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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Why is a relativistic quantum theory of a finite number of particles impossible?

In Dyson's book Advanced Quantum Mechanics , he said "These two examples (the discovery of antimatter and meson) are special cases of the general principle, which is the basic success of the ...
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1answer
71 views

Conceptual questions on the path integral formulation of QFT

I'm currently trying to teach myself the path integral formulation of QFT (having studied the canonical approach previously), but I'm having some conceptual difficulties that I hope I can clear up ...
2
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0answers
85 views

Polarization Sums in QCD for the calculation of parton model splitting functions

Before i state the actual problem, here's a premise. In the case of a Spin 1 massive particle it's possible to demonstrate that $$\sum_{\lambda=0,\pm1}\epsilon_{\lambda}^{* \ ...
3
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0answers
30 views

Intrinsic parity

When we apply parity on a field two times, we demand that we should get back the same field. This gives us, $P^{2} =1$, which implies, $ P \psi = e^{i \theta} \psi$ . This extra phase factor is ...
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3answers
50 views

With respect to the Casimir effect, why can't the wavelengths of the virtual particles between two plates just “pass through” the plates themselves?

I've read over the years that the suppression of many of the possible wavelengths between the two plates in a Casimir experiment is what causes the phenomenon (top comment on this Askscience thread is ...
2
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1answer
114 views

How does a laser emit light in a coherent state?

Lasers work by stimulated emission of atomic transitions. Stimulated emission produces two photons which, because the particle number is well-defined, projects the field into a Fock state. However, it ...
6
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1answer
160 views

Why are the quantum observables defined on opens sets a presheaf and not a sheaf?

In local quantum field theory or AQFT one can mathematically describe over each open set $U$ of a spacetime $M$ the quantum states or observables of the theory. This structure is commonly referred as ...
2
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1answer
5k views

What is the difference between Quantum Physics, Quantum Theory, Quantum Mechanics, and Quantum Field Theory?

What is the difference between Quantum Physics, Quantum Theory, Quantum Mechanics, and Quantum Field Theory? Are they the same subject? I believe that they are not the same subject! Maybe there is not ...
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0answers
33 views

Locality defined in terms of the Lagrangian density

I've been reading through Matthew Schwartz's book "Quantum Field Theory and the Standard Model" and in chapter 24 there is a section on locality (section 24.4). In it he defines locality in terms of ...
5
votes
1answer
319 views

Determinant for a coupled fluctuation Lagrangian

Lets consider a bosonic physical system in variables $t, x$ and $y(x)$ ($x$ dependent) with a classical Lagrangian $L$. To first order in fluctuations $x \to x+\xi_1$ and $y \to y+\xi_2$ the ...
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0answers
18 views

Hypermultiplet as BPS particles

In the third paragraph of page 7 of the paper arxiv:1112.3984 it mentions that we form a basis out of hypermultiplets on the charge lattice $\Gamma$. My questions are: In what sense do we form such ...
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0answers
61 views

Why photon have zero rest mass?

If photon have zero rest mass then the term E=hf should also be zero because if rest mass is zero then relativistic mass is also zero and so on by Einstein mass energy relation energy shoud be zero ...
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44 views

Need help with Weinberg II (19.5.42)

In "The Quantum Theory of Fields", Volume II, p. 202, I can't see how eq. (19.5.42) leads to the next equation. The transformation seems to go the wrong way; for example, in order to get $\sigma$ ...
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1answer
406 views

What is the difference between quantum fluctuations and thermal fluctuations?

Start with a simple scalar field Lagrangian $\mathcal{L}(\phi)$ at zero temperature $T = 0$, which has a hidden symmetry and spontaneously break it. By the standard procedure a field $\phi$ is ...
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2answers
211 views

How are the field operator and quantum state after a beam splitter and a polarizing beam splitter individually?

How are the field operator $\hat{a}$, $\hat{a}^\dagger$ and the quantum state (like coherent state $|\alpha>$, Fock state $|n>$) changed after a beam splitter and a polarizing beam splitter ...
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2answers
790 views

Deriving Feynman rules from a Lagrangian for vertex factors for “more complicated” interactions

I am trying to derive Feynman rules from a given Lagrangian and I got stuck on some vertex factors. What for example is the vertex factor that corresponds to the four-scalar interaction that is ...
3
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2answers
86 views

What all has intrinsic spin?

