# Tagged Questions

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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### What is the Lorentz group representation for a general spin?

Setup, as I understand things so far: One way to think about where the spin of a quantum field comes from is that it is a consequence of the ways that different types of fields transform under ...
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### Integrated Ward Identity

Suppose you have the following ward identity : $$\int_{M} d^4x\ \epsilon(x)\ \partial_{\mu} \langle j_{\mu}(x)O(y)\rangle = - \ \langle\delta O(y)\rangle$$ where $\delta O(y)$ can be written in the ...
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### What is a soft photon?

I accidentally came across the words "soft photon" today after reading a few blogs. There was some discussion of special situations involving gauge redundancies and a theorem by Weinberg. What is a ...
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### Why do the different lepton generations have different masses?

I've been reading Mark Srednicki's book on Quantum Field Theory, and toward the end (Chapter 88), he describes how the different generations of leptons acquire mass via Yukawa interactions. However, I'...
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### Preference of Chirality

I was interested to see that , $$\gamma^5 \psi = \psi_R - \psi_L$$ By the definition of chirality projection operator and that $\psi = \psi_R + \psi_L$. since $\gamma^5 \psi$ pops up a lot in QED,...
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### SUSY Multiplets

Why is it that in vector supermultiplets, the left and right chiral components of the gauginos must transform in the same representations of all gauge groups, i.e a chiral theory for such fermions is ...
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### Why do we exclude the quark condensate in the OPE?

In every QCD paper I open people say that in the OPE, the lowest order non-trivial condensate is the gluon condensate, whose dimensions are 4. Nonetheless, I knowof the existence of the quark ...
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### Magnetic field of rotating capacitor [duplicate]

Does the rotating charged capacitor (both plates) produce magnetic field? and what about rotating both plates in opposite directions?
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### How could we describe the electric bound state like hydrogen by QED? [duplicate]

We can solve the Schrodinger equation for the Hamiltonian operator from the classical Hamiltonian of hydrogen bound state, consisting of proton and electron attracting each other electrodynamically, ...
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### Has anyone studied anomalous supersymmetry?

In this paper (and others), the authors study a supersymmetric model where the supercharge suffers an ABJ anomaly. Has anyone studied a supersymmetry with a 't Hooft anomaly (gauging the ...
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Below are two statements from my notes and I am trying to verify them explicitly. In both cases the fields are assumed to transform under the fundamental representation of $O(N)$ - --'The kinetic ...
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### Quantum field theory: zero vs. finite temperature

I have recently been made aware of the concept of thermal field theory, in which the introductory statement for its motivation is that "ordinary" quantum field theory (QFT) is formulated at zero ...
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### Concepts regarding BCS Theory of superconductivity and Cooper pairs

I have a little conceptual doubt about the BCS theory of superconductivity. A visual model of the Cooper pair attraction has a passing electron which attracts the lattice, causing a slight ripple ...
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### The Origins of the Second Quantization

I've been studying quantum theory for a while now and have a number of closely related questions that are not giving me any peace. I am not sure if such a long format is appropriate here, but I'd like ...
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### Cutoff-dependent “inverse propagator” for renormalization

In Zee's QFT in a Nutshell, when introducing mass renormalization, he calculates the "inverse propagator" for a $\phi^4$ scalar field theory to order $\lambda^2$ by considering the two diagrams shown: ...
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### Gravity modeled by warping of spacetime or by field field theory?

I've recently read "Fields of Color" by Rodney Brooks who states that there are currently two ways of understanding the phenomenon of gravity. One involves a warping of 4D spacetime a la Einstein, ...
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### Why would renormalization be necessary without divergent integrals? [duplicate]

Weinberg uses the LSZ reduction formula to introduce field renormalization,and on page 441, he says: As this discussion should make clear: the renormalization of masses and fields has nothing to ...
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### Electroweak instanton calculations

Consider an electroweak instanton in a model beyond the Standard Model with explicit baryon plus lepton number ($B+L$) violation. This instanton decays into nine quarks $q$ and three leptons $l$, ...
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### Polarization vectors in Quantum Electric Field

The quantum electric field is written as, \mathbf{E}(\mathbf{r})=i\sum_{\mathbf{k},\lambda}\sqrt{\frac{\hbar \omega}{2 V \epsilon_0}}\left(\mathbf{e}^{(\lambda)}\hat{a}^{(\lambda)}(\...
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### Is the Noether charge always a Hermitian operator?

Noether's theorem tells us that to every continuous symmetry of the Lagrangian there corresponds a conserved current $j^\mu$. From the time component of this current, we can then define the Noetherian ...
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### Is Lorentz invariant differential measure arbitrary?

In Srednicki, we chose a function $f(\mathbf k)$ to make $d^3\mathbf k/f(\mathbf k)$ Lorentz invariant. The way to do this is to first start from a 4 dimensional measure and multiply it by a Dirac ...
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### relation between operator and matrix

Recall that in quantum mechanics, the three components of s of a spin-$\frac{1}{2}$ particle satisfied the anticommute relation: $$\{s^i, s^j\}=\delta^{ij}$$ and we could parametrize the operators ...
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### Feynman Propagator in Peskin & Schroeder

To prove Wick's Theorem, Peskin & Schroeder define the contraction of two fields: \begin{align} \text{Contract}[\phi(x)\phi(y)]\equiv \begin{cases} [\phi^+(x),\phi^-(y)] & \text{for }x^0>y^...
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### Does there exist finite dimensional irreducible rep. of Poincare group where translations act nontrivially?

I read several textbooks of QFT and find that there are two ways to classify the particles or fields. The first one is to study the irreducible representation of Lorentz group (or exactly the ...
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### Single particle state in $\phi^4$ theory

I'm quite happy with the idea that a multi-particle state in a free scalar field theory has a discrete energy spectrum, and that turning on a quartic coupling $\frac{\lambda}{4!}\phi^4$ acts as a ...
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### What is the axial current?

The axial current is defined as $$j^\mu_5 = \bar{\psi} \gamma^\mu \gamma_5 \psi.$$ This quantity is important when studying anomalies. Explicitly working out components, the axial current is just the ...
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### Decay width in 2 & 3 body decays, calculating momentum integrals

I'm considering a toy model with two types of scalar particles, one massive $(\Phi)$ and one massless $(\phi)$ with an interaction of the form $$L_{int}=-\lambda \phi\phi\Phi$$ I'm interested in a ...
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### Feynman rules from interaction Lagrangian with electromagnetic tensor (vertex)

I am currently studying for my QFT exam and in particular learning the methods of reading the Feynman rules directly off the Lagrangian. However, I'm still a bit uncertain how to deal with ...
I've been reading about the quantisation of the Dirac field $\psi(x)$ and it is stated that the general solution to the Dirac equation $(i\gamma^{\mu}\partial_{\mu}-m)\psi(x)=0$ is given by the ...
This is probably a simple question. Von Neumann entropy is defined to be $$S_A=-tr_A\rho_A \log\rho_A$$. And it's said that it can be calculate from the "Replica trick": S_A=\lim_{n\to 1}\frac{tr_A \...