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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Virtual particles and the scaling effect on valence quarks

Summary from Carrolls: "Particle at the end of the Universe", page 101. Inside a proton there are 3 valance quarks. In addition, there is constant creation and annihilation of gluon, quarks and ...
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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 ...
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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) ...
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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 ...
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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 ...
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Fermion commutation relations QFT question

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 ...
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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 ...
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38 views

Spontaneous symmetry breaking - Goldenstone theory

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 ...
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44 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 ...
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57 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 ...
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75 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: ...
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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?
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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} ...
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87 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 ...
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64 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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+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 ...
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69 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 ...
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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 ...
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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 ...
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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 ${\cal N}=1$ ...
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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} ...
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44 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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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45 views

Quantum particles hopping in spacetime

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, ...
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Is dark energy & matter God? [closed]

The bible is the only book that helps clarify the confusion spouted in other ancient texts. Like who are priest kings? The bible says Fallen angels. Where did ancient sumer & egypt get thei ...
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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 ...
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125 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 ...
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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 ...
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73 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}: ...
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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 ...
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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 ...
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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: ...
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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} ...
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122 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 ...
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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 ...
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50 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
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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 ...
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1answer
70 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 ...
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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 ...
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2answers
60 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' ...
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1answer
67 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 ...
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103 views

Perspectives of QFT [closed]

From the answer to this question Computing $\langle0|T[Q(t_2)Q(t_1)]|0\rangle$, I have discovered that there is two perspectives to QFT. I am doing a course which is unfortunately a summary of QFT and ...
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Why are $SU(N)$ gauge theories easier to handle for $N\rightarrow \infty$?

I was wondering if there was a intuitive/heuristic argument to understand why generalizing the QCD gauge group $SU(3)$ to $SU(N)$ and taking $N\rightarrow \infty$ simplifies the analysis of the ...
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83 views

Is there any theory in physics that might support the existence of tachyons?

According to Einstein, we all know that light is the fastest thing and it's impossible to beat it's speed. But isn't there a way to go around this? I read somewhere that tachyons gain speed per the ...
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Why isn't the path integral rigorous?

I've recently been reading Path Integrals and Quantum Processes by Mark Swanson; it's an excellent and pedagogical introduction to the Path Integral formulation. He derives the path integral and shows ...
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78 views

Writing down many particle Hamiltonian

We are given that \begin{align}\mathrm{tr} e^{-\frac{i}{\hbar}\hat{H}t}&= \int D[a_1,\dots,a_n]\times\\&\qquad\exp\left[\int_0^t dt' \left(\frac{1}{2}\sum_j ...