What does and does not have intrinsic spin? Wikipedia Spin (Physics) https://en.wikipedia.org/wiki/Spin_(physics) says: “In quantum mechanics and particle physics, spin is an intrinsic form of ...
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1answer
180 views
+50

Peskin eqn 7.2 contradiction

They state $\langle\Omega|\phi(x)|\lambda_p\rangle=\langle\Omega|e^{iP\cdot x}\phi(0)e^{-iP\cdot x}|\lambda_p\rangle$ where $|\lambda_p\rangle$ is a state of momentum $\textbf{p}$. They then rewrite ...
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4answers
181 views

What role does “spontaneously symmetry breaking” played in the “Higgs Mechanism”?

In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneously symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of ...
14
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8answers
6k views

Is gravity just electromagnetic attraction?

Recently, I was pondering over the thought that is most of the elementary particles have intrinsic magnetism, then can gravity be just a weaker form of electromagnetic attraction? But decided the ...
0
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0answers
46 views

QED+Classical Background Renormalization

I would like to ask a question related to quantum corrections and renormalization in QED. We have the QED vertex $\overline{\psi}[-ie \gamma^{\mu}(B_{\mu}+A_{\mu})]\psi,$ being $B_{\mu}$ a classical ...
2
votes
2answers
55 views

What justifies the perturbative expansion in chiral perturbation theory?

The Lagrangian of chiral perturbation theory is ordered following a momenta power counting scheme, having terms at leading order (which is two 2 $O(p^2)$) next to leading order ($O(p^4)$) and so on. ...
4
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0answers
71 views

Free probability in Physics

Recently I have started reading some materials on non-commutative probability. IN this area mathematicians sometimes consider quantum theory as a non-commutative version of classical probability, with ...
2
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1answer
157 views

Momentum eigenstates in an interacting quantum field theory

Context for the following questions: two widely stated claims hinge on what appears to be an inconsistent argument. The claims are that (1) an interacting field can produce, in addition to ...
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0answers
15 views

Repulsive potential for free fermions

My question -which is probably easy to answer for a physicist- stems from trying to understand the repulsive interaction between fermions. For instance the fact that states of multifermion systems are ...
4
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1answer
76 views

State space of interacting theories

Haag's theorem states that in general, an interacting quantum field and the corresponding free field have unitary-inequivalent state space representations. I would like to have an example of a state ...
13
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2answers
2k views

Time ordering and time derivative in path integral formalism and operator formalism

In operator formalism, for example a 2-point time-ordered Green's function is defined as ...
6
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1answer
245 views

Casimir Forces and its associated Feynman Propagator

This is a continuation to my previous question, in which I began an attempt solve the Casimir Force problem using path integrals. As one of the answers there suggest I solve the Feynman propagator ...
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0answers
30 views

Electric field operator in 2D geomatry

In the free field (3D), transverse electric field operator is given by the below expression; $$e^{\bot}(\textbf{R}) =i \sum_{\textbf{p},\lambda}\Big( \frac{\hbar cp}{2V\epsilon_{0}}\Big)^{1/2} ...
7
votes
1answer
89 views

Why is a vertex a derivative of the propagator?

Where can I find the proof to this nice trick: if the momentum $q$ is small, the vertex is the derivative with respect to the mass of a propagator times a factor $(-m/v)$ like in the picture:
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votes
2answers
110 views

Is there any $SU(\infty)$ gauge theory in quantum field theory?

The groups $U(N)$ and $SU(N)$ are the most important Lie groups in quantum field theory. The most popular are the $U(1),SU(2),SU(3)$ groups (these gauge groups form the Standard model). But is there ...
1
vote
1answer
62 views

Distinction of Dirac monopole and Polyakov-'t Hooft monopole

Can anybody explain the physical difference between Dirac monopole and Polyakov monopole? First, let me write down what I know briefly. Dirac monopole It comes from the symmetry of Maxwell ...
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2answers
202 views

Is entropy a meaningful concept on a quantum level?

My naive assumptions, as I really am at a pretty basic stage in QM, are as follows: Classically, entropy gives us a practical measure of the direction of time, as opposed to our physical laws which, ...
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0answers
39 views

Can I Wick-contract terms with derivatives with terms without derivatives?

