum theoretic conformality of $\cal{N}=2$ super-Chern-Simon's theory in $2+1$ dimensions -Part 2

This is in continuation to what I was asking here earlier - Argument for quantum theoretic conformality of $\cal{N}=2$ super-Chern-Simon's theory in $2+1$ dimensions Or one can look at this ...
7
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3answers
391 views

why certain superpositions of quantum states are supressed?

it has been said that the electron is the fundamental representation of the Poincare group, with only two conmuting observables, $( \sigma , p_{\mu})$. This question regards what is usually called the ...
11
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1answer
17k views

Where does this equation originate from? (found in the Big Bang Theory)

Recently, I've been watching "The Big Bang Theory" again and as some of you might know, it's a series with a lot of scientific jokes in it - mostly about Physics or Mathematics. I understand most of ...
4
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1answer
202 views

Argument for quantum theoretic conformality of $\cal{N}=2$ super-Chern-Simon's theory in $2+1$ dimensions

I am using the standard symbols of $V_\mu$ for the gauge field, $\lambda$ for its fermionic superpartner and $F$ and $D$ be scalar fields which make the whole thing a $\cal{N}=2$ vector/gauge ...
4
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4answers
308 views

Massive particles and speed of their propagation

Can one show that in quantum field theory at least some example massive particles propagate with speed less than speed of light, while massless travel at speed of light? Well, motion is a different ...
6
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1answer
275 views

Superpartner for the stress-energy tensor

I would like to understand what is meant when one introduces a generator $G(z)$ as the superpartner of the energy-momentum tensor $T(z)$. How does one decide that this $G(z)$ should have a ...
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6answers
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Stronger than Newton's laws?

According to the Newton mechanics, the force is responsible for changing the body velocity, and the body mass is the body inertia - a property to resist to the applied force. These two things make a ...
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0answers
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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: ...
4
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2answers
288 views

Can the electroweak/strong forces, and/or quantum mechanics be thought of as geometric?

Can the electroweak and strong forces be written as geometric theories? - Why and why not? Can quantum mechanics in general? For example, the Kaluza-Klein theory explains the electromagnetic field ...
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3answers
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What does the ordering of creation/annihilation operators mean?

When a system is expressed in terms of creation and annihilation operators for bosonic/fermionic modes, what exactly is the physical meaning of the order in which the operators act? For example, for ...
9
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1answer
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Questions about the Dyson equation

I'm studying finite temperature many-body perturbation theory, and am trying to understand The Dyson equation. In particular, I'm using Mattuck - A guide to Feynman diagrams in the many body problem. ...
3
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1answer
306 views

Does kaon decay etc prove “CP violation” or just “CP or CPT violation”

Shlomo Sternberg (math professor at Harvard) wrote a book called "Group theory and physics". On p156 (link) there's a strange offhand comment: "Experiments done in 1964 by Fitch and Cronin seem to ...
8
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1answer
252 views

Is there literature on a continuous mass spectrum for the Higgs field?

Various masses for the Higgs field are compatible with experiment, but is it possible that the Higgs field is not observable because it has a continuous mass spectrum? Work in the 60s and 70s on free ...
8
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402 views

Quantizing EM field

Why when we quantize EM field, whe quantize the vector potential $A^\mu$ obtaining vectorial particles (photons) like the elastic field (phonons) and we can't quantize directly the EM-field tensor ...
9
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550 views

Spontaneous breaking of Lorentz invariance

Is it possible to spontaneously break Lorentz invariance, i.e., have a Lagrangian that respects LI but a vacuum which does not? If it is possible, why isn't there even the slightest hint of the ...
5
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3answers
422 views

bound states of massless fields?

Question: are they mathematically possible at all? physically? with finite mass systems, usually the binding energy contributes to the rest-mass of the system. It would seem that even if you could ...
6
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0answers
287 views

1-form formulation of quantized electromagnetism

In a perpetual round of reformulations, I've put quantized electromagnetism into a 1-form notation. I'm looking for references that do anything similar, both to avoid reinventing the wheel and perhaps ...
5
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0answers
248 views

When can the source term of a partition function be put in?

