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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How can dimensional regularization “analytically continue” from a discrete set?

The procedure of dimensional regularization for UV-divergent integrals is generally described as first evaluating the integral in dimensions low enough for it to converge, then "analytically ...
4
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2answers
104 views

Why do people say that the Higgs mechanism gives mass to the gauge bosons without mentioning the fermions?

Many presentations of the Higgs mechanism only explain it as giving mass to the $W$ and $Z$ gauge bosons, but don't mention the quarks or charged leptons. For example: ...
3
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1answer
57 views

Why use coherent state path integral? What is its motivation or goal?

In almost all textbooks of quantum field theory for high energy, they insert the position and momentum eigenstate to formulate the path integral. While in condensed matter field theory, they insert ...
6
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2answers
304 views

Why does the non-linearity of the string action prohibit stretching due to strong excitations?

From 't Hooft's String Theory lecture notes on page 8 (paraphrased): To understand hadronic particles as excited states of strings, we have to study the dynamical properties of these strings, and ...
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11 views

Antiunitary operators in the tenfold way

In the classification of free fermion systems in condensed matter, physicists usually divide the systems into ten symmetry classes, first discovered by Altland and Zirnbauer. In their classification, ...
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4answers
3k 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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1answer
35 views

Magnetic monopoles gauge theories

I'm quoting 't Hooft: "[...] Locally stable field configurations may exist that have some topological twist in them [...].Careful analysis of the existing Lie groups and the way they may be ...
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12 views

Why do we use a vector space for gluons? [on hold]

One gluon state cannot be added to another since qcd heavily violates superposition. Why do we still use vector spaces to describe them?
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0answers
12 views

why is it so successful to start of with a pair potential before quantizing [on hold]

As soon as we use the quantum theory all orders of correlation functions start to appear if we move from one scale to another. Why was it so successful to start of with a simple pair potential in the ...
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1answer
55 views

Why doesn't the four-gluon vertex give mass to gluons?

We have a four-gluon vertex and a gluon vacuum condensate. Why doesn't this provide us with gluon masses, as in the NJL model where the condensate gives rise to an effective mass term?
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0answers
36 views

Electromagnetic waves and photons? [duplicate]

Electromagnetic waves are photons or photons cause electromagnetic waves ? Its said that when charges are accelerated we get electric and magnetic field that carries energy but then they say that this ...
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2answers
54 views

Electromagnetic Radiation and Communication!

I read that the accelerated charges create electromagnetic field/spectrum which consists of following different waves: gamma, X-rays, ultraviolet, visible light, infrared, microwaves, & radio ...
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25 views

scalar field boundary condition in background with U(1) isometry

I have a simple question about Lewkowycz and Maldacena's paper In section 2, they consider the scalar field in BTZ background ground and require boundary condition of the scalar field, $\phi \sim ...
4
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1answer
229 views

Do the position-momentum uncertainty and time-energy uncertainty really exist in QFT?

It is well known from the Quantum Mechanics(QM) that for a particle, there is a position-momentum uncertainty relation: $$\Delta x\cdot \Delta p\geq \frac{1}{2}\hbar,$$ which bascically can be derived ...
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1answer
425 views

Do we need virtual particles?

I understand the $\Delta t \cdot \Delta E \geq \hbar / 2$ relationship and the idea behind them. However, I don't understand why do we need them at all. I'm a physics undergraduate. As far as I know, ...
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2answers
562 views

Quantum entanglement definition [on hold]

How can we define Quantum entanglement (in QFT)? What are the known mathematical settings and special physical (or logical) conditions of QE applied to Quantum computing?
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0answers
32 views

The $T\rightarrow \infty $ limit in quantum field theory

I am new to quantum field theory. Prior to this, I have been using quantum mechanics for a few years. I am reading the book by A. Zee, ''quantum field theory in a nutshell'', 2nd Ed.. On page 18, ...
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1answer
64 views

What gives a particle its identity?

