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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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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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 ...
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964 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 ...
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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 ...
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705 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 ...
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450 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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310 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}}, ...
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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 ...
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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) = ...
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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?
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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 ...
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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 ...
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823 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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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 ...
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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, $U(1)$)?
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275 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 ...
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1answer
126 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 ...
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1answer
868 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 ...
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399 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) ...
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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 ...
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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 ...
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829 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 ...
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1answer
713 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 ...
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399 views

In SUSY why does electroweak symmetry breaking only happen in the SM sector?

This is a difficult question to phrase succinctly, so I hope the title makes sense. What I want to understand is what seems like a lack of symmetry (besides SUSY-breaking) between the SM sector and ...
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681 views

Feynman rules with helicity states.

Whenever Feynman rules are stated they are always without any mention of the helicities - this I find to be very confusing. How does one introduce and account for that? Is there an intuitive/simple ...
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Discussions of the axioms of AQFT

The most recent discussion of what axioms one might drop from the Wightman axioms to allow the construction of realistic models that I'm aware of is Streater, Rep. Prog. Phys. 1975 38 771-846, ...
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697 views

Wick rotation and spinors

I am quite familiar with use of Wick rotations in QFT, but one thing annoys me: let's say we perform it for treating more conveniently (ie. making converge) a functional integral containing spinors; ...
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Is the form of the Lagrangian relevant before the renormalization procedure?

In the renormalization procedure, is writing things like $$\varphi=\sqrt{Z_{\varphi}}\ \varphi_R\ ,\ \ m_0^2=Z_m\ m_R^2\ ,\ \ g_0=Z_g \mu^{\epsilon}\ g_R$$ and $$Z_i=1+\sum_{\nu=1}^\infty ...
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264 views

Irrelevance of parastatistics for space dimension > 2

Consider a system of $n$ undistinguishable particles moving in $d$-dimensional Euclidean space $E^d$. The configuration space is $M=((E^d)^n \setminus \Delta)/S_n$ where $\Delta$ is the diagonal ...
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1answer
403 views

Thermodynamic limit “vs” the method of steepest descent

Let me use this lecture note as the reference. I would like to know how in the above the expression (14) was obtained from expression (12). In some sense it makes intuitive sense but I would ...
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418 views

Anomalous magnetic moment of electron

It is known that the value of 2 of the electron g-factor arises from the Dirac equation. As far as I can see from the various sources, this value is obtained in non-relativistic limit, in particular ...
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282 views

Does the existence of dualities imply a more fundamental structure?

I was wondering if the existence of some kind of duality in physics always implies the existence of some underlying more fundamental structure/concept? Let me give a few example from history: ...
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1answer
213 views

Colour decomposition of $n-$gluon tree amplitude

I have here a $SU(N_c)$ Yang-Mill's theory and let the index $i$, label the $n$-gluons, and $\{k_i, \lambda_i, a_i\}$ be its momenta, helicity and colour index and $\cal{A}_n^{tree/1-loop}(\{k_i, ...
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654 views

Discreteness of Spacetime and Violation of Lorentz symmetry

It is usually said that existence of discrete spacetime violates Lorentz symmetry. What quantity is used to quantify such violation? I mean could someone points a reference for a derivation that shows ...
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333 views

Does path integral and loop integral in a Feynman diagram violate special relativity?

Consider a correlation function between two points $A(x_1,t_1)$ and $B(x_2,t_2)$, we need to integrate over paths which could be infinite long. But the time length $(t_1-t_2)$ is finite, so if $A$ ...
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1k views

quantum optics of a polarizing beam splitter

I would like to use the Heisenberg picture in quantum field theory to model a polarizing beam splitter. Is there an easy way for someone to show me how the field operators ($a^\dagger_{input1}$, ...
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1answer
333 views

half Skyrmion vs Meron

Is there a difference between a half skyrmion and a meron? I'm asking this in regard to half skyrmion theories of High Tc Superconductors. It would be interresting to know if the proposed half ...
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1answer
183 views

Is the long range neutron-antineutron interaction repulsive?

I can model this interaction as Zee does in "Quantum field theory in a nutshell". In chapter I.4 section "from particle to force" he uses two delta functions for the source. The integral gives ...
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1answer
341 views

SU(2) yang-mills EOM

I'm just playing around tonight trying to better myself, but I'm having trouble with some indices on my yang-mills lagrangian. I have a gauge group $SU(2)$ and a field strength tensor $$ ...
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4answers
418 views

Different kinds of S-matrices?

It seems to me that the notion of an "S-matrix" refers to several different objects One construction you can find in the literature is allowing the coupling constant to adiabatically approach 0 in ...
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707 views

Quantum harmonic oscillator

I read somewhere that a quantum field can be thought of as a tiny bowl at every point in space with a ball doing SHM (quantum harmonic oscillator). It was given that the amplitude of this SHM is ...
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665 views

Interesting topics to research in mathematical physics for undergraduates

I'm planning on getting into research in mathematical physics and was wondering about interesting topics I can get into and possibly make some progress on. I'm particularity fond of abstract algebra ...
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373 views

What is known about quantum electrodynamics at finite times?

I'm aware that we can describe the time evolution of states/operators (choose your favourite picture) of non interacting quantum fields and that perturbation theory is very effective in computing S ...
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464 views

Calculating lagrangian density from first principle

In most of the field theory text they will start with lagrangian density for spin 1 and spin 1/2 particles. But i could find any text where this lagrangian density is derived from first principle.
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535 views

Derivation of the effective potential between a quark and an anti-quark

Typically in particle physics books (not in QFT books!) I have often seen this statement that the potential between a heavy quark and its anti-quark can be "empirically" represented as $V(r) = ...
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1answer
174 views

Electron shell bombardment

If you bombard an electron shell with a photon below the critical level to promote the electron to a higher state, will the shell absorb nothing and the photon get deflected with the same amount of ...
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1answer
336 views

Can a photon see ghosts?

Does it make sense to introduce Faddeev–Popov ghost fields for abelian gauge field theories? Wikipedia says the coupling term in the Lagrangian "doesn't have any effect", but I don't really know ...
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Can we use only the observables of Fermion fields?

There are legion ways to consider fermionic Dirac spinor fields, but is it possible to consider the asymptotic free field only in terms of observables, which in the case of the Dirac spinor field must ...
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1answer
364 views

How does physics scattering experiments relate to real life? And what does the scientist gain from such experiments?

How does physics scattering experiments relate to real life? And what does the scientist gain from such experiments? I am having a hard time figuring the answer out. Please help.
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103 views

Nonabelian gauge theories and range of the corresponding force

Do all nonabelian gauge theories produce short range force?