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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QED as a Wightman theory of observable fields? With a collision theory?

[Note: I'm using QED as a simple example, despite having heard that it is unlikely to exist. I'm happy to confine the question to perturbation theory.] The quantized Aᵘ and ψ fields are non-unique ...
12
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1answer
553 views

What are the limitations of the superspace formalism?

Just from reading this slightly technical introduction to supersymmetry and watching these Lenny Susskind lectures, I thought that the Lagrangian of any "reasonable" supersymmetric theory can always ...
2
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1answer
217 views

Phase space suppression in loop integrals

Often (if not always) when calculating loop integrals in QFT one encounters extra 2 $\pi$'s that serve to suppress higher order corrections more so than the most naive guess would give. This happens ...
5
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1answer
381 views

How do we measure $i[\hat\phi(x),\hat\phi(y)]$ in QFT?

What operational procedure is required to measure $i[\hat\phi(x),\hat\phi(y)]$ in an interacting (or non-interacting) QFT? [assume smearing by test-functions, or give an answer in Fourier space, for ...
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2answers
863 views

Where does the wave function of the universe live? Please describe its home

Where does the wave function of the universe live? Please describe its home. I think this is the Hilbert space of the universe. (Greater or lesser, depending on which church you belong to.) Or maybe ...
5
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1answer
337 views

Conceptual quantum field theory

Often papers and books give some bold(deep physical insight) statements in quantum field theory which are not backed by mathematics, and seldom by citing papers. Being a student I don't grasp the real ...
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1answer
443 views

Spin-Statistics Theorem (SST)

Please can you help me understand the Spin-Statistics Theorem (SST)? How can I prove it from a QFT point of view? How rigorous one can get? Pauli's proof is in the case of non-interacting fields, how ...
2
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0answers
100 views

Why/When can the gauge superfield and/or chiral superfield kinetic term in $(2,2)$ SUSY be ignored?

This is in reference to the argument given towards the end of page $61$ of this review paper. There for the path-integral argument to work the author clearly needed some argument to be able to ignore ...
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2answers
220 views

Could motives aid in the study of the Navier-Stokes equations?

Recently, mathematicians and theoretical physicists have been studying Quantum Field Theory (and renormalization in particular) by means of abstract geometrical objects called motives. Amongst these ...
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0answers
174 views

The Paper by Fateev and Zamolodchikov

I would like to read the following paper by Fateev and Zamolodchikov. Operator Algebra and Correlation Functions in the Two-Dimensional Wess-Zumino SU(2) x SU(2) Chiral Model. In addition to the ...
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4answers
7k views

Why don’t photons interact with the Higgs field?

Why don’t photons interact with the Higgs field and hence remain massless?
6
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1answer
472 views

About the definition/motivation/properties of the twisted chiral superfield in ${\cal N}=2$ theories in $1+1$ dimensions

The following is in the context of the ${\cal N}=2$ supersymmetry in $1+1$ dimensions - which is probably generically constructed as a reduction from the ${\cal N}=1$ case in $3+1$ dimensions. In ...
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4answers
1k views

What is anti-matter?

Matter-- I guess I know what it is ;) somehow, at least intuitively. So, I can feel it in terms of the weight when picking something up. It may be explained by gravity which is itself is defined by ...
4
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0answers
165 views

From vertex function to anomalous dimension

In a $d$ dimensional space-time, how does one argue that the mass dimension of the $n-$point vertex function is $D = d + n(1-\frac{d}{2})$? Why is the following equality assumed or does one prove ...
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0answers
26 views

Does it make sense to speak of amplitudes of finite closed boundaries in QFT?

A example of amplitude in Relativistic Quantum Mechanics or specifically in QFT is the amplitude of a field configuration on a space-like hyper-surface of space-time to "lead" to another field ...
6
votes
1answer
164 views

Asymptotic Completeness, generalized free fields, and the relationship of thermodynamics with infinity

Asymptotic completeness is a strong constraint on quantum field theories that rules out generalized free fields, which otherwise satisfy the Wightman axioms. If we were to take a limit of a list of ...
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2answers
343 views

What is the interaction with Higgs field(s) that give the quarks so much different masses?

The masses of quarks are: mu 2∼3 MeV md 4∼6 MeV mc 1.3 GeV ms 80∼130 MeV mt 173 GeV mb 4∼5 GeV
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1answer
193 views

Any case of a particle seemingly decaying into copies of itself?

Is there any case reported that seems to resemble the following: there is a particle and at some moment, the particle seems to break down into two or more particles that are all identical to the ...
5
votes
0answers
152 views

Does it make sense to speak of amplitudes of finite closed boundaries in QFT?

A example of amplitude in Relativistic Quantum Mechanics or specifically in QFT is the amplitude of a field configuration on a space-like hyper-surface of space-time to "lead" to another field ...
3
votes
2answers
342 views

A question from Weinberg QFT text

In page 71 Weinberg's QFT, $$A\Psi^{\theta }_{a,b} ~=~(a\cos{(\theta )}-b\sin{(\theta )})\Psi^{\theta }_{a,b}.$$ He says that massless particles represented by $\Psi ^{\theta }_{a,b}$ are not ...
6
votes
1answer
128 views

$\pm$ (light-cone?) notation in supersymmetry

I would like to know what is exactly meant when one writes $\theta^{\pm}, \bar{\theta}^\pm, Q_{\pm},\bar{Q}_{\pm},D_{\pm},\bar{D}_{\pm}$. {..I typically encounter this notation in literature on ...
2
votes
2answers
272 views

Gauge invariant scalar potentials

If $\Phi$ is a multi-component scalar field which is transforming in some representation of a gauge group say $G$ then how general a proof can one give to argue that the potential can only be a ...
7
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2answers
216 views

Why aren't the spin-3/2 fields in the (3/2,0)+(0,3/2) representation?

Why is it that spin-$\frac 32$ fields are usually described to be in the $(\frac 12, \frac 12)\otimes[(\frac 12,0)\oplus(0,\frac 12)]$ representation (Rarita-Schwinger) rather than the $(\frac ...
5
votes
1answer
601 views

A certain gluon scattering amplitude

I am stuck with this process of calculating the tree-level scattering amplitude of two positive helicity (+) gluons of momentum say $p_1$ and $p_2$ scattering into two gluons of negative (-) helicity ...
3
votes
1answer
337 views

Spinor integration

I am learning on-shell methods for one loop integrals from this paper: Loop amplitudes in gauge theory: modern analytic approaches by Britto. Starting with formula (18) spinor integration is ...
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2answers
212 views

How important are electromagnetic tidal effects in QFT? Can they be used to determine whether a particle is point-like?

I just did a back-of-the-envelope calculation, which surprised me. I calculated the difference in acceleration (due to repelling like-charges) experienced by two sides of an electron the size of the ...
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1answer
478 views

Gauge invariance and the form of the Rarita-Schwinger action

in Weinberg Vol. I section 5.9 (in particular p. 251 and surrounding discussion), it is explained that the smallest-dimension field operator for a massless particle of spin-1 takes the form of a field ...
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3answers
3k 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 ...
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4answers
347 views

Faster-than-$c$ photons

As far as I know, according to quantum field theory, there are some photons that go faster than c, which is the speed of light in vacuum. However, there seems to be a paper and a corresponding ...
13
votes
1answer
970 views

What is a general definition of the spin of a particle?

In quantum field theory, one defines a particle as a unitary irreducible representations of the Poincaré group. The study of these representations allows to define the mass and the spin of the ...
4
votes
1answer
210 views

What does the appearance of a classical particle fundamentally reduce to?

