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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Magnetic moment in four-fermion theory

I'm trying to calculate the neutrino magnetic moment in the theory with this additional term in the Lagrangian: $\frac{a}{M^2}(\bar{\nu}\sigma_{\mu\nu}\nu)(\bar{e}\sigma^{\mu\nu}e)$, where ...
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71 views

Naive quantization of Schrödinger field

I just started learning QFT and I was wondering if one is able to quantize the Schrödinger field similar to the way one is able to quantize electromagnetic or elastic mechanical wave modes. E.g. ...
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56 views

Simple generalization of the Feynman rules for QFT to thermal QFT?

Assuming that one knows Feynman rules for QFT, what is the simplest way to generalize them for $T \neq 0$ case? What is the main difference? Can we just read them off from Lagrangian the same way as ...
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51 views

EFT and Renormalizability

Was trying to understand renormalizability in EFT. This is a little confusing especially the part of the misnomer. Can someone please explain this? Text taken from Wikipedia: "However, in an ...
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1answer
61 views

Significance of $U(1)$ extensions of SM [closed]

Let's assume $U(1)$ extensions of SM with some detalizations: 1) Fermion sector of SM is extended by adding new very massive fermions; 2) Gauge group of SM is extended by adding new spontaneously ...
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44 views

Are hilbert spaces invariant under gauge transformations?

I'm trying to work out if the physical hilbert space is invariant under any gauge transformation? I have found situations where under some transformations they don't change but I've now gotten very ...
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1answer
77 views

Does scale invariance imply massless or continuous mass distribution?

$\newcommand{\ket}[1]{\lvert #1 \rangle}\newcommand{\bra}[1]{\langle #1 \rvert}\newcommand{\scp}[2]{\langle #1 \vert #2 \rangle}$ In his 2008 slides Unparticle Phenomenology (PDF), Tzu-Chiang Yuan ...
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58 views

Relativistic Fermi Golden Rule?

On online slide notes, it is mentioned that: Fermi Golden Rule: $$P_{if}=\frac{2\pi}{\hbar}|M_{if}|^2\rho_f$$ where $\rho_f$ is density of final sates --number of quantum states per unit volume - ...
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101 views

Path Integral Evaluation

I've seen the path integral formulation now in a couple contexts (propagator in quantum mechanics, and coherent state functional integral in many body physics). I'm now struggling with how to actually ...
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157 views

If proton spin emergence from quarks and gluons is mysterious, why is silver atom spin not?

A recent Scientific American article brought up an old issue, which is this: According to quantum chromodynamic models, the emergence of exactly 1/2 unit of spin in a proton (or a neutron, or any ...
3
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179 views

Can bosons have anti-particles?

Can bosons have anti-particles? In the past, I would have answered this question with a yes, primarily because I can imagine writing down a QFT for complex scalars that has a U(1) symmetry that ...
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45 views

quantum fluctuations and the virtual particles

In the introduction of chapter-12 of “An Introduction to Quantum Field Theory” by Peskin and Schroeder I encountered this line: “The quantum fluctuatuations at arbitrarily short distances appear in ...
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70 views

Wick's Theorem For Product of Fields [closed]

I am trying to write an expression for $$\langle (\phi(x,t))^m (\phi(x',t'))^n \rangle$$ where $n$ and $m$ are even with respect to a real Gaussian action, in terms of $$\langle \phi(x,t) ...
2
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1answer
127 views

Why does the electromagnetic and weak coupling strength do not meet at the electroweak scale?

The running of the coupling strengths is usually visualized on a logarithmic scale like here What surprises me is that the weak and the electromagnetic coupling strength do not meet before the GUT ...
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2answers
109 views

Elementary question about endpoint singularities

In George Sterman's book "An Introduction to Quantum Field Theory", on pages 413-414, there is a description of the endpoint singularity. One begins with the function $$ I(w) ~=~ ...
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262 views

Can you take the cutoff to infinity at a conformal fixed point?

