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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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, ...
12
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1answer
196 views

Explaining causal completion axiom in Haag-Kastler axioms?

There are several variants of the Haag-Kastler axioms for algebraic quantum field theory. Usually one associates an algebra $\mathcal{A}(O)$ to each open region $O$ of spacetime. An often-suggested ...
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2answers
528 views

Why do single particle states furnish a rep. of the inhomogeneous Lorentz group?

Following up on this question: Weinberg says In general, it may be possible by using suitable linear combinations of the $\psi_{p,\sigma}$ to choose the $\sigma$ labels in such a way that $C_{\...
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0answers
24 views

Construction of Primaries of WZWN CFT

Is it possible to construct primaries of $SU(2)_{k+1}$ by using primaries of lower levels?. E.g. If I have a primary of $SU(2)_2$, let's say $\Phi^{(1/2)}$, the field with spin $1/2$ and another ...
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1answer
164 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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1answer
111 views

Pseudoscalar particle decay

Suppose I want to calculate amplitude of pseudoscalar particle decay into electