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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546 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; ...
4
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1answer
157 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 ...
2
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1answer
92 views

Inverse of gauge covariant derivative

Consider the gauge covariant derivative defined by $$ D_z = d_z + \Delta_z $$ or explicitly $$ (D_z)^a{}_c = \delta^a_c d_z + (\Delta_z)^a{}_c = \delta^a_c d_z + f_{bc}{}^a A_z^b $$ Here, $d_z$ is the ...
1
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1answer
79 views

Feynman diagrams for scalar field: which particle are we drawing?

Chapter I.7 of Zee's Quantum Field Theory in a Nutshell is an introduction for Feynman diagrams in the context of a scalar field $\varphi$, with Lagrangian $\mathcal{L} = \frac12[(\partial ...
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0answers
21 views

Gordon decomposition of Dirac current for massless electron?

We know Gordon decomposition of Dirac current is applicable only for massive (nonzero mass) Dirac particles. Is there an analog for massless Dirac particles? (I have made an attempt to answer ...
0
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1answer
50 views

Terminology of Higgs boson and Goldstone boson

I know, the from the Higgs Mechanism, or Spontaneous symmetry breaking, the massless Goldstone boson becomes massive. So in some sense Goldstone bosons are eaten by gauge "boson". Here I got ...
12
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1answer
536 views

Instantons, anomalies, and 1-loop effects

A symmetry is anomalous when the path-integral measure does not respect it. One way this manifests itself is in the inability to regularize certain diagrams containing fermion loops in a way ...
11
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3answers
321 views

Are there really left-chiral particles?

A chiral eigenstate is always a linear combination of a particle and an antiparticle state and a particle or antiparticle state is always a linear combination of chiral eigenstates. Now, how can we ...
6
votes
3answers
291 views

Modular invariance for higher genus

As far as I understand, there are roughly 2 "common" kinds of 2D conformal field theories: Theories that are defined only on the plane, more precisely, on any surface of vanishing genus. Such a ...
3
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0answers
29 views

Why do gauge bosons/leptoquarks not mediate proton decay in the Pati-Salam model?

In the Pati-Salam $\mathrm{SU}(4)_c\times\mathrm{SU}(2)_L\times\mathrm{SU}(2)_R$ model, I see Wikipedia and some slides mention this model doesn't predict gauge mediated proton decay without giving ...
0
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1answer
128 views

Stimulated emission direction

Place a sub-micron clump of crystal violet molecules in front of a multipixel detector. Raise the molecules to an electronically excited state with a beam of 590 nm light, illuminating from the side ...
1
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1answer
66 views

Treating the spinors as Grassmann numbers or as c-number objects

In the literature on supersymmetry, the following spinor summation convention is often used (eg. Wess & Bagger's book Supersymmetry and Supergravity) $$ \psi\chi = \psi^{\alpha}\chi_{\alpha} = ...
2
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1answer
130 views

Vacuum stability in quantum field theory

What exactly do people mean when they talk about the scale dependence of the effective potential ($V$)? I explain the motivation for my question (and hence my confusion) below. Please correct me as ...
2
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1answer
107 views
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2answers
33 views

What are the end points in the action integral of field theory?

In the mechanics of particles when we apply the principle of the least action the two end points are two spatial coordinates. Therefore, if we consider the variation of the action with respect to the ...
13
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1answer
2k views

How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$ ?

This question is based on problem II.3.1 in Anthony Zee's book Quantum Field Theory in a Nutshell (I'm reading this for fun- it isn't a homework problem.) Show, by explicit calculation, that ...
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0answers
95 views

How to count and 'see' the symmetry factor of Feynman diagrams?

Could somebody explain how one can derive the symmetry factor both by counting possible contractions and by looking at the symmetry of a diagram. Consider for example this diagram in $\phi^4$-theory ...
9
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1answer
224 views

The problem in Sredniki's textbook: How do I calculate loop corrections for $\phi\phi\to\phi\phi$ with this Lagrangian?

