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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Is $\langle k \vert k_1k_2\rangle=0$

Using that $$ \vert k_1k_2\rangle = a^\dagger({\bf k_1})a^\dagger({\bf k_2})\vert 0 \rangle$$ and the commutation relations $$[a({\bf k}),a^\dagger({\bf k'})]=(2\pi)^32\omega\delta^3(\bf {k}- \bf ...
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1answer
1k views

How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$ ?

This question is based on problem II.3.1 in Anthony Zee's book Quantum Field Theory in a Nutshell (I'm reading this for fun- it isn't a homework problem.) Show, by explicit calculation, that ...
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201 views

Nature of Microscopic space-time

I am going through the introductory chapter's of Schwinger's Source theory. He writes, It [Source Theory] is a phenomenological theory, designed to describe the observed particles. No speculations ...
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1answer
32 views

A question about propagator of Maxwell field in different gauge

The propagator of Maxwell theory is different, depending on the gauge fixing procedure used. Then why will the S-matrix elements be the same for the same process in different gauges?
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1answer
58 views

References on $C^{*}$-algerbas, $W^{*}$-algebras and Quantum Theories

I would like to know some references regarding $C^{*}$ and $W^{*}$-algebras and quantum theories. I'm interested in concrete physical applications, models and problems. Here it is the list of ...
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1answer
184 views

Determinant for a coupled fluctuation Lagrangian

Lets consider a bosonic physical system in variables $t, x$ and $y(x)$ ($x$ dependent) with a classical Lagrangian $L$. To first order in fluctuations $x \to x+\xi_1$ and $y \to y+\xi_2$ the ...
3
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1answer
118 views

Negative sign in the Dirac term from the SUSY Kahler potential

I want to calculate the Dirac term from the canonical Kahler potential, \begin{equation} K = \Phi ^\ast \Phi \tag{1} \end{equation} but I'm coming across a pesky negative sign in the final result. I ...
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1answer
182 views

How does the nature of nuclear force change between attractive or repulsive based on distance?

I know that the nuclear force is responsible for binding the protons and neutrons together in the nucleus. The force is powerfully attractive at small separations and rapidly decreases as the distance ...
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4answers
693 views

How exact is the analogy between statistical mechanics and quantum field theory?

Famously, the path integral of quantum field theory is related to the partition function of statistical mechanics via a Wick rotation and there is therefore a formal analogy between the two. I have a ...
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71 views

Functional integral aproach for Feynman rules

I am familiar with the basic ideas of quantum field theory but I feel uncomfortable when I have to derive Feynman rules by myself for a given action (for example in non-linear sigma models or ...
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1answer
62 views

Fermi Energy Variation

What would be a good Internet link that would properly explain Fermi Energy? How does the Fermi Energy of a material vary with external influence, such as doping of the material, and applied ...
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1answer
87 views

How to prove useful property of logarithm of generating functional in QFT?

How to prove that $\ln(Z(J))$ generates only connected Feynman diagrams? I can't find the proof of this statement, and have only met its demonstrations for case of 2- and 4-point.
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1answer
213 views

Feynman propagators for scalar fields

If there are few massless scalar field, are the propagators of those different massless scalar fields indistinguishable?
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1answer
22 views

Why is the periodicity of fields in finite temperature QCD consequence of Trace in the action?

In finite temperature QCD, the gauge fields must be periodic in temporal direction. They say this is the consequence of trace in the action for gauge fields. How does trace imply that the fields must ...
5
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1answer
60 views

Gauge fixing of an arbitrary field

How to count the number of degrees of freedom of an arbitrary field (vector or tensor)? In other words, what is the mathematical procedure of gauge fixing?
2
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1answer
100 views

Connection between QFT and statistical physics of phase transitions

I have heard that there is a deep connection between QFT (emphasized by its path-integral formulation) and statistical physics of critical systems and phase transitions. I have only a basic course in ...
2
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1answer
114 views

How to think about antiparticles in KG equation?

I am a beginner to study QFT and have a problem. I know, in Dirac equation, thanking to the Pauli exclusion principle and believing that the vacuume is the state that all the negative energy states ...
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2answers
215 views

What forbids the existence of a $\lambda (A^\mu A_\mu)^2$ term in the Stueckelberg action?

In QFT, the Stueckelberg "trick" is often used to show how one can write a fully gauge invariant Lagrangian out of one that is not. For example, if we have $\mathcal{L} = ...
2
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1answer
135 views

Lagrangian density of an interacting real scalar field theory

Srednicki writes the Lagrangian density of an interacting scalar field theory as $$ \mathcal{L} = -\frac{1}{2} Z_\phi \partial^\mu \phi \partial_\mu \phi -\frac{1}{2} Z_m m^2 \phi^2 + \frac{1}{6} Z_g ...
9
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1answer
356 views

How to determine if an emergent gauge theory is deconfined or not?

2+1D lattice gauge theory can emerge in a spin system through fractionalization. Usually if the gauge structure is broken down to $\mathbb{Z}_N$, it is believed that the fractionalized spinons are ...
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1answer
75 views

Allowed interactions in bosonic string theory

In a quantum field theory, only a finite set of interactions are allowed, determined by the Lagrangian of the theory which specifies the interaction vertex Feynman rules. In string theory, an ...
8
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1answer
294 views

Nambu-Goldstone bosons from a quantum anomaly symmetry breaking?

We know that: Nambu-Goldstone bosons come from Goldstone theorem: a spontaneous (continuous)-symmetry breaking of the system leads to massless scalar modes. quantum anomaly: is the anomalous ...
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1answer
78 views

QCD string breaking and glueballs

When one tries to pull two quarks appart, a flux tube is created. The tube eventually breaks, creating quark anti-quark pairs and eventually hadrons. Can there also be creation of gluons to form ...
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1answer
166 views

Seiberg-Witten theory and Superconductivity

There seems to have some (deep) relation between Seiberg-Witten theory and superconductivity. e.g. this Witten paper. Q: Could someone introduce the relations between the twos both physically in ...
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3answers
183 views

Green's function for adjoint Dirac Equation

If $S_F(x-y)$ is the Green's function for the Dirac operator $(i\gamma^\mu\partial_\mu-m)$, that is, I assume the following matrix equation holds: $$ (i\gamma^\mu\partial_\mu-m)S_F(x-y)=i\delta(x-y) ...
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0answers
26 views

Understanding Bose enhancement in reheating

I'm struggling to understand the Bose enhancement in reheating. I've read that: At the end of inflation, the inflaton field, $\phi$, is something like a condensate with excitations of a single ...
2
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1answer
147 views

Is there a simple explanation for Schwinger's relation $g=2+\frac{\alpha}{\pi}+{\cal O}(\alpha^2)$ for the $g$-factor of the electron?

Schwinger has on his grave (it seems) the relation between the g-factor of the electron and the fine structure constant: $$g~=~2+\frac{\alpha}{\pi}+{\cal O}(\alpha^2)$$ Did Schwinger or somebody ...
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1answer
111 views

The difference between $\mathcal{N}=2$ short multiplets and BPS states

I have some questions about the construction of $\mathcal{N}=2$ supermultiplets for chiral matter. I know that the supermultiplet should not include spin one states since they are always in the ...
4
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2answers
227 views

QCD in the non-perturbative regime

In the list of unsolved problems in physics. Confinement: the equations of QCD remain unsolved at energy scales relevant for describing atomic nuclei. How does QCD give rise to the physics of nuclei ...
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2answers
109 views

QCD mass gap finite temperature

QCD has a mass gap. Does heating up QCD to a finite temperature change this fact, or is it a property which is independent of temperature?
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1answer
99 views

Renormalizing composite operators

Consider the QED Lagrangian, \begin{equation} {\cal L} = \bar{\psi} ^{(0)} ( i \partial_\mu \gamma^\mu - m ) \psi ^{(0)} - e A _\mu ^{(0)} \bar{\psi} ^{(0)} \gamma ^\mu \psi ^{(0)} - \frac{1}{4} ...
8
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1answer
146 views

Anomalously broken conformal symmetry

I'm trying to understand an argument made by Bardeen in On Naturalness in the Standard Model. The argument is about quadratic divergences in Standard Model. My notation is that the SM Higgs potential ...
7
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1answer
175 views

Generator of local symmetries

Let us only consider classical field theories in this discussion. Noether's theorem states that for every global symmetry, there exists a conserved current and a conserved charge. The charge is the ...
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44 views

Zero Energy States in 2D Systems

Since we are on a planar system (2D system) the massless Dirac equation reads $$\vec{\alpha}\cdot(\vec{p}-e\vec{A})\psi_E=E\psi_E$$ Here Dirac matrices are Pauli matrices ($\alpha^1=-\sigma^2$ , ...
14
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1answer
217 views

Infrared-free QED and Higgsless standard model phenomenology

This is one of those "what if" fantasy world type questions. I like hard sci-fi so please no "well, you changed one thing about the world so now anything goes." :) What if the Higgs had no vev? That ...
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0answers
56 views

Scattering theory of Dirac equation in curved space-time in presence of a strong magnetic field

What is the exact solution of the Dirac equation in curved space-time in the presence of a strong magnetic field? The solution should be in momentum space for simplicity to calculate scattering cross ...
0
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1answer
130 views

Why do we assume that Dirac spinor $\Psi$ describe the particle, not the field?

It is a well-known fact that Klein-Gordon scalar $\Psi(x)$, $$ (\partial^{2} + m^2) \Psi (x) = 0 $$ as well as 4-vector $A_{\mu}(x)$, $$ (\partial^{2} + m^{2})A_{\mu} = 0,\quad ...
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3answers
134 views

Can virtual particles, in particular gravitons, interfere?

Question 1. Can virtual particles, in particular gravitons, interfere? Virtual particles are created and annihilated in a distance too small and a time too short to be measured. Their existence is ...
1
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1answer
82 views

Spin-statistics theorem proof details

Recently I have read one book where there was some incomprehensible proof of the Pauli's spin-statistics theorem. I want to ask about a few details of the proof. First, the author derives ...
3
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2answers
138 views

The Fifth Gamma Matrix

This is regarding $\gamma^5$, the fifth gamma matrix in quantum field theory. I know its defining properties, namely, $$\gamma^5= -i\gamma^0 \gamma^1 \gamma^2 \gamma^3 $$ with ...
2
votes
2answers
114 views

electron in the nucleus

In the event that the electron is in nucleus of the atom (via tunneling effects and other things I don't understand), How does QED deal with this situation?
2
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2answers
49 views

Electron Electric Field Mass?

I am confused of whether or not the expected electromagnetic field generated by the point-like electric charge of the electron distributed smoothly across space as a probability distribution creates ...
2
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0answers
72 views

Entanglement entropy and area law

I am currently reading a review "Area law for the entanglement entropy" by Eisert, Cramer and Plenio (2010). From what I understand: In one dimension, for local gapped models, we have an area law ...
6
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0answers
32 views

Normalization of Source Terms in Large-N Gauge Theory

Typically when you do the counting for large N gauge theory, you rescale fields so that the Lagrangian takes the form \begin{equation} \mathcal{L}=N[-\frac{1}{2g^2}TrF^2+\bar{\psi}_i\gamma^\mu D_\mu ...
7
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2answers
736 views

Is Zitterbewegung an artefact of single-particle theory?

I have seen a number of articles on Zitterbewegung claiming searches for it such as this one: http://arxiv.org/abs/0810.2186. Others such as the so-called ZBW interpretation by Hestenes seemingly ...
5
votes
2answers
199 views

One Loop Higgs Mass Correction

I am attempting to compute the one loop correction to the Higgs mass, which requires the evaluation of a scattering amplitude, namely $$\require{cancel} \mathcal{M} = (-)N_f \int \frac{\mathrm{d}^4 ...
3
votes
1answer
123 views

Paths in the path integral

In the path integral approach one defines in some heuristic way the functional path integral \begin{equation} Z=\int{\cal{D}}\phi e^{iS(\phi)} \end{equation} and the one claims that one must ...
4
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1answer
139 views

CP violation from the Electroweak SU(2)$_{weak,flavor}$ by $\int \theta F \wedge F $

Question: Why there is NO Charge-Parity (CP) violation from a potential Theta term in the electroweak SU(2)$_{weak,flavor}$ sector by $\theta_{electroweak} \int F \wedge F$? (ps. an explicit ...
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0answers
53 views

Why Green's function will diverge at the same spacetime point?

In $d+1$ dimensional quantum field theory, the 2-point Green's function will diverge at the same spacetime point when $d\geq1$. When $d=0$, $\phi(t)=q(t)$, that is the case of QM, and 2-point Green's ...
2
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1answer
113 views

Weinberg dimension 5 operator

How to prove that the $\Delta L=2,$ dimension=5 Weinberg operator $LLHH$ is the unique operator which violates lepton number by two units, without derivative couplings, etc.??