More specifically, in quantum field theory books, we usually have this: \begin{equation} Z = \int D(\bar{\psi}, \psi) e^{-S + \int_0^\beta d\tau \sum_l [\bar{\eta}_l (\tau) \psi_l (\tau) + ...
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5answers
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Online QFT video lectures

I'm aware of Sidney Coleman's 1975/76 sequence of 54 lectures on Quantum Field Theory. Are there any other high-quality QFT lecture series available online?
9
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2answers
419 views

Is there any interacting quantum field theory of massless spin-1 fields expressed locally entirely in terms of F, with no vector potential?

Is there any interacting quantum field theory of massless fields with helicity $\pm 1$ which can be expressed entirely locally in terms of the field strength Fμν with no reference to vector ...
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1answer
569 views

What is the most natural definition of the weak hypercharge coupling constant if grand unification is wrong?

A tricky question. Here is the famous graph of the running of the three coupling constants in the standard model: http://www-ekp.physik.uni-karlsruhe.de/~deboer/html/Forschung/unification_eng.eps . ...
7
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0answers
358 views

Descent equation and anomaly polynomial

I am just reading Ryu, Moore and Ludwig's paper on classifications of topological insulators and quantum anomaly. They are trying to relate the quantum anomaly as a signal of the presence of a ...
8
votes
1answer
558 views

Does de Sitter space admit an asymptotic S-matrix?

From the Penrose diagram of de Sitter space, we see it has a future and past conformal boundary, and they are both spacelike. So, does de Sitter space admit an asymptotic S-matrix? Sure, in the usual ...
3
votes
1answer
861 views

What is the value of the fine structure constant at Planck energy?

At low energy, 511 keV, the value of the fine structure constant is 1/137.03599... At Planck energy $\sqrt{\frac{\hbar c^5}{G}}$, or 1.956 $\times$ 109 Joule, or 1.22 $\times$ 1028 eV, it has a ...
3
votes
2answers
475 views

How is perturbation theory applied to the Bunch-Davies state for an interacting quantum field theory?

Feynman diagrams are ordinarily the usual method of perturbative analysis for weakly interacting quantum field theories. However, over a de Sitter background, the total number of particles isn't even ...
5
votes
2answers
862 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 ...
3
votes
1answer
402 views

Seiberg Witten theory

I'm currently reading the Seiberg-Witten paper on $N=2$ supersymmetric Yang Mills pure gauge theory (i.e. no hypermultiplets). I have the following question: How does one understand that the metric ...
3
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1answer
238 views

The vacuum as trigger

Do the apperance in the atomic nucleus of virtual matter-antimatter particle pairs play a role in the random nature of radioactive decay?
7
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2answers
561 views

Why is the spinor field anti-commutator not made gauge invariant?

When we introduce minimal coupling for the Dirac spinor field, we introduce terms into the Lagrangian, by the substitution $i\frac{\partial}{\partial x^\mu}\mapsto i\frac{\partial}{\partial ...
12
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3answers
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Why is there a flux of radiation in the Hawking effect but not in the Unruh effect? (and other questions)

This question is slightly related to this one Do all massive bodies emit Hawking radiation?, which I think was poorly posed and so didn't get very useful answers. There are several questions in this ...
6
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1answer
495 views

Generalization of spin coherent states for an arbitrary group?

My question is inspired by the analogy of the Berry phase in the spin coherent state representation of a rotator and the Aharonov-Bohm phase of a magnetic monopole (see e.g., Section 1.8.3 in ...
14
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3answers
931 views

Does the Unruh effect violate Mach's principle?

Mach's principle says that it is impossible to tell if something is accelerating unless there is something else in the universe to compare that motion to, which seems reasonable. However, if you had ...