The problem in Sredniki's textbook 10.5 : For a free scalar field $\psi$, the Lagrangian is $$\cal{L}= -\frac{1}{2}\partial^\mu\psi\partial_\mu\psi-\frac{1}{2}m^2\psi^2$$ Here we use the metric ...
6
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1answer
196 views

What is the physical meaning of anti-commutator in quantum mechanics?

I gained a lot of physical intuition about commutators by reading this topic. What is the physical meaning of commutators in quantum mechanics? I have similar questions about the anti-commutators. ...
3
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1answer
246 views

Do all the particles acquire mass in the Standard Model due to the Higgs mechanism only?

I know that a mass term for an intermediate boson is not compatible with the gauge symmetry. But in principle a mass term for the electron field does not violate a gauge symmetry. However to build an ...
3
votes
1answer
65 views

The index of a Dirac operator and its physical meaning

I recently read Witten's paper from the 1980s and he often uses the notion of the index of a Dirac operator in K-theory. What is the meaning of the index of a Dirac operator? What exactly is the ...
4
votes
1answer
97 views

Apparent spacetime dependence of creation and annihilation operators

I'm currently going through An Introduction to Quantum Field Theory by Hartmut Wittig I've stumbled upon. Having trouble with equation (2.29), I'm asking the question: Do creation and annihilation ...
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0answers
42 views

Klein-Gordon propagator integral in the light-like case

In Kerson Huang's Quantum Field Theory From Operators to Path Integrals (Amazon link), pages 28 and 29, he calculates the propagator in the following case: time-like, space-like and light-like. First ...
2
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0answers
101 views

Are there eight or four independt solutions of the Dirac equation?

I edited the question as a result of the discussion in the comments. Originally my quesiton was how to interpret the four discarded solutions. Now I'm making a step back and hope that someone can ...
23
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4answers
1k views

Why do or don't neutrinos have antiparticles?

This was inspired by this question. According to Wikipedia, a Majorana neutrino must be its own antiparticle, while a Dirac neutrino cannot be its own antiparticle. Why is this true?
3
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0answers
29 views

How to work with singular gauge transformations in QFT [closed]

I was recently considering a problem analogous to the Aharonov-Bohm (AB) effect but in the context of quantum field theory. Consider then Dirac electrons minimally coupled to an AB flux and described ...
3
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1answer
222 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 ...
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0answers
37 views

A question about Ising model

If $H$ is the Hamiltonian of an Ising model of $n$ spins on a lattice then is the following quantity look like something one has seen? $([uI-H]^{-1})_{ii} - \frac{1}{n}Tr[[uI - H]^{-1}]$ where $u$ ...
3
votes
1answer
84 views

Making sense of the canonical anti-commutation relations for Dirac spinors

When doing scalar QFT one typically imposes the famous 'canonical commutation relations' on the field and canonical momentum: $$[\phi(\vec x),\pi(\vec y)]=i\delta^3 (\vec x-\vec y)$$ at equal times ...
6
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1answer
97 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 ...
2
votes
1answer
36 views

Finding the normal ordered momentum operator for free theory

I am asked to show that the normal ordered momentum operator for free theory is $$\hat{p^\mu} = \int \frac{d^3 p}{(2 \pi)^3} p^\mu \: a_p^\dagger \:a_p.$$ The free theory Lagrangian is given by ...
2
votes
1answer
46 views

Can the vacuum energy be made finite with quantized space

From what I know the reason we have infinite vacuum energy is because according to Quantum Field Theory at every point in space we something analogous to a harmonic oscillator but since the Zero Point ...
1
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1answer
74 views

A test for virtual particles by measuring gravity fluctuations possible?

Ok to begin I will begin by talking briefly about my discussions with my Quantum Mechanics (specializes in Particle physics) professor and my Cosmology Professor (who studies particle physics with ...
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19 views

Materials on charged black brane

everybody! Does anyone know some good materials on charged black branes in AdS/CFT and the role of chemical potential in theses cases?
5
votes
4answers
692 views

Uncertainty Principle for Information?

