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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Probability of $\alpha$-decay

In standard Gamow model we assume that $\alpha$ particle is already in the nucleus, i.e. four nucleons are "glued" together and this particle is emitted. So, we assume that the probability of the ...
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What are the actual conventions for the standard model particles' intrinsic parities?

It is known that by fixing the intrinsic parity of three particles with linearly independent quantum numbers B, L and Q, the other particles' parities are fixed by the request that parity be conserved ...
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zee model of radiative neutrino mass

Without computing the expression for radiatively generated neutrino mass matrix $M_{\alpha\beta}$, in Zee model, is it possible to guess that the diagonal elements of the mass matrix vanishes? I ...
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61 views

Making mathematical sense on a Feynman's path integral equation

Usually we find this relation in the context of Feynman's path integral (see, for example, Maggiore's book on QFT, pg 223): $ \int_{q_i}^{q_f}[dq] = \int_{-\infty}^{\infty}d\bar{q}\int_{q_i}^{\bar ...
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21 views

Comoving and physical momentum in a Friedmann universe

It is most probably a very basic question, but I'm a bit stuck with it. Let us consider a spatially flat Friedmann universe with the usual metric ...
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27 views

Evaluating Compton scattering cross-section

In deriving the cross-section of Compton scattering, we require to perform the polarization sum $$\sum\epsilon_{\mu}\epsilon_{\nu}\sum\epsilon_{\alpha}\epsilon_{\beta}$$ using the identity ...
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30 views

Why doesn't the four-gluon vertex give mass to gluons?

We have a four-gluon vertex and a gluon vacuum condensate. Why doesn't this provide us with gluon masses, as in the NJL model where the condensate gives rise to an effective mass term?
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51 views

How to relate classical field and quantum operator?

Recently I listened to a lecture from perimeter institute. There was an idea which I found interesting. That is, roughly, for a field $\phi(x)$ we can assume the relation with the creation operator ...
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52 views

Decomposing massless N=8 SUGRA multiplet into multiplets of massless N=4

The only massless $N=8$ SUGRA multiplet is given by $(g_{\mu\nu},\psi_\mu^{\Sigma},A_\mu^{[\Sigma\Pi]},\chi_{\alpha}^{[\Sigma\Pi\Lambda]} ,\phi^{[\Sigma\Pi\Lambda\Omega]})$ where the greek upper ...
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61 views

Relation between the reduced Green's function and the full Green's function

Let us assume that we have some Hamiltonian and we know its spectrum $$H_0 \psi_n = E_n \psi_n .$$ We define the Green's function in as $$ G(x,y,E) =\sum_m \frac{\psi_m^*(x)\psi_m(y)}{E-E_m}, $$ and ...
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63 views

Why do the conserved charges in the case of SSB of a global symmetry not exist?

Reading "From Linear SUSY to Constrained Superfields" by Komargodski and Seiberg, I got a bit confused regarding the existence of the conserved charges in a theory with spontaneous symmetry breaking ...
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68 views

Definition of partity in quantized Dirac Theory.

I'm studying from the book "An Introduction to Quantum Field Theory" from Michael E. Peskin and Daniel V. Schroeder, and I read the following: "The operator P should reverse momentum of a particle ...
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74 views

What is spin in QFT, non-relativistic QM, and classical physics? When can we ignore spin? [closed]

In section 4.1.1 of quantum field theory book by M. Schwartz, the author wants to calculate electron scattering by photons and writes the following interaction: $$ V= \frac{1}{2}e\int dx ...
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46 views

Lorentz group in SUSY

Why do we carry Lorentz group to be included also in supersymmetry? That is after we extend our symmetry to supersymmetry, we carry with us the Lorentz group. Why not other group instead?
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Baryonic operators in ${\cal N}=1$ $U(N)$ SQCD in four dimensions

Seiberg's duality is usually considered as a duality for $SU(N_c)$ theories with $N_f$ flavors. In his case, the vacuum for $N_f \geq N_c$ is parameterized by mesons $M$ and baryons ${\bar B}$ and ...
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45 views

Why is the angular momentum added for two independent electron system? (no problem)

There is no problem now. But somebody may be confused by the same analysis when studying QM or Group theory. (actually my motivation for asking this question comes from the SU(5) Grand Unification ...
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47 views

Quantum field theory text on entanglement entropy

I am looking for a quantum field theory book in which entanglement entropy for quantum fields is explained but I can not find such a book. Is there such a book?
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Canonical second quantization vs canonical quantization with multisymplectic form in AQFT

First of all, I'm a mathematician that knows less than the basics of QFT, so forgive me if this question is trivial. Please, keep in my mind that my background in physics is very poor. 1) The usual ...
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750 GeV diphoton resonance: KK graviton?