I've been reading an article that describes what seems to be a classical particle as a regularity in the global wavefunction over a quantum configuration space: When you actually see an electron ...
5
votes
1answer
719 views

The nature of time, according to quantum field theory

I will try my best to ask the question that best fits something I have been pondering on for a few days. Are virtual particles really constantly popping in and out of existence? Or are they ...
3
votes
1answer
455 views

Current formula and form factor

I am currently struggling with the formula for an exact current in QFT, a fermion with an upcoming momentum $p$ and an outgoing momentum $p'$. My problem is to show whether or not a term of the ...
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vote
3answers
311 views

EM field quantization

I'm trying to quantize the electromagnetic field by solving the vector potential wave equation, that is: $$\nabla^{2} \mathbf{A} = \dfrac{1}{c^{2}} \dfrac{\partial ^{2} \mathbf{A}}{\partial t^{2}}, ...
7
votes
1answer
118 views

Some more questions about the BCFW reduction

This question is a continuation of this previous question of mine and I am continuing with the same notation. One claims that one can actually split this $n$-gluon amplitude such that there is just ...
2
votes
0answers
83 views

Factorization of fermionic scattering integral in 2d momentum rep

the scattering integrals for fermions involves both momentum ($k$) and energy ($k^2$) conservation and a nonlinear phase space factor of a distribution function $f(k)$. $$\begin{multline}I(k) = ...
5
votes
1answer
193 views

Hawking radiation: direct matter -> energy conversion?

When a black hole evaporates, does it turn all the matter that has fallen in directly to energy, or will it somehow throw back out the same kind of matter (normal or anti) that went in?
22
votes
5answers
4k views

Why not using Lagrangian, instead of Hamiltonian, in non relativistic QM?

When we studied classical mechanics on the undergraduate level, on the level of Taylor, we covered Hamiltonian as well as Lagrangian mechanics. Now when we studied QM, on the level of Griffiths, we ...
7
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0answers
269 views

Instantons and Borel Resummation

As explained in Weinberg's The Quantum Theory of Fields, Volume 2, Chapter 20.7 Renormalons, instantons are a known source of poles in the Borel transform of the perturbative series. These poles are ...
9
votes
1answer
832 views

Identification of the state of particle types with representations of Poincare group

In the second chapter of the first volume of his books on QFT, Weinberg writes in the last paragraph of page 63: In general, it may be possible by using suitable linear combinations of the ...
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vote
1answer
384 views

Is there orbital angular momentum for all particles?

Light as an electromagnetic wave can be polarized in different ways, e.g. linear or circular. As far as I understand it currently this can be compared to the spin direction of a propagation electron ...
3
votes
1answer
115 views

Charge of a field under the action of a group

What does it mean for a field (say, $\phi$) to have a charge (say, $Q$) under the action of a group (say, $U(1)$)?
4
votes
1answer
282 views

The difference between projection operators and field operators in QFT?

Is there a good reference for the distinction between projection operators in QFT, with an eigenvalue spectrum of $\{1,0\}$, representing yes/no measurements, the prototype of which is the Vacuum ...
5
votes
1answer
130 views

Renormalization of the R-charge?

In general I would like to know as to known or what is/are the standard references about R-charge renormalization in supersymmetric theories. When does it do so and what is expected or known to be ...
9
votes
1answer
876 views

Kramers-Kronig relations for the electron Self-Energy Σ

I'm currently studying an article by Maslov, in particular the first section about higher corrections to Fermi-liquid behavior of interacting electron systems. Unfortunately, I've hit a snag when ...
4
votes
3answers
406 views

How does one interpret the Dirac equation with a self-field potential?

EVERY QFT text I've ever examined states that if there is an external vector potential, $A_\mu$, then one writes the Dirac eq.(or Klein-Gordon eq.) using a covariant derivative to include this U(1) ...
5
votes
1answer
256 views

what is a kink-kink-meson vertex?

These are questions I have after reading the Rajaraman's book "Solitons and instantons". So I think you must have read the book if want to answer. And also know about quantum solitons. Rajaraman ...
6
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1answer
389 views

Some questions about the BCFW reduction

I am trying to give a fast sketch of what the BCFW reduction does and embed within it some questions at the steps which I don't seem to understand clearly. The first bullet point is sort of a very ...
5
votes
3answers
841 views

Unitarity of S-matrix in QFT

I am a beginner in QFT, and my question is probably very basic. As far as I understand, usually in QFT, in particular in QED, one postulates existence of IN and OUT states. Unitarity of the S-matrix ...
2
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1answer
729 views

How are fundamental forces transmitted?

How are the fundamental forces transmitted? In particular I wonder, are all "processes" local, i.e. without superluminal distant interactions? But if they are local, then particles would have to ...