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
0answers
11 views

Dependence of finite part of loop integral on regularization

Recently I've calculated some process in which arise triangle loop with running two $W$ bosons and one massless fermion. The expression for integral is following: $$ I_{\alpha \beta}(r, q) = \int ...
1
vote
0answers
15 views

Does a momentum-independent interaction not renormalize mass?

I recently had to calculate the effective mass to second-order in a momentum-independent interaction in a Fermi liquid, and I found that it was the same as the bare mass. What's more, the first-order ...
1
vote
0answers
38 views

Equivalence of delta functions when calculating decay rate [on hold]

$\newcommand{\bs}{\boldsymbol}$ Hello, I'm currently working through the lecture notes of my Theoretical Particle Physics course, and there, we are calculating the decay rate of the following process ...
2
votes
0answers
35 views

Form of the S matrix for interacting scalar field [on hold]

The solution for the equation $ S^{-1} c_k^{in} S = c_k^{in} + f_ k $ is S= $ exp(f_k^{*}c_k^{in} - f_kc_k^{in*})$. Here $c_k^{in}$ is an operator and $f_k$ is a c number. This is the equation for ...
2
votes
1answer
58 views

Vacuum has zero spin in Dirac theory

I have troubles trying to prove a statement made by Peskin-Schroeder in page 61, section 3.5 where he says that the "spin" operator $J_z$ given by the non numbered equation $$ J_z= \int d^3 x ...
3
votes
1answer
47 views

Origin of the quark condensate VEV

Consider the QCD lagrangian : $$L_{QCD}=-\frac{1}{4}G^a_{\mu\nu}G^{a\mu\nu}+\sum\bar{\psi}_q(i\not{D}-m_q)\psi_q$$ Textbooks explain that this lagrangian is spontaneously broken by the VEV of quark ...
1
vote
0answers
53 views

Virtual particles and the scaling effect on valence quarks

Inside a proton there are 3 valance quarks. In addition, there is constant creation and annihilation of gluon, quarks and anti-quarks. The number of virtual particles we observe depends on how ...
1
vote
0answers
30 views

is there any molecular transition which emits a photon in certain direction

i know molecules having magnetic moment would be aligned in certain direction but do they emit photon in any certain direction when excited? are there any molecules which would emit photon in tthe ...
0
votes
1answer
26 views

Time evolution of generalized angular momentum operator

We define this operator : $$M^{\mu\nu} = \int d^3x~(x^{\mu}T^{0\nu} - x^{\nu}T^{0\mu})$$ where $T_{\mu\nu}$ is the energy momentum tensor (see e.g. Energy momentum tensor from Noether's theorem) ...
4
votes
1answer
78 views

Why is tree-level interaction between neutral scalar and photons non-renormalizable?

I've read that the decay of a neutral scalar particle into two photons, i.e., $$ S(p+q) \to \gamma(p) + \gamma(q) $$ can't happen via tree diagrams and instead is caused by loop diagrams (such as a ...
2
votes
0answers
48 views

Calculating imaginary part of a loop diagram using cutting rules for phi^4 theory

I'm trying to calculate the imaginary part of this diagram in $\phi^4$ theory, using the optical theorem, and I'm having trouble. The cutting rules seem to suggest that this diagram is equal to ...
0
votes
0answers
36 views

Fermion commutation relations QFT question [on hold]

Consider left-handed fermions in two spacetime dimensions $(t,x)$: $\psi_L=\frac{1}{2}(1-\gamma_5)\psi_D$ with $J_0^\epsilon(t,x)=\psi_L^+(x+\epsilon)\psi_L(x-\epsilon)$. (a). Use canonical ...
1
vote
1answer
39 views

Using the optical theorem to calculate the imaginary part of a loop diagram

I'm trying to calculate the imaginary part of this diagram in $\phi^4$ theory, using the optical theorem, and I'm having trouble. All of the examples I can find use the theorem to relate the ...
0
votes
0answers
39 views

Spontaneous symmetry breaking - Goldenstone theory [on hold]

i want to describe inverse interaction in Goldstone theory in which respective generators and operators in assymetric vacuum takes away mass eigenvalue from other mass particles .Can you ...
1
vote
0answers
52 views

Anomaly for Majorana fermion?

In 4-spacetime dimension, is there U(1) gauge field chiral anomaly associated with Majorana fermion (or I am not sure if it is equivalent, majorana representation)? Besides, I have read from several ...
0
votes
0answers
58 views

Why do we use Fourier transforms in QFT? [duplicate]

I ask this question, as someone has recently asked me this and I'm not sure I gave them a satisfactory/correct answer. I explained that in QFT we describe particles (and there interactions) in terms ...
1
vote
2answers
76 views

Identify for $f(\infty)+f(-\infty)$ in quantum field theory [duplicate]

In Matthew Schwartz's textbook, Quantum Field Theory and the Standard Model, equation 14.68 on page 266 says the following: ...
1
vote
1answer
21 views

Translational versus dilatational zero modes?

Why are the zero modes of the SU(2) Yang Mills instanton referred to as translational or dilatational zero modes? Is this standard terminology?
4
votes
1answer
65 views

Why does this proof show the gluon propagator comes from the first two terms?

I am reading the book "QCD: Renormalization for the Practitioner" and i am having trouble understanding something. In page 70 the gluon propagator is written as follows $$\begin{multline} ...
3
votes
2answers
89 views

How to count the number of modes/polarizations of a Gaussian field theory?

A Gaussian (free) field theory is described by a quadratic action of the field, e.g. $S=\int\psi^\dagger K\psi$ (or $S=\frac{1}{2}\int\phi^\intercal K\phi$ for real fields). Usually one just need to ...
2
votes
1answer
71 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 ...
2
votes
0answers
55 views
+50

Viability of a Fayet Iliopoulos term in the MSSM

Why is a Fayet Iliopoulos term $-kD$ in the MSSM (Minimal Susy Standard Model) not relevant (or subdominant to an F-term)? According to Martin (A Supersymmetry Primer, p.70) it's because squarks and ...
1
vote
2answers
71 views

Why does the Higgs field have less energy when it's non-zero than when it's zero?

Why does the Higgs field have less energy when it's non-zero than when it's zero? There are references to this question on the site, but they are too heavy going for me for a while yet. Anybody want ...
4
votes
1answer
63 views

Is there a 2D manifold on which the Dirac equation has a zero mode?

The two-dimensional (2D) Dirac equation $(\sigma_1iD_1+\sigma_2 iD_2)\psi=E\psi$ admits zero mode ($E=0$) solutions on a non-trivial gauge background, such as the zero mode at the core of a U(1) gauge ...
3
votes
0answers
45 views

Polology in Functional Integration

Completeness of Hilbert space (on-shell states) is a very powerful concept in canonical quantization, for example, to study the nonperturbative characteristics of the S-matrix, like polology (pole and ...
2
votes
0answers
42 views

Questions about the existence of 5d & 6d version of 4d ${\cal N}=2$ SCFTs

Given a 4d N=2 Superconfomal field theory (SCFT) with a global flavor symmetry ( $\mathfrak{f}$ as the corresponding lie algebra), can we clam that this theory can always flow from a 5d ${\cal N}=1$ ...
3
votes
2answers
67 views

Functional integral in spontaneous symmetry breaking

So, functional integral is defined to be (with $\lvert\Omega\rangle$ is the vacuum state): $$\frac{\langle\Omega\rvert ... \lvert\Omega\rangle}{\langle\Omega\vert\Omega\rangle} = \int \mathcal{D} ...
3
votes
1answer
45 views

Operator Dimension and Field Transformation under Rescaling

In conformal field theory the operator dimension $\Delta$ determines how fields and thus correlation functions behave under rescaling. I am having trouble seeing how this number arises from a scale ...
2
votes
1answer
37 views

Does the spatial momentum of the ground state of a Poincare symmetric QFT vanish?

Consider a flat space QFT, the Lagrangian (in general interacting) has Poincare symmetry, and $\lvert\Omega\rangle$ is the ground state (or just merely no insertion at the far boundaries, from ...
0
votes
1answer
80 views

Is there something wrong with quantizing two times in second quantization?

Second quantization is sometimes considered to be a bad name, because a single quantization is enough. For electrons, we can either start from a many body viewpoint and introduce field operators or we ...
1
vote
0answers
92 views

Computations for Quantum Vacuum Fluctuations

For quite some time the notion of quantum vacuum fluctuations is bothering me. What exactly is the theoretical origin of this notion? This notion has become quite common in physics and is used to ...
1
vote
1answer
26 views

Under what cases is the Batalin-Vilkovisky (BV) operator nilpotent?

It is understood that when we deal with gauge algebras which close on-shell only after using equations of motion or where the space-time is curved, we can no longer just do away with BRST ...
2
votes
1answer
33 views

Coset construction of Tricritical Ising CFT

In http://iopscience.iop.org/1742-5468/2008/03/P03010 the authors state that the Tricritical Ising Model (TIM) CFT can be obtained from a Wess Zumino Witten construction based in the coset ...
-1
votes
0answers
46 views

Quantum particles hopping in spacetime [on hold]

Quantum mechanics assumes a non-empty vacuum. There can be created pairs of particles for a short time. Suppose that there are Special vacuum fluctuations that arise from unsteady particle Motion, ...
2
votes
1answer
69 views

Clarification: Why the gauge symmetry of pure Yang-Mills is $PU(n)$ and not $SU(n)$? [closed]

I am quoting the following from the Wikipedia article on the projective unitary group: In the pure Yang–Mills $SU(n)$ gauge theory, which is a gauge theory with only gluons and no fundamental ...
4
votes
2answers
127 views

Spontaneous Symmetry Breaking - struggling with physics based understanding?

Although I am a mathematician by nature, I'm writing an essay in my third year of my undergraduate on Spontaneous Symmetry Breaking in Physics, and as such I've become a little confused by how the ...
3
votes
0answers
48 views

Renormalization group and minimum substraction

I have several questions about renormalization group and minimum substraction scheme in particular. My first question is: 1) Why is the beta function typically just a function of coupling? In other ...
2
votes
1answer
74 views

Issues with the Operator to State map using Path Integral

Suppose your QFT has a Hilbert space $\mathcal{H}$, and let $\text{End}(\mathcal{H})$ be the set of operators on $\mathcal{H}$. It is often stated that in QFT there is a map $$\mathcal{F}: ...
0
votes
0answers
38 views

Can quantum fluctuation happen outside space-time? [duplicate]

So far I know, quantum fluctuations happen inside the vacuum which resides in the space-time. So, can it happen outside space-time? Because, one proposition suggest, big-bang was result of some kind ...
2
votes
1answer
68 views

Expressing the Schrödinger equation in terms of spinors

I appreciate that the Dirac equation can be thought of in terms of spinors, as it directly implies the presence of spin, in addition to initiating the concept of treating fields as operators. From ...
0
votes
0answers
35 views

W boson one loop electroweak contribution to muon g-2

I want to calculate the one loop W boson contribution (triple gauge boson vertex WW-Photon) to the muon anomalous magnetic moment g-2 with the help of Dimensional Regularization. Diagram given below: ...
2
votes
1answer
28 views

How does the electric field operator change inside an optical cavity

In the free field, transverse electric field operator is given by the below expression; $$d^{\bot}(R)=i \sum_{p,\lambda}\Big( \frac{\hbar cq}{2V\epsilon_{0}}\Big)^{1/2} ...
1
vote
3answers
125 views

What is the difference between the Higgs Boson particle and an electron moving through the Higgs field?

I am watching a lecture by Sean Caroll titled "Particles, Fields, and the Future of Physics". I am not a physicist by any means but enjoy the subject in my spare time hoping to understand it. This ...
9
votes
3answers
728 views

Is Maxwell's field the wave function of the photon?

In his ArXiv paper What is Quantum Field Theory, and What Did We Think It Is? Weinberg states on page 2: In fact, it was quite soon after the Born–Heisenberg–Jordan paper of 1926 that the idea ...
3
votes
1answer
53 views

Most general separable solution of free Dirac equation

In relativistic quantum mechanics, the solution of the free Dirac equation is assumed to be $$\Psi(\textbf{r},t)=u(\textbf{p})e^{i(\textbf{p}\cdot \textbf{r}-Et)}$$ How do I know that this is the most ...
2
votes
1answer
49 views

Green's Functions from Gell-Mann and Low Theorem

What I want to do: $\newcommand{\ket}[1]{\left|#1\right\rangle}$ $\newcommand{\bra}[1]{\left\langle#1\right|}$ $\newcommand{\braket}[1]{\left\langle#1\right\rangle}$ The Gell-Mann Low Theorem tells ...
2
votes
1answer
71 views

Connection of “spin” to conformal dimension

I have read The spin and weight of a primary field in CFT but it does not answer my question, short of a restatement of the question itself. So I hope this post does not risk being removed.. In ...
0
votes
2answers
36 views

How many photons are absorbed during Rabi oscillations?

In my understanding, Rabi oscillations are derived using the classical approximation for the electromagnetic field. I don't get how this picture fits with a quantized EM field though. Say you excite a ...
2
votes
2answers
61 views

Why photon propagator has metric tensor additionally?

Klein Gordon propagator is (Peskin p-30) $$ D_F(x-y)=\frac{i}{p^2-m^2} $$ which is actually Green function of KG field. But photon has $g_{\mu\nu}$ additionally in the numerator. I would expect its' ...
1
vote
1answer
68 views

What is the Meaning of the equation $\frac{d\sigma}{d\Omega}=\left|f(\theta,\phi)\right|^2$

In the "Preface for Students" of the book "Quantum Field Theory" by Mark Srednicki is a set of equations. Quoting from the author: "In order to be prepared to undertake the study of quantum field ...