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 is the path integral exactly?
I asked a question here about path integrals and QFT. I just want to confirm something. Is the path integral in quantum field theory a mathematical tool only? I thought the path integral meant that ...
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3answers
353 views
Noether theorem, gauge symmetry and conservation of charge
I'm trying to understand Noether's theorem, and it's application to gauge symmetry. Below what I've done so far.
First, the global gauge symmetry. I'm starting with the Lagragian
...
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1answer
252 views
Generalized propagator
I don't understand how to calculate this generalized two-point function or propagator, used in some advanced topics in quantum field theory, a normal ordered product (denoted between ::) is subtracted ...
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1answer
545 views
What is the difference which leads to attraction in e+e- scattering and repulsion in e-e- scattering in QFT
What is the theoretical difference between the physical elementary interaction that causes an e+ to attract an e− when they exchange a virtual photon? Why is this exchange different from an e-e- ...
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2answers
1k views
Virtual photon description of B and E fields
I continue to find it amazing that something as “bulky” and macroscopic as a static magnetic or electric field is actually a manifestation of virtual photons.
So putting on your QFT spectacles, look ...
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3answers
465 views
Grassmann paradox weirdness
I'm running into an annoying problem I am unable to resolve, although a friend has given me some guidance as to how the resolution might come about. Hopefully someone on here knows the answer.
It is ...
6
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1answer
850 views
Measured Higgs mass and vacuum stability
There is such a thing, called "stability bound" on mass of the Higgs boson.
The basic idea (as I understand it) is that we take Higgs self-coupling, and calculate its renormalization running. And it ...
3
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1answer
178 views
Twistor notation in space-time (Part 1)
This is sort of a continuation of this and this previous discussions.
In the first of my links one sees the surjective isometry between real or complex $(1,3)$ signature Minkowski space and the real ...
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1answer
281 views
Why path integral approach may suffer from operator ordering problem?
In Assa Auerbach's book (Ref. 1), he gave an argument saying that in the normal process of path integral, we lose information about ordering of operators by ignoring the discontinuous path.
What did ...
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3answers
139 views
Regularization of the Casimir effect
For starters, let me say that although the Casimir effect is standard textbook stuff, the only QFT textbook I have in reach is Weinberg and he doesn't discuss it. So the only source I currently have ...
15
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3answers
917 views
Is decoherence even possible in anti de Sitter space?
Is decoherence even possible in anti de Sitter space? The spatial conformal boundary acts as a repulsive wall, thus turning anti de Sitter space into an eternally closed quantum system. Superpositions ...
12
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2answers
1k views
Why isn't Higgs coupling considered a fifth fundamental force?
When I first learned about the four fundamental forces of nature, I assumed that they were just the only four kind of interactions there were. But after learning a little field theory, there are many ...
10
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3answers
763 views
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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4answers
644 views
Spinning Tachyons
In all examples that I know, tachyons are described by scalar fields. I was wondering why you can't have a tachyon with spin 1. If this spinning tachyon were to condense to a vacuum, the vacuum ...
9
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3answers
449 views
“Slightly off-shell”?
I'm not new to QFT, yet there are some matters which are quite puzzling to me. I often come across the statement that real particles (the ones we actually measure in experiments, not virtual ones) are ...
8
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8answers
594 views
Why do physicists believe that particles are pointlike?
String theory gives physicists reason to believe that particles are 1-dimensional strings because the theory has a purpose - unifying gravity with the gauge theories.
So why is it that it's popular ...
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1answer
463 views
Difference between 1PI effective action and Wilsonian effective action
What is the simplest ay to describe the difference between these two concepts, that often go by the same name?
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1answer
258 views
Gauge covariant derivative in different books
It puzzles me that Zee uses throughout the book this definition of covariant derivative:
$$D_{\mu} \phi=\partial_{\mu}\phi-ieA_{\mu}\phi$$
with a minus sign, despite of the use of the $(+---)$ ...
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2answers
369 views
Charge conjugation in Dirac equation
According to Dirac equation we can write,
\begin{equation}
\left(i\gamma^\mu( \partial_\mu +ie A_\mu)- m \right)\psi(x,t) = 0
\end{equation}
We seek an equation where $e\rightarrow -e $ and which ...
4
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1answer
159 views
In quantum field theory with a mass gap, why do states in the asymptotic future/past turn out to have a Fock space structure?
In quantum field theory with a mass gap, why do states in the asymptotic future/past turn out to have a Fock space structure? For a free quantum field theory, that's trivial, but why is that the case ...
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3answers
111 views
uncertainty of fields with many harmonic modes
In most basic level introduction to the quantum harmonic oscillator formulation of fields, it is assumed that the commuting variables for the fields $p_m$, $q_m$ are
$$ \lbrack p_m , q_n \rbrack = ...
4
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4answers
496 views
What is the fundamental probabilistic interpretation of Quantum Fields?
In quantum mechanics, particles are described by wave functions, which describe probability amplitudes. In quantum field theory, particles are described by excitations of quantum fields. What is the ...
4
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3answers
474 views
Nomenclature: Yang-Mills theory vs Gauge theory
If you're writing about a theory with Yang-Mills/Gauge fields for an arbitrary reductive gauge group coupled to arbitrary matter fields in some representation,
is it best to call it a Yang-Mills ...
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1answer
299 views
Canonical quantization of quantum field
The canonical quantization of a quantum field prescribes that given a lagrangian, one can quantize the theory by imposing the commutation relations between the field operators and their conjugated ...
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4answers
654 views
What are field quanta?
Just assume that I understand that a field in quantum field theory is an operator-valued distribution. For simplicity, forget about the distribution and think about a function
$\varphi:M \rightarrow ...
