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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Casimir forces and its associated Feynman propagator

This is a continuation to my previous question, in which I began an attempt solve the Casimir Force problem using path integrals. As one of the answers there suggest I solve the Feynman propagator ...
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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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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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27 views

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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103 views

How can we calculate pion decay constant in Chiral Perturbation Theory ?

Above diagram is an one-loop contribution to the Pion decay constant $f_\pi$. For example in this paper (Eq.7) they have written down the pion decay constant to one loop, but the calculation is not ...
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138 views

Derivation of eq 6.17, Peskin and Schroeder

I am having trouble following a derivation in Peskin and Schroeder's textbook, namely equation 6.17 on page 182. It seems benign at first, but I am completely stuck. Essentially, we have an expression ...
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1answer
43 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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1answer
483 views

Eikonal approximation in QFT

Does the eikonal approximation for calculating a scattering amplitude in QFT provide the exact result in the limit of $s\rightarrow\infty$ at finite $t=0$ ($s$ and $t$ are the usual Mandelstam ...
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2answers
2k views

What's the relation between virtual photons and electromagnetic potentials?

Given that: 1) virtual photons mediate the electric and magnetic force fields 2) the magnetic field is the curl of the magnetic vector potential 3) the electric field is the negative gradient of ...
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198 views

Heat kernel expansion for entanglement entropy

Can somebody please let me know where I can find a reference for calculating heat kernel coefficients on a manifold with conical singularities? I am trying to compute the entanglement entropy for ...
2
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1answer
266 views

Entanglement entropy for $U(1)$ lattice gauge theory

Can someone please let me know if there is some reference for the calculation of entanglement entropy of $U(1)$ lattice gauge theory? I have seen a few references where Z2 lattice gauge theory has ...
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0answers
45 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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2answers
147 views

Doppler effect of matter waves

We all know that the relativistic mass of a moving object in Special relativity increases for an observer who is measuring it for a moving object. We also know the the concept of particle-wave ...
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99 views

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 ...
3
votes
1answer
427 views

Unitary Lorentz transformation on quantized Dirac spinor

I am stuck again on page 59 of Peskin and Schroeder. In particular, I do not know how they get equation (3.110). Let me first give some background in the way that I understand it (but I might be ...
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0answers
161 views

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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1answer
53 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 ...
8
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1answer
451 views

Is this field redefinition for free scalar field theory non-local?

The action of free scalar field theory is as follows: $$ S=\int d^4 x \frac{\dot{\phi}^2}{2}-\frac{\phi(m^2-\nabla^2)\phi}{2}. $$ I have been thinking to redefine field as ...
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3answers
169 views

How can quantum wavefunctions be smooth/continuous when particles are created/destroyed/changed?

My (admittedly limited) understanding of the Schrodinger equation tells me that the vector differential operators are only meaningful over a differentiable phase space. For example, if the dimensions ...
0
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1answer
135 views

Expanding free scalar field in terms of ladder operators

I'm having some difficulty with the finer points of expanding a field in terms of ladder operators. Note that this is not identical to the other related question I asked. From Peskin / Schroeder; ...
9
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2answers
393 views

Peskin's book page 334 proof of $Z_1=Z_2$ to all orders in QED perturbation theory

Peskin in his QFT page 334 argued that $Z_1=Z_2$ to all orders in QED perturbation theory, but I couldn't understand his argument: ... With a generalization of the argument given there (section ...
95
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0answers
6k views

Superfields and the Inconsistency of regularization by dimensional reduction

Question: How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)? Background and some references: ...
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2answers
410 views

Eigenstate of field operator in QFT

Why don't people discuss the eigenstate of the field operator? For example, the real scalar field the field operator is Hermitian, so its eigenstate is an observable quantity.
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1answer
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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0answers
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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0answers
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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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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13 views

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 ...
4
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1answer
254 views

A question about the implication of UV divergence in QFT

I have a basic question about the logic of renormalization in quantum field theory (QFT). We met the ultraviolet (UV) divergence in loop corrections. The standard argument is, our current field theory ...
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3answers
148 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 ...
9
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1answer
214 views

Non-covariance of the higher rank propagator (from Weinberg's QFT textbook)

In chapter 6.2 of Weinberg's QFT Vol.1, he gave the general form of Wick contractions of all possible fields(scalar, spinor, vector, etc.), he showed ...
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4answers
793 views

Why the Hamiltonian and the Lagrangian are used interchangeably in QFT perturbation calculations

Whenever one needs to calculate correlation functions in QFT using perturbations one encounters the following expression: $\langle 0| some\ operators \times \exp(iS_{(t)}) |0\rangle$ where, ...
4
votes
1answer
367 views

Fierz identity for Weyl spinors in tensor currents

Using Fierz identity I found that certain four-fermion operator with left $l_i$ and right-chiral $r_i$ Weyl spinors vanish $\bar{l}_1\sigma_{\mu\nu} r_2 \bar{r}_3 \sigma^{\mu\nu} l_4 =$ $ ...
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33 views

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 ...
3
votes
1answer
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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18 views

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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3answers
2k views

Equation of everything

Is this equation in the image true? Can you give some topics that I can cover the equation? Similar equation from http://www.preposterousuniverse.com:
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1answer
250 views

What is the relation between the representation the Higgs field transforms under, the types of couplings in the theory and Higgs/Coulomb branches?

When reading about Higgs and Coulomb 'phases' I came across two separate definitions: The first tells us that the Higgs/Coulomb phases are determined by the representation that the Higgs field ...
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0answers
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 ...
6
votes
3answers
255 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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1answer
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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3answers
182 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 ...
19
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1answer
3k 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 Show, by explicit calculation, that $(1/2,1/2)$ is the Lorentz Vector. I see that the ...
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0answers
56 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 ...
0
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0answers
44 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 ...
0
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1answer
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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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^*+ ...
3
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1answer
362 views

QFT question, scalar field and so on

$\newcommand{\bbraket}[3]{\langle #1 | #2 | #3 \rangle} \newcommand{\ket}[1]{|#1\rangle} \newcommand{\bra}[1]{\langle #1 |}$ I have such a problem with a proof. I'm studying the two point correlation ...
2
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1answer
89 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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0answers
64 views

Question about interacting fields and feynman diagrams [closed]

The picture is taken from Chapter 4: 'Interacting Fields and Feynman Diagrams in An Introduction to Quantum Field Theory by Peskin and Schroeder. There is a two point correlation function ...