A conformal fixed point is defined by $$\beta(g)=0$$ We hence know that couplings, masses and dimensions of operators do not flow in the effective Lagrangian when we change the renormalization ...
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207 views

Epstein-Glaser causal perturbation theory

Why does causal perturbation theory in the sense of Epstein Glaser fall under algebraic QFT rather than heuristic QFT in renormalization?
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144 views

Chiral Scale and Conformal Invariance in 2D QFT

I am reading a paper by Hofman and Strominger. In the appendix A, I have reproduced the equations (A10). Now they made a statement that "The Jacobi identity can be used to show that $O_h$ and $O_p$ ...
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1answer
84 views

Is gauge invariance essential to a theory be renormalizable?

Let's consider a model of New Physics in which all operator have dimension smaller than four, but which breaks explicitly $SU(2)_L$ gauge symmetry. Is this model necessarily renormalizable? ...
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39 views

How can I prove that $\gamma^0$ is the parity operator for Dirac fields? [closed]

How can I prove that the parity operator on a Dirac field is $\gamma^0$? I was trying to prove it through Lorentz transformations but failed shortly.
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1answer
70 views

Pauli Villars Regularization

Consider the t-channel diagram of phi-4 one loop diagrams. Evaluated it is, with loop momenta p, $\frac{\lambda^2}{2}\displaystyle\int\frac{d^4p}{(2\pi)^4}\frac{1}{(p+q)^2-m^2}\frac{1}{p^2-m^2}$ If ...
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1answer
110 views

Equivalence principle for test fields

My question is very simple. We all know that, for a test particle(classical) in a gravitational field, the motion is only determined by the geodesic lines(let's forget about the initial conditions for ...
3
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196 views

Effective field theories and gauge anomalies cancellation

Lets assume some theory which concludes sets of generations of fermions (lets call them $A$ and $B$). Fermions $A$ have some gauge group $G_{A}$ (for example, SM), while fermions $B$ are charged under ...
2
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1answer
70 views

Computation of the QCD vector two point function

I am following some notes on the computation of the vector two point function in QCD and I would like somebody to make some intermediate steps more explicit. Let's consider ...
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1answer
74 views

Why does Srednicki insist on $\phi$ having zero VEV?

Let $\phi$ be a scalar field in an interacting theory ($\phi^3$ or $\phi^4$, for example). If $|0\rangle$ is the vacuum of the interacting theory and $P^\mu$ is the four-momentum operator, we have ...
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81 views

Why switching from Heisenberg picture to Interaction does not change the (Lorentz) transformation law of fields?

In his book, The theory of quantum fields, Weinberg builds the most general interacting picture (i.e. free) field by listing all possible Poincarè representation. These fields change so that, if we ...
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156 views

How to mathematically describe a spin-0 particle [closed]

I don't know all the technical things like Eigenstates. I want to know, mathematically written out for beginners, how to make a quantum field theory of a scalar boson. To spare confusion- I understand ...
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1answer
54 views

Non-pertubative renormalization and correctness of a theory

Even if I start to understand why perturbative renormalization is necessary, I'm not exactly sure why non perturbative renormalization is. After asking the question to several theorists, what I think ...
2
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1answer
59 views

Scalar Yukawa theory derivation

I am using Tong's notes for QFT, and on page 59 there is a derivation for the scattering amplitude of $\psi\psi \rightarrow \psi\psi$ in Scalar Yukawa theory. It goes from here: $$\langle ...
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1answer
35 views

Higgs mass and EW precision tests

I'm trying to understand how the Higgs mass can influence EW precision tests. In order to do that I'm using the following document (section 4.3): http://arxiv.org/pdf/0706.0684v1.pdf There are a ...
2
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3answers
226 views

Realistic interacting QFT construction

May I ask is it true that all the interacting 4 dimension qft couldn't be constructed and defined consistently and rigorously? If we are able to rigorously constructed lower dimension qft, what are ...
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0answers
47 views

Why are the particles called irreps of Poincare group? [duplicate]

Why are particle excitations called irreducible representation of the Poincare group? It will be very helpful if someone can illustrate with one concrete example of a particle. EDIT : But how does ...
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25 views

Problem in the derivation of the Ward identities

This is a follow up to my previous Phys.SE question. The last equation in that question is $$-a\frac{1}{k^2+i\eta}k^{\lambda}i\Pi_{\lambda\rho}(k)iD^{\rho\nu}(k)=0$$ which we can further simplify as ...
2
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2answers
107 views

Is this symmetry factor in Peskin wrong?