As everybody of you may know at LHC they found this probable resonance (https://cds.cern.ch/record/2114808, https://cds.cern.ch/record/2114853?ln=en). It may be a scalar or a KK graviton mode. Now, ...
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54 views

Is spin angular momentum conserved?

According to the Noether theorem, we only have the conserved quantity $$J+S,$$ where $J$ is the orbital angular momentum and $S$ is the spin angular momentum. But I am always impressed that the spin ...
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36 views

Construct fields from from unitary representation of Poincaré group

I am trying to understand how construct fields from unitary representation of Poincaré group and the reasoning that Weinberg give in his book is the cluster decomposition principle and Lorentz ...
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33 views

Is there any book on the level of Weinberg [duplicate]

I'm searching for a book on the level of Weinberg quantum field foundation. Is there anyone?
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52 views

How to construct fields from from unitary representation of the Poincaré group?

I want to construct fields from unitary representation of the Poincaré group but I do not know how. In Weinberg book he proposed that the Hamiltonian should be of certain kind and from that he derived ...
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39 views

How operators transforms

I know that Under lorentz transformation states transfrom as $\sum_i C_{ij} |\Lambda p,j >$.But how can we prove from this that operators should transform as $U^\dagger(\Lambda) \Phi_k(x) ...
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What is the precise duality between spin systems and gases on a lattice?

In Operator Algebras and Quantum Statistical Mechanics : Equilibrium States. Models in Quantum Statistical Mechanics by Bratelli, Quantum Spin Systems on a $\nu$-dimensional lattice are stated to have ...
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45 views

multi-dimensional renormalization group flow?

Suppose you have $\lambda \phi^3$ theory, and that you renormalize the 2 and 3 point one-particle irreducible graphs, $\Pi_R(p^2)$ and $\Gamma_R(p_1,p_2,p_3)$, by Taylor expanding about $p=\mu_0$ for ...
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Renormalization Group Invariance of Scattering Amplitude

How can one show that the scattering amplitude is renormalization group invariant using the fact that the bare Green's function $G_0^{(n)}$ is renormalization group invariant? We have: $(1) \quad ...
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Mass difference in particle oscillation from weak lagrangian

Looking for an answer to how an expression to $\Delta M = M_2 - M_1$ arise in QFT I have found the approximation \begin{equation} \Delta M_K \approx \frac{G_F^2}{4\pi} m_K f_K^2 \sum_{q=u,c,t} m_q^2 ...
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78 views

Which are some best sources to learn Algebraic Quantum Field Theory (AQFT)?

Which are some best sources to learn Algebraic Quantum Field Theory (AQFT)? I am a beginner and I am currently following Haag's Local Quantum Physics and feel like I need some more notes or some ...
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38 views

What does a body visible to the human eye moving at constant speed look like in QFT?

In regular $QM$ A single particle is going to have a wave function that solves the free schrodinger equation of energy and momentum such that $$dE/dp = v$$. Obviously the sense of nearness of ...
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54 views

Poincare group representation and complete set

In Weinberg's book of Qft, chapter 2 of volume 1, he uses the eigenstates of the four-momentum to construct the unitary irreducible representations of the Poincare group. My question is, since ...
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187 views

Is “quantizing” a field different from “quantizing” a particle?

As I understand it, quantum mechanics for particles was developed to replace classical mechanics for particles. In essence, we realized that particle cannot be given an exact place and momentum but ...
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57 views

Am I understanding correctly the argument that leads to the need for field and mass renormalization?