A lot of very smart people have stitched together the standard model, and I accept it. I don't understand it, but I assume there should be a mechanism of sorts that gives a particle some fundamental ...
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0answers
42 views

Wick rotating vector fields in QFT

Suppose we perform a Wick rotation $t \rightarrow i\tau$ from Lorentzian to Euclidean signature. Consider its action on the generator of boosts in the 01-plane: $$\zeta = t\partial_x + x\partial_t.$$ ...
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1answer
62 views

Operator formalism in QFT in Euclidean space-time

In QFT there are two very useful general approaches to study quantum fields (on the Minkowski space-time): path integrals and operator formalism. Sometimes they give the same results, sometimes one ...
5
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1answer
336 views

What's the Coulomb Branch and why is it important?

I'm studying the introduction of flavour degrees of freedom in the AdS/CFT correspondence and now I'm supposed to calculate the mass spectrum of mesons in the Coulomb branch. I have searched the ...
0
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0answers
48 views

Klein-Gordon field quantization [closed]

I'm taking my first QFT course and I have a problem when solving the Klein-Gordon equation for a free, non-interacting, field. When solving it, I start making a Fourier transform and expand the field ...
4
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1answer
148 views

BRST quantization and norm

States with definite ghost number have zero norm (since ghost number is anti-hermitian and has real eigenvalues). E.G. when quantizing relativistic point particle, physical spectrum turns out to ...
8
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2answers
407 views

Scalar field divergent mass correction interpretation question (hierarchy problem)

Simple power counting tells you that a scalar field coupled to some fermions at one-loop picks up a correction to the mass of the order $\Lambda^2$. Based on this people say things like "it's natural ...
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1answer
31 views

Placement of indices in canonical commutation relations of coordinates and conjugate momenta as well as fields and conjugate momenta

The canonical commutation relations between generalised coordinates $q_a$ and their conjugate momenta $p^a$ are given by $[q_a,q_b]=[p^a,p^b]=0$ $[q_a,p^b]=i\delta^b_a$. Furthermore, the canonical ...
5
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1answer
76 views

Spontaneous symmetry breaking of a spinor / vector field [duplicate]

Why does SSB deal only with scalar fields and not with fermion or vector fields? My professor told me that it's closely related to the Lorentz invariance of the theory, but I don't understand at all ...
3
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3answers
983 views

Why cannot fermions have non-zero vacuum expectation value?

In quantum field theory, scalar can take non-zero vacuum expectation value (vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory ...
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2answers
456 views

QFT question, scalar field and so on

$\newcommand{\bbraket}[3]{\langle #1 | #2 | #3 \rangle} \newcommand{\ket}[1]{|#1\rangle} \newcommand{\bra}[1]{\langle #1 |}$ I have a problem with a proof. I'm studying the two point correlation ...
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0answers
255 views

Regulating the sum in Casimir Force

I am trying to evaluate the Casimir force using a Gaussian regulator (I know there are other much easier ways to do this, but I want to try this!) We then are reduced to evaluating the sum $$ ...
3
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0answers
63 views

S-matrix and derivative interaction

I just read in some lecture notes that formally we can write the S Matrix as: $$S=T(e^{-\int_{-\infty}^{+\infty} H_{int}dt}) $$ Where $T$ is the normal product and $H_{int}$ is in the interaction ...
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0answers
18 views

Construct recurrence relation for the temporal evolution of a Master equation

Say that we have a system evolving over discrete timesteps. The quantity we are interested is X and is given by a distribution $P_X$. This distribution is evolving temporally, and we have a ...
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1answer
55 views

Time-ordered product of two normal-ordered products of fields

Suppose you have a scalar field theory with field operators $\phi(x)=\phi(x)_+ + \phi(x)_- $ that can be decomposed into terms of annihilation and destruction operators. Let $$ D(x-y) = ...
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0answers
58 views

Path integral (sum over paths where $v>c$) [on hold]

The path integral formalism is used to get for example the propagator of particles. In this formalism we integrate over all mathematically possible paths (and weight them with the non-relativistic ...
5
votes
1answer
308 views

Antiparticles, charge conjugation and chirality

(Why/how) are antiparticles and charge-conjugates different things? I am trying to understand the effect of discrete symmetries on spinor fields (neutrinos in particular). In the article, Dirac, ...
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0answers
20 views

Superficial degree of divergence for scalar theories

I have a few questions regarding the derivation of the degree of divergence for feynman diagrams. The result is $$D = [g_E] - \sum_{n=3}^{\infty} V_n [g_n]$$ (following notation in Srednicki, $P118$) ...
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0answers
30 views

What is quantum foam?

