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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Can we quantize Maxwell-Chern-Simon Theory through Gupta-Bleuler approach?

In 3+1 QED we covariant quantize the Maxwell theory through Gupta-Bleuler method. But I have seen that MCS theory is explicitly covariant quantized using Nakanishi auxiliary field. Why cannot we take ...
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1answer
40 views

Doubts in understanding the role if quantum corrections in the Hierarchy Problem

Trying to understand the Hierarchy problem many questions come to my mind that I am unable to answer due probably to my poor understanding of renormalization. The basic set up of the hierarchy ...
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22 views

Why the heat capacity doesn't diverge in the Kosterlitz-Thouless (KT) phase transition?

The KT transition has a special properties that, during the phase transition the heat capacity stay finite (so the behaviour of the heat capacity cannot reflect any critical behaviours). However, the ...
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3answers
69 views

Negative energy of free particle: classical and quantum picture

Classically, the energy of a free particle consists of only the kinetic energy given by $E=\frac{|\textbf{p}|^2}{2m}$ Since $|\textbf{p}| $is real and $m>0$, $E\geq 0$. However, since ...
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1answer
38 views

Dirac field creation and annihilation operators [on hold]

i have to prove the following equations. Can someone give me a hint please?
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1answer
51 views

Chiral Fermion Problem and the String Net Model

In Xiao-Gang Wen's book "Quantum Field Theory of Many-Body Systems", he mentions that (the string-net condensation picture)...has a problem: we do not yet know how to produce the $SU(2)$ part of ...
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57 views

Fermionic path integral on the disk - Recovering the vacuum state

I'm trying to get a better feel for the operator to state map in quantum field theory. There is a general claim for 2d theories that doing the path integral on a disk with no operator insertions gives ...
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24 views

What is the procedure to follow if I want to renormalize a given operator $\cal{O}$ or a given coupling?

Consider QED. I know that the renormalization constant of the mass can be obtained from considering the electron propagator, regularizing it and renormalizing it. I know that from this process we can ...
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24 views

How can we see that a 4D N = 2 sigma model will yield a 3D N = 4 sigma model when compactified on a circle?

I have a question about sigma models in 3D. If we have $\mathcal{N}=2$ field theory on $\mathbb{R}^4$ and compactify it on $\mathbb{R}^3 \times S^1_R$ (in which $S^1_R$ is a circle of radius $R$) we ...
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27 views

How to quantize Dirac field? [on hold]

How do you quantize a Dirac field? Can you give me the mathematics and describe what and how the field which now become operator can be relate to a matrix (Heisenberg formulation)?
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24 views

what are sone good string theory video lectures? [on hold]

What are some good and advanced string theory video lectures for a guy with qft and sm knowledge?
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32 views

Questions on QFT and SM

What are some question paper to solve/practice on Quantum Field theory and Standard model, I read the theory but not practiced?
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45 views

Is it a good time to start or I need to work on some more subjects? [on hold]

Is it a good time to start string theory when I did a course on Quantum field theory and on standard model but not the renormalization theory? I used following books: Some chapters of Peskin Some ...
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65 views

What is renormalization? [on hold]

What is renormalization? I would want a rough description before I go and work on it properly (I did a course on QFT and on SM (which was 3rd course in the series) but skipped the 2nd course which ...
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26 views

Supersymmetry invariants

On page 158 of Fields, the supersymmetry algebra is represented in terms of the action on supercoordinates as $$\delta \theta^\alpha = \epsilon^\alpha$$ $$\delta\bar{\theta}^{\dot{\alpha}} = ...
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1answer
23 views

colliding point particles

when I draw e.g. the diagram of compton scattering I assume that the electron of given momentum gets 'hit' by a photon and interacts with it. How close does the photon have to get to the electron that ...
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28 views

Counting Degrees of Freedom in Field Theories

I'm somewhat unsure about how we go about counting degrees of freedom in CFT, and in QFT. Often people talk about field theories as having 'infinite degrees of freedom'. My understanding of this is ...
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32 views

One loop effective potential of Standard Model

The one loop Coleman-Weinberg contribution of a scalar field to the effective potential (in MSbar scheme) is: \begin{equation} const. \times m^4(\phi_c) \left( log \left( ...
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44 views

Can we just replace the finite part of $Z_m$ in a renormalization scheme at leading order

Suppose that we have to determine the finite part of $Z_m$ how it differs from common schemes, but we are free to choose the other renormalization constants in QCD (at Leading order). Could we make ...
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37 views

Can we change the point form $\not p = m$ to $\not p = 0$ in on-shell renormalization scheme condition?

In the on-shell scheme, in QCD, one can impose the counterterms action to vanish the part of 1PI diagrams on external lines. The on-shell condition can be written as follows: \begin{equation} {\left. ...
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1answer
91 views

Relation between Wilson approach to renormalization group and 'standard' RG

While studying renormalization and the renonormalization group i felt that there wasn't any completely satisfying physical explanation that would justify those methods and the perfect results they ...
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1answer
85 views
+500

What is meant by the phrase “this operator does not renormalize this other operator”, and how can understand it using diagrammatic arguments?

I am trying to understand some sentences in a paper. In section two the following theory of a (complex) massless scalar coupled to a $U(1)$ gauge boson is introduced ...
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2answers
160 views

Do virtual particles actually physically exist?

I have heard virtual particles pop in and out of existence all the time, most notable being the pairs that pop out beside black holes and while one gets pulled away. But wouldn't this actually violate ...
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38 views

Intro to Super Yang Mills theory

I'm looking to start learning Super Yang Mills theory. Currently I have studied Peskin and Schroeder up to the Renormalization Group, but don't know supersymmetry yet. I know some Conformal Field ...
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102 views

Geometric interpretation of quantum Yang-Mills field

In most books\articles review geometric interpretation of classical Yang-Mills field in terms of principal bundle, connections...etc. What are geometric interpretation of quantum Yang-Mills field? ...
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1answer
54 views

Retarded and advanced Green's function

Is there a use of advanced Green's functions? If yes then when or in which context? Why in quantum field theory, we always use Feynman's prescription for finding the propagator and not the retarded ...
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1answer
82 views

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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55 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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1answer
43 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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43 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
55 views

Significance of $U(1)$ extensions of SM

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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38 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
73 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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36 views

Relativistic Fermi Golden Rule?

In his slide notes, Georgi mentions: 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 - states in a ...
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1answer
64 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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1answer
85 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 ...
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1answer
137 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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1answer
36 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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56 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) ...
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1answer
75 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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97 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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53 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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93 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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130 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
63 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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0answers
29 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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0answers
36 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
64 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 ...
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107 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 ...