I'm studying Quantum Field Theory from Weinberg's book, and I'm to the point where he introduces the concept of renormalization. I'd like to know if I'm getting the point that Weinberg makes when ...
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151 views

Symmetry at quantum level in quantum field theory

In nonrelativistic quantum mechanics, a symmetry is a transformation on states in the Hilbert space which keeps the Hamiltonian invariant and this implies that the generator of the transformation must ...
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45 views

Is the Symmetry factor different in Path integral Formalism?

Is the Symmetry factor different in Path integral Formalism and the Perturbation theory (canonical) formalism? For example, the order-1 4-point cross X diagram in the $\phi^4$ theory has symmetry ...
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41 views

Complex scalar field coupled to real scalar field - how are amplitudes non-zero?

Given a Lagrangian coupling a complex scalar field $\psi$ to a real scalar field $\phi$: $$\mathcal{L} = \frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi + \partial_{\mu}\psi\partial^{\mu}\psi^*+ ...
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98 views

Enhancing the QED $U(1)$ gauge symmetry

QED is a gauge theory based on $U(1)$ gauge symmetry, which gives rise to photon as the gauge boson mediating the interaction. Mathematically, I think it is perfectly allowed to implement a ...
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90 views

What's wrong with my Quantum Early Warning System (Thought Experiment) [closed]

I'm a lay physics enthusiast and I came up with a thought experiment that I can't fully wrap my head around: Alice and Bob are worried about an impending attack by the dreaded Xenomorphs, so they ...
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122 views

What justifies the dependence of the coupling renormalization constant in the dimensional regularization regulator?

I wanna clarify some issues about renormalization in the $\bar{MS}$ scheme that I glossed over when I first learnt about this stuff. I am following http://arxiv.org/abs/1411.7853 section 3.1. The ...
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Doubt performing a Borel transform in the review by Beneke

This is strictly speaking a math question which nonetheless appears in a physics context and I believe it may be better to ask it here. In any case, consider page 6 on section 2 in the following ...
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26 views

Correct Yukawa Term with a SU(2) Higgs Triplet?

Given $SU(2)$ doublet fermions $\Psi^1$ and $\Psi^2$ and a $SU(2)$ triplet Higgs $H$, how does the correct Yukawa term look like in tensor notation? Schematically, we have $$ 2 \otimes 2 \otimes 3 ...
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35 views

Can I use Pauli-Villars and dimensional regularization together?

There are at least two ways to compute the electron-self energy. You can use Pauli-Villars or dimensional regularization, for example. On Weinberg's book, it's chosen the first method, while on my ...
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63 views

Non-perturbative effects: classical or quantum?

Are non-perturbative effects (solitons) classical or quantum effects (corrections) ? (examples ?) My confusion stems from the fact that, for instance, an instanton is a classical solution of the ...
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260 views

Self Teaching QFT

I am currently in the process of teaching myself QFT. It is not an easy task. I have armed myself with many of the standard textbooks. However, I am slow learner. I get stuck on a thousand ...
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39 views

2-loop $\phi^4$ at finite temperature [closed]

When evaluating diagrams that contribute to the 2-loop effective potential $V_{eff}$ in $\lambda \phi^4 $ theory at finite temperature one has to calculate diagrams of such type which equals to ...
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Non-Linear Behavior of Iterated Functional Maps

The universal behavior of certain iterated nonlinear function maps (ie period doubling bifurcation route to chaos): $$x_{i+1}=f(x_i)$$ have been known since Feigenbaum: (see ...
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83 views

How does one compute position and momentum in QFT?

In QM one takes the inner product (phi|x|phi) and (phi|p|phi) to compute the position and momentum expected values, but what does one do in QFT? What is the relationship to the wavefunction in QM to ...
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Charge Conjugation for $SU(N)$?

For $SU(2)$ the charge conjugation operator $C$ reads explicitly $$ C \Psi = i \sigma_2 \Psi^\star ,$$ where $\sigma_2$ is a Pauli matrix. What is the generalized charge conjugation for $SU(N)$?
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Book Recommendation for relativistic scattering theory [duplicate]

I am looking for books on relativistic scattering theory with particular emphasis on application to experimental high energy physics. Does anyone have excellent recommendation?
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161 views

What is the effective (quantum) lagrangian of a fermion field for fixed electromagnetic field?

... or, put it another way, what are the loop corrections to the dirac equation in the presence of a fixed (external) electromagnetic field?. Background Let $\mathcal ...