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 ...

learn more… | top users | synonyms (1)

1
vote
1answer
47 views

Read-off particle from (projected) Dynkin labels

In the review of Slanksy "Group theory for unified model building" in chapter 6: How do one relate the projected Dynkin diagrams from for example $\overline{5}+10$ of $su(5)$ to the corresponding ...
1
vote
0answers
37 views

Apparent elimination of overlapping divergences

The integral, $$ \iint_{\mathbb{R}^{2+}}\frac{xy}{1+x+y} \mathrm{d}y \, \mathrm{d}x$$ possesses an overlapping divergence when $ x \to \infty $ and $ y \to \infty $. However, under a change of ...
3
votes
1answer
75 views

How does one prove that the current of a spontaneously broken symmetry generates a particle?

I am having a hard time arguing that, after spontaneous breaking of a continuous symmetry of a field Lagrangian, local fluctuations around the vacuum can be interpreted as particles (without referring ...
0
votes
1answer
34 views

Ladder operator on momentum basis

Since in Quantum mechanics momentum operator can be written in terms of ladder operators $$\widehat{p}=-i\sqrt\frac{{\hbar m \omega}}{2}(\widehat{a}-\widehat{a}^\dagger)$$ these operators operate on ...
5
votes
0answers
56 views

Topology-dependent groud state degeneracy of $B \wedge F + B \wedge B$ and $B \wedge F + B \wedge B \wedge B$

There are some examples of topological BF theory with extra terms allow it still being topological. See this Ref. paper In 4d (3+1D), we have the trace of: $$ \int\frac{k}{2\pi}\text{Tr}[B \wedge F + ...
3
votes
1answer
131 views

Reducibility of tensor products of Lorentz group representations

Consider the statement: (34.29 in Srednicki's QFT text) $$\tag{34.29} (2,1)\otimes(1,2)\otimes(2,2)~=~(1,1)\oplus\ldots$$ Where of course, $(a,b)$ label representations of Lorentz group in the usual ...
0
votes
0answers
43 views

Feynman Rules in Momentum space

What's the difference between Feynman rules in momentum space for $\phi^3$ theory and for $\phi^4$ theory? I know it's only a slight difference and perhaps found in the vertex factor? But for some ...
2
votes
0answers
47 views

Integration of Dirac propagator

I've got confused with Dirac (or Spinor) Propagator. Everywhere in books I have examples of integration Klein-Gordon propagators, which are quite easy. But I don't understand how to integrate ...
3
votes
1answer
74 views

$\gamma^5$ factor in Quantum Field Theory

I have a problem with interpretation of $\gamma^5$ factor in the interaction Hamiltonian. I know that $\frac{1\pm\gamma^5}{2}$ is a helicity projection and it requires helicity conservation in ...
4
votes
1answer
57 views

Number of Goldstone bosons in paramagnetic-to-ferromagnetic phase transitions

In paramagnetic-to-ferromagnetic phase transitions, the symmetry spontaneously breaks down from SO(3) to the subgroup SO(2) below $T_\text{crit}$. This implies that there should be two Goldstone modes ...
0
votes
1answer
84 views

Physical meaning of the creation or annihilation operators for a N-electron gases?

For a N-electron gases in a finite volume V, what is the meaning of the first "=" in the following expression: ...
4
votes
2answers
97 views

What guarantees the existence of unitary operators implementing Lorentz Transformations?

This should be a very basic question. In introductory QFT books, often one of the first things we see is the following claim: for every Lorentz transformation $\Lambda$, we can associate an unitary ...
1
vote
0answers
37 views

Long range order in the BCS ground state

I am trying to prove the following equivalent form for long-range-order in superconductivity (Annett's book states something like this) : \begin{equation}\lim_{|R-R'|\to ...
8
votes
0answers
81 views

Monopoles and the magnetic Higgs mechanism

In a paper of 't Hooft about the rôle of magnetic monopoles for a model of quark confinement, I don't understand the following sentence (end af paragraph 14) [...] in order for monopoles to ...
2
votes
1answer
40 views

Transformations of a left-handed gauge field

In a set of lectures I'm watching on Effective Field Theory the professor introduces a spurion vector field, $\ell_\mu$. He then says that we take it to transform as a "left handed gauge field" and ...
3
votes
1answer
123 views

Quantum Field Theory without LSZ, how is it possible?

Most modern texts spend some time deriving the LSZ reduction formula that connects S matrix elements to time ordered field correlation functions. It seems essential, and really helps clear up what you ...
2
votes
0answers
34 views

Question about canonical normalization

Are there ever instances where it is more convenient or more physically meaningful to work in terms of fields which are not canonically normalized? Obviously, nothing 'measurable' should be affected, ...
2
votes
0answers
54 views

Conformal Coupling for QFT in Curved Spacetime

I have seen it stated but not explained that consistency requires you to couple massless fields to gravity using the conformal coupling, so that $trT_{\mu \nu}=0$. What is the reason for this?
3
votes
0answers
80 views

Propagator in massless scalar field theory

Suppose we have the following Lagrangian: $\mathcal{L} = \frac{1}{2} \phi \Box \phi + V(\phi)$, where $\Box = \partial _ {\mu} \partial ^ {\mu}$ and $V$ is the interaction term. We use the $(-+++)$ ...
4
votes
0answers
85 views

Could energy be stored into (not extracted from) the quantum zero point field (like a battery)?

In order to explain the question clearly, I will make a short introduction. In 1962, Josephson predicted that for a sufficiently thin insulating layer, it should be possible for Cooper pairs to ...
1
vote
1answer
102 views

Feynman Diagram in $\phi^3$ theory

I'm slightly befuddled by is what it means when I'm asked to Draw the Feynman diagram in momentum space for the two point function of $\frac{\lambda}{3!}\phi^3$ theory for order $O(\lambda^2).$ ...
3
votes
0answers
52 views

Symmetry factor of tree diagram

In Mark Srednicki's Quantum field theory(page 89) it says This is a general result for tree diagrams (those with no closed loops): once the sources have been stripped off and the endpoints ...
2
votes
0answers
60 views

Feynman rules of a theory in non-standard form

I am currently studying lecture notes by Akhmedov on interacting scalar field theory in de Sitter space. In these notes, he considers a scalar field theory of the form ...
2
votes
1answer
48 views

Commutation Relations for Creation & Annihilation Opertors of Two Different Scalar Fields

Let us consider two different scalar fields $\phi$ and $\chi$. The commutation relations for the creation and annihilation operators of the scalar field $\phi$ are given by $$ [a(\textbf{k}), ...
2
votes
1answer
116 views

Do particles travel backward in time in a particle interpretation of field theory?

In this Phys.SE answer Ron Maimon stats: there is no relativistic particle formalism in which the particles have postive energies and casual propagation. You can either deal with fields in which ...
0
votes
0answers
31 views

What does the notion of basis sets for photons in number of particle picture?

Since $$|n.\rangle=|u_{k_1}\rangle\otimes...\otimes|u_{k_1}\rangle\otimes|u_{k_2}\rangle\otimes...\otimes|u_{k_2}\rangle\otimes...\otimes|u_{k_m}\rangle\otimes...\otimes|u_{k_m}\rangle$$(There are ...
5
votes
1answer
48 views

How can one (formally) determine the particle content of a free field theory?

Here's my question: Suppose I'm given a free field theory, where my fields are functions $\phi:\mathbb{R}^4 \rightarrow V$, and the equations of motion are a system of linear Lorentz-invariant ...
3
votes
1answer
107 views

Calculating 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) = ...
1
vote
1answer
93 views

A formula in Sung-Sik Lee's paper

I want to ask if anyone has gone through the derivation of the second equality in the following formula which comes from http://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165102.
2
votes
0answers
40 views

Recommendation: Advanced topics in quantum field theory [duplicate]

I have read Srednicki's Quantum Field Theory book. I want to learn more about advanced topics in field theory, such as geometry and topology in field theory, topology defect, anomaly, soliton, ...
3
votes
2answers
239 views

Domain walls intersection

I was reading this article(On domain shapes and processes in supersymmetric theories). In the paragraph about domain walls intersection (paragraph $4$, page $7$) the authors say: In a one-field ...
6
votes
0answers
79 views

Is the Higgs bare mass larger than the physical mass?

The Higgs boson propagator can be written $$\frac{1}{p^2-m^2+\Sigma(p^2)}$$. If we take $p^2=m_P^2$ the physical mass, we get $m_P^2=m^2-\Sigma(m_P^2)$. Now, if $\Sigma\sim \Lambda^2$, we get ...
12
votes
1answer
211 views

Self-dual Maxwell equations, the second homology group, and topological invariants of a four manifold

In Witten's paper Quantum Field Theory and the Jones Polynomial, he mentioned that: Geometers have long known that (via de Rham theory) the self-dual and anti-self-dual Maxwell equations are ...
2
votes
0answers
34 views

Optical Theorem ,how can experiment distinguish the unscattered wave from the forward scattered wave?

How can experiment distinguish the unscattered wave from the forward scattered wave? The Optical Theorem says the imaginary part of the forward wave determines the cross section for an initial ...
5
votes
1answer
170 views

A question about Feynman diagram and symmetry factor

Consider a $\varphi^3$ theory: $$ Z_1(J) \propto \exp\left[\frac{i}{6} Z_g g\int \mathrm{d}^4 x \left(\frac{1}{i}\frac{\delta}{\delta J}\right)^3\right] Z_0(J), $$ where $$ Z_0(J) = ...
4
votes
1answer
107 views

A question about causality and Quantum Field Theory from improper Lorentz transformation

Related post Causality and Quantum Field Theory In Peskin and Schroeder's QFT p28, the authors tried to show causality is preserved in scalar field theory. Consider commutator $$ [ \phi(x), \phi(y) ...
2
votes
0answers
39 views

Definition of the Effective Particle

We define the effective particle creation and annihilation operators which are collectively and commonly denoted by $\hat{q}_s$: $$\hat{q}_s := \hat{U}_s \, \hat{q}_0 \, \hat{U}^\dagger_s $$ where ...
4
votes
1answer
94 views

Feynman graphs of Compton scattering

Compton scattering is usually described two Feynman graphs (in the second-order perturbative expansion of scattering matrix) that can be described in the following way: annihilation of a ...
5
votes
0answers
115 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 ...
2
votes
1answer
47 views

Unit determinant for relevant symmetry groups in QFT

When treating QFT we want our theory to be invariant under different symmetry groups, for example, the Standard Model is a non-abelian gauge theory with the symmetry group $U(1)×SU(2)×SU(3)$. ...
5
votes
0answers
64 views

Quantum Logic and Quantum Field Theory

Quantum Logic is a very interesting and powerful answer to the problem of Quantum Mechanics foundations. Nevertheless this approach is usually developed in a non-relativistic framework. Is it still ...
6
votes
3answers
119 views

VEV of tensor fields

Is it possible to have a VEV (vacuum expectation value) for tensor field? I am mainly concerned about second rank tensors. It seems it can have a VEV which will be proportional to the metric tensor ...
2
votes
2answers
72 views

Gauge symmetry for p-forms

It is well known that the Lorentz invariance of the S-matrix implies Gauge redundancy for 1-forms,'photons'. Does this argument go through to p-forms? That is does lorentz invariance of s-matrix of ...
6
votes
1answer
84 views

A question about a complex integration in Peskin's QFT textbook

In page 27 (2.52), the integration is $$\int_{-\infty}^{\infty}dp \frac{p e^{ipr}}{\sqrt{p^2+m^2}}$$ He says that there are two branch cuts starting from $\pm im$ But I learn in complex analysis ...
4
votes
1answer
92 views

Gravitational Chern-Simons theory for bosons and fermions

Q1: What is the difference of boson and fermions for their Gravitational Chern-Simons theory? I suppose in general if the metric is not flat, we have vierbein ${e_{\hat{b}}}^{\nu}$, with $$ ...
5
votes
3answers
293 views

Is there any relationship between gauge field and spin connection?

For a spinor on curved spacetime, $D_\mu$ is the covariant derivative for fermionic fields is $$D_\mu = \partial_\mu - \frac{i}{4} \omega_{\mu}^{ab} \sigma_{ab}$$ where $\omega_\mu^{ab}$ are the spin ...
5
votes
1answer
74 views

Free Field theory to Interacting Field theory

Free field theory: Why is it said that different Fourier modes in case of a free field (say, real Klein-Gordon field) are independent of each other? Interacting field theory: How exactly does the ...
2
votes
1answer
105 views

Equations of motion for the Yang-Mills $SU(2)$ theory

I have an exercise for Yang-Mills theory. I can't find answer anywhere. Derive equations of motion for the Yang-Mills theory with the gauge group $SU(2)$ interacting with $SU(2)$ doublet of scalar ...
0
votes
3answers
115 views

Is Space-Time a special form of energy?

I know space-time can be influenced by matter and energy, so it must be somehow mingled in with the mix of it all, but does space-time have a fundamental particle? Can we make a little bit of ...
0
votes
3answers
118 views

Duality behavior of light and effect of system scale on its behavior [closed]

Does an electromagnetic wave that makes by antenna behaves purely as wave for all the times? or it can change its behavior as photon? and does the scale of system effect on behaving as EM wave or ...