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3answers
624 views
What are some approaches to discrete space-time used in modern physics?
This thought gave rise to some new questions in my mind.
What are the consequences for:
How would it affect duality i.e. particle, wave property of photons?
How does this statement affect the ...
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2answers
223 views
The derivation of the Belinfante-Rosenfeld tensor
It seems me that there is a "difference" (at least apparently) in how the Belinfante-Rosenfeld tensor is thought of in section 7.4 of Volume 1 of Weinberg's QFT book and in section 2.5.1 of the ...
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The exchange of photons gives rise to the electromagnetic force
Pardon me for my stubborn classical/semiclassical brain. But I bet I am not the only one finding such description confusing.
If EM force is caused by the exchange of photons, does that mean only when ...
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1answer
329 views
Why Zeta regularization is not valid for multiple-loops?
Why zeta regularization only valid at one-loop?
I mean there are zeta regularizations for multiple zeta sums.
Also we could use the zeta regularization iteratively on each variable
to obtain finite ...
3
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1answer
230 views
What's the deepest reason why QCD bound states have integer charge?
What's the deepest reason why QCD bound states have integer electric charge, i.e. equal to an integer times the electron charge?
Given that the quarks have the fractional electric charges they do, ...
3
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1answer
174 views
Quantum Zeno effect and unstable particles
Is it possible to increase indefinitely the lifetime of unstable particles by applying the quantum Zeno effect? Is there a bound from theoretical principles about the maximum extension one can get in ...
3
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0answers
49 views
uncertainty deviations for vacuum astronomy
Since i've done this question, i've been trying to improve and make more precise the statements regarding cosmic squeezed states and how different uncertainties affect the vacuum energy, but as it ...
3
votes
1answer
474 views
Dimensional reduction from $3+1$ to $2+1$ for $\cal{N}=2$ vector superfield
Let the supersymmetry transformations for the chiral multiplet $(z_k,\psi_{kL},f_k)$ be,
$\delta z_k = 2i \bar{\alpha} \psi_{kL}$
$\delta \psi_{kL} = D_\mu z_k \gamma ^\mu \alpha_R + f_k \alpha_L$
...
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1answer
459 views
What is the difference between pole and running mass?
For example, when we meassure Higgs boson mass to be 125 GeV, do we think about renormalized or pole mass? Should the mass of the Higgs change if it is produced at higher energies?
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1answer
130 views
Solving the soliton equation without energy
In this passage from Srednicki's Quantum Field Theory (page 576)
The solution of interest is time independent, so we can set $\dot\varphi = 0$. We can also rewrite the remaining terms in $E$ as
...
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3answers
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Electromagnetic Field as a Connection in a Vector Bundle
I would like to know more about Ehresmann connections in vector bundles and how they relate to the electromagnetic field and the electron in quantum mechanics.
Background: The Schrödinger equation ...
15
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6answers
2k views
Why should the Standard Model be renormalizable?
Effective theories like Little Higgs models or Nambu-Jona-Lasinio model are non-renormalizable and there is no problem with it, since an effective theory does not need to be renormalizable. These ...
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4answers
3k views
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?
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3answers
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Equivalence of canonical quantization and path integral quantization
Consider the real scalar field $\phi(x,t)$ on 1+1 dimensional space-time with some action, for instance
$$ S[\phi] = \frac{1}{4\pi\nu} \int dx\,dt\, (v(\partial_x \phi)^2 - \partial_x\phi\partial_t ...
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4answers
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“Velvet way” to Grassmann numbers
In my opinion, the Grassmann number "apparatus" is one of the least intuitive things in modern physics.
I remember that it took a lot of effort when I was studying this. The problem was not in the ...
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2answers
876 views
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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3answers
320 views
MVH amplitudes and the unitarity method
In the last 5 years there has been a silent revolution in QFT called the unitarity method and the Maximum Violating Helicity (MVH) Amplitudes that basically consist an alternative way to obtain the ...
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6answers
600 views
What are the various physical mechanisms for energy transfer to the photon during blackbody emission?
By conservation of energy, the solid is left in a lower energy state following emission of a photon. Clearly absorption and emission balance at thermal equilibrium, however, thermodynamic equilibrium ...
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votes
1answer
260 views
Symmetries in Wilsonian RG
I wanted to know if there is a theorem that in writing a Lagrangian if one missed out a term which preserves the (Lie?) symmetry of the other terms and is also marginal then that will necessarily be ...
8
votes
2answers
499 views
Regularisation of infinite-dimensional determinants
Can a regularisation of the determinant be used to find the eigenvalues of the Hamiltonian in the normal infinite dimensional setting of QM?
Edit: I failed to make myself clear. In finite ...
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9answers
2k views
Is a “third quantization” possible?
Classical mechanics: $t\mapsto \vec x(t)$, the world is described by particle trajectories $\vec x(t)$ or $x^\mu(\lambda)$, i.e. the Hilbert vector is the particle coordinate function $\vec x$ (or ...
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7answers
1k views
Is the wave-particle duality a real duality?
I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. I most recently heard this in this video. However, I wonder; is this actually a duality? ...
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1answer
383 views
A reading list to build up to the spin statistics theorem
Wikipedia's article on the spin-statistics theorem sums it up thusly:
In quantum mechanics, the spin-statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin ...
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1answer
425 views
Emergent symmetries
As we know, spontaneous symmetry breaking(SSB) is a very important concept in physics. Loosely speaking, zero temprature SSB says that the Hamiltonian of a quantum system has some symmetry, but the ...
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491 views
Why are some solitons formed from bosonic fields fermionic?
Some topological solitons formed from bosonic fields have fermionic statistics. Why?