Can someone please explain me what quantum foam is? Is it the space-time fabric or just any other field? Also please explain this image
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0answers
10 views

Deep Inelastic Scattering - electromagnetic current

When one tries to compute the deep inelastic scattering for the process: where $l$ is a lepton with incoming momentum $k$ and outgoing $k'$, $h$ is an hadron with momentum $P$, $q$ denotes some ...
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0answers
40 views

Entanglement in Quantum field theory [duplicate]

How is entanglement represented in a field theory? For instance how can I represent a maximally entangled state such as a Bell state? Would such an approach also apply in a Conformal field theory ...
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2answers
226 views

Field transformations

I'm reading Maggiore's book "A modern introduction to quantum field theory" and I'm very confused by what he did in chapter 2.6 page 31 eq. (2.80). He basically wants to find the generators of the ...
2
votes
1answer
93 views

What does it mean by “infinities” when dealing with QFT? [closed]

I found this PDF online here while browsing Nobel Prize winner contributions, which explains a bit about renormalization (a concept for which Kenneth G. Wilson won the Nobel). However I was somewhat ...
6
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2answers
1k views

Invariance, covariance and symmetry

Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from quantum field theory? ...
4
votes
2answers
111 views

Are the path integral formalism and the operator formalism inequivalent?

Abstract The definition of the propagator $\Delta(x)$ in the path integral formalism (PI) is different from the definition in the operator formalism (OF). In general the definitions agree, but it is ...
0
votes
1answer
45 views

Fine structure constant and unit conversion [closed]

In a paper I'm reading, the author writes down the following formula: $$\Gamma=\dfrac{\alpha^2}{576\pi^3}\dfrac{\left(4+z\right)^2}{z}\dfrac{m^5}{m^2_\pi f_\pi^2}$$ $\Gamma$ is a function of $m$ (in ...
9
votes
1answer
462 views

Calculating $\mathrm{Tr}[\log \Delta_F]$

I am stuck with this problem for quite sometime. I have a propagator in the momentum representation (from this question), which looks like $$ \widetilde\Delta_F(p) = ...
4
votes
2answers
200 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 ...
2
votes
1answer
673 views

QCD color factors from quark gluon vertices

The color factors in QCD tell us the relative strength of the coupling of a quark emitting a gluon, a gluon emitting a quark-antiquark pair or a gluon emitting two gluons. To calculate let them we ...
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0answers
27 views

Transverse and longitudinal random forces

I am trying to read following article: http://arxiv.org/pdf/1410.1262v1.pdf According to the equation (2.10) and (2.11), the random force is defined as $ \langle f_i(x) \ f_j(x) \rangle = ...
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1answer
109 views

What are skeleton diagrams and what is their use in qft and many-body physics?

How does one construct skeleton diagrams from specific Feynman diagrams (e.g. for the electronic Green function in QED and in many-body gases, for the polarization function, for the vertex function, ...
3
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1answer
144 views

Is an electron technically a set of two particles?

The electron - described as a four-spinor in the Dirac equation - transforms according to the $(1/2,0)\oplus(0,1/2)$ representation of the Lorentz group, so it is actually a direct sum of a left- and ...
0
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1answer
50 views

Coulomb law and photons

When we consider process like $e^- e^- \to e^- e^-$ in QED, we see that from exchanges of one photon (tree-level diagrams) one can obtain Coulomb's law, while loop-diagrams give quantum corrections ...