I am trying to compute the symmetry factor of a Feynman diagram in $\phi^4$ but i do not get the result Peskin Claims. This is the diagram I am considering ...
4
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1answer
207 views

Is the exact form of the Higgs potential known?

Usually the Higgs potential is given as $$ \frac{1}{2}\mu^2\phi^2 - \frac{1}{4}\lambda^2\phi^4 $$ but I never quite understood if this just serves to give us an idea of how symmetry breaking works, or ...
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1answer
87 views

Topological entanglement entropy in transverse quantum Ising model?

I have seen from literature that the $Z_2$ lattice gauge theory in 2d could be mapped into a quantum Ising model with gauge constraints on the Hilbert space by dual transformation. The deconfined ...
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3answers
141 views

Why are complex fields in the Lagrangian?

I know that a complex field has twice the number of degrees of freedom of a real field, and that fields (in QFT) aren't observables so we don't really care if they are real. But why the need for ...
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1answer
42 views

Multiply creation operator by a phase factor

A basic question, but I'm not completely confident what I'm doing is legit. I can multiply a creation operator by an arbitrary phase factor and it doesn't change any physics. True? I have a ...
1
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1answer
148 views

Scale invariance in QFT?

About scale invariance in "beyond the standard model". At the base of the analysis is the principle of scale invariance. So what is being said: what if there were another sector of the theory that ...
2
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1answer
114 views

Why does not Bhabha scattering contain u-channel diagram?

$e^+e^-\rightarrow e^+e^-$ is called Bhabha scattering. Let us only consider the tree level Feynman diagrams of this process. Apparantly, there are s-channel and t-channel diagrams as shown in the ...
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1answer
110 views

Poincaré' lemma and EM potential $A^{\mu}$

My lecturer said that given the sourceless Maxwell's equations $$ \partial_{\mu}\, ^ *F^{\mu\nu} = 0 $$, we can find a solution $$ F^{\mu\nu} = \partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu},$$ that ...
8
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3answers
290 views

Problem understanding the symmetry factor in a feynman diagram

I am trying to understand a $1/2$ in the symmetry factor of the "cactus" diagram that appears in the bottom of page 92 In Peskin's book. This is the diagram in question (notice that we are in $\phi^4$ ...
4
votes
1answer
86 views

Why doesn't a renormalizable $\phi^4$ theory have odd diagrams?

I've been reading Zee's QFT textbook and trying to follow some lecture notes online whenever I can't grasp something. I really don't understand one thing regarding the renormalization of theories, ...
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28 views

Correction to the residue in QED using $\overline{MS}$ contains IR divergence

I'm Calculating the next-to-leading orders in QED, but I'm using $\overline{MS}$ scheme, as known in $\overline{MS}$ the residue is no longer one and I have to calculate the correction to the residue ...
2
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122 views

What exactly is NASA's proposed mechanism for “propellantless” “EM Drive” propulsion? [duplicate]

Of course, this question runs perilously close to this site's prohibition against discussing non-mainstream physics. However, the accepted answer in meta about what is acceptable and what is not ...
4
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1answer
78 views

Point splitting technique in Pesking and Schroeder

One of the cornerstones of point splitting technique of calculating chiral anomaly (Peskin and Schroeder 19.1, p.655) is a symmetric limit $\epsilon \rightarrow 0$. And this is the point that I don't ...
2
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2answers
141 views

Does the time ordering operator have a rigorous definition?

In quantum field theory, the time ordering operator (TOO) appears in the formal expressions for the scattering amplitudes. It acts upon a product of operators that each depends on time, and returns ...
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2answers
87 views

Covariant commutation relations in Mandl and Shaw

In page 47 of Mandl and Shaw, the $\Delta$-function can be written as $$ \Delta(x) = \frac{-1}{(2 \pi)^3} \int \frac{d^3k}{\omega_k} \sin(kx) \tag{3.43} $$ and as equation $$ \Delta(x) = ...
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24 views

What are instanton fugacities?

I have seen this term many times in various papers but I could not find anywhere a good explanation on what instanton fugacity is. Can you explain and provide some reference if possible please?
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Dropping creation/annihilation terms when quantising a field theory

There is something I don't understand in the procedure that is often done while quantising a field theory. Say, we have operators $a_k, a^{\dagger}_k, b_k, b^{\dagger}_k$ which obey the commutation ...