I'm not familiar (yet) on how Information theory can be emerged/used in QM/QFT but I was thinking about this question: While we have Heisenberg uncertainty principle on measuring coupled observables, ...
2
votes
1answer
88 views

QFT propagator, time reversal and the Born rule

As far as I understand it a propagator, $D(x-y)$, gives the amplitude for a flow of positive energy-momentum from an earlier event $y$ to a later event $x$. Addendum: Instead of talking about energy ...
2
votes
1answer
45 views

Fast and slow modes, and the vanishing of certain diagrams during re-normalization

In the middle of pg. 452 of Atland and Simonss Condensed Matter Field Theory, they state the following: Terms of $\mathcal{O}(\phi _{\text{s}}^3\phi _{\text{f}})$ do not arise because the addition ...
16
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3answers
2k 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 ...
2
votes
2answers
283 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 $A$ ...
1
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0answers
47 views

Help with derivation of the Casimir Effect?

I am at the very last part of a relatively long derivation of the Casimir effect, and I just don't understand the final step D: So far, I have derived the ground state energy to be $$\langle 0| ...
3
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0answers
77 views

History of QFT after 1973 [closed]

Where I can read about history of development quantum field theory after 1973? I'm interested in historical reviews, like as first chapter of the Weinberg's book.
2
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1answer
443 views

Time-ordering in QFT

In Srednicki QFT page 37. In the derivation of LSZ reduction formula, he introduces the time-order operator $T$, so no time-dependent creation/annihilation operators are left in the transition ...
1
vote
1answer
29 views

The one-loop contribution to a time ordered product of conserved currents

In two dimensions one can define for a Lagrangian describing free Dirac fermions with $N$ associated flavours by $$\mathcal{L}=i\bar{\psi}_i\gamma^\mu \partial_\mu \psi^i $$ and associate vector ...
3
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0answers
29 views

Question on finite temperature field theory

In quantum field theory at zero temperature, the expectation values of operators are taken with respect to the vacuum. Is it the case that in quantum field theory at finite temperature, the ...
1
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1answer
49 views

Normal ordering for a two fermion case

I am trying to understand how normal ordering works. I am considering a system of two photons, with $\hat{f}_i$ and $\hat{f}_i^\dagger$ being the annihilation and creation operators, respectively. I ...
3
votes
0answers
58 views

Why is only the third component of weak isospin used as a conserved quantity?

Using Noether's theorem \begin{equation} \partial_0 \int d^3x \left(\frac{\partial L}{\partial(\partial_0\Psi)} \delta \Psi \right) = 0 \end{equation} we get three conserved quantites $Q_i$ from ...
6
votes
2answers
240 views

How to replace $T$-product with retarded commutator in LSZ formula?

I am reading Itzykson and Zuber's Quantum Field Theory book, and am unable to understand a step that is made on page 246: Here, they consider the elastic scattering of particle $A$ off particle $B$: ...
3
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1answer
154 views

Branch cuts in two-point function

The propagator of a QFT is known to have a branch cut as a function of the (complex) external momentum. The branch point (as done by, say, Peskin & Schroeder in eqn.7.19 section 7.1) is ...
2
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1answer
30 views

Photon polarization sum prescription in $e^-e^+\to{}2\gamma$

In calculating the amplitude for the process $e^-\gamma\to{}e^-\gamma$ the substitution $\sum\epsilon_{\mu}\epsilon^*_{\nu}\to-\eta_{\mu\nu}$ is useful to sum over photon polarizations. If we ...
0
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1answer
65 views

Can the energy of the universe ever be infinite in qunatum physics? [closed]

Suppose that the universe runs under some variants of QFT, with universal wavefunction and Hamiltonian. Then would infinite energy of the universe ever be possible? According to what I am thinking, ...