Consider for example the QCD three point vertex, can I contract a gluon field with the gluon field with a derivative in the vertex?
4
votes
1answer
258 views

Does tunneling transmission probability depend on the density of states or velocity?

In some quantum text books [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. ($T(E) = C \times DOS_1(E) \times DOS_2(E)$, where C ...
3
votes
1answer
201 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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0answers
24 views

time as consequence of hadronics [closed]

it has occurred to me that time is solely consequence of non-electric fields, with latest work being reading about «anapole» cite: Simple theory may explain dark matter due to ...
0
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1answer
42 views

Are the particle-antiparticle pairs produced in vacuum virtual particles, and can they interact with normal particles?

If it is true that due to energy fluctuations of a vacuum being able to produce a particle-antiparticle pair that shortly annihilate with each other and disappear again, is the following circumstance ...
5
votes
1answer
152 views

Phase Transition at Zero Temperature (Not QPT)

As is well known the Ising model exhibits a phase transition, except the one dimensional case in which the phase transition occurs strictly at $T=0$. Now I have always thought that this makes the case ...
7
votes
1answer
341 views

Eikonal approximation in QFT

Does the eikonal approximation for calculating a scattering amplitude in QFT provide the exact result in the limit of $s\rightarrow\infty$ at finite $t=0$ ($s$ and $t$ are the usual Mandelstam ...
0
votes
0answers
66 views

Klein-Gordon Field Angular Momentum Operator in Terms of Creation and Annihilation Operators [on hold]

I am computing the angular momentum operator for real Klein-Gordon field (essentially question six of here (though please note this is not a homework question, I am following through Tong's course via ...
0
votes
0answers
20 views

If we considered chiral perturbation theory with coplex $\phi$-s, wold the next lo leading order renormalization $\gamma$-s change?

The Lagrangian of chiral perturbation theory (with two quark flavors) is written using the following matrix $U$ $$U=e^{i\sigma^i\phi_i/f}$$ where $\sigma^i$ are the Pauli matrices, $\phi_i$ are three ...
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0answers
27 views

Covariant projection method - Meson bound states

I have seen many papers that discuss the production or decay of mesons ( quark bound states ) to make use of the covariant projection method where the product $\upsilon\bar{u}$ of the quark spinors ...
1
vote
1answer
50 views

A question to gauge fixing in nonabelian gauge theories

In quantum gauge theories it is usual to fix the gauge with the equation $\partial^\mu A_\mu = 0$ where $A_\mu$ is the gauge connection. From this gauge fixing condition the remaining gauge degree of ...
2
votes
2answers
63 views

Compact QED and Non-compact QED - Polyakov textbook

This question is related with Polyakov, "Gauge Fields and Strings" section 4.3 Firstly, Polyakov define a QED on a lattice Compact QED \begin{align} S = \frac{1}{2} \sum_{x, \alpha, \beta} ...
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votes
0answers
37 views

how could the sun photons be the source of light to our vision? [closed]

if the atom has 99.99% empty space and the photon has no mass while our universe is 2dimensional flat so how could the sun photons be the source of our vision? how could photons be reflected by ...
7
votes
2answers
307 views

Peskin's book page 334 proof of $Z_1=Z_2$ to all orders in QED perturbation theory

Peskin in his QFT page 334 argued that $Z_1=Z_2$ to all orders in QED perturbation theory, but I couldn't understand his argument: ... With a generalization of the argument given there (section ...
4
votes
1answer
197 views

Can the Higgs condensate be described in terms of creation operators?

In superconductivity, the BCS condensate can be described in terms of 2 creation operators (the 2 electrons of the pair) acting on the vacuum. I'm wondering whether a similar description can be given ...
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1answer
120 views

Can you express the Feynman propagator as a limit?

At first I thought that the Feynman propagator was the limit of: $$ G(x) = \frac{1}{x^2 + i \varepsilon} $$ But if you apply the wave equation to this you get: $$ \Box G(x) = ...
1
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1answer
36 views

Do contractions with Dirac matrices involve a metric?

When figuring out where the spacetime metric enters an equation it is often useful to write all vector indices as covariant indices and write out the inverse metrics that are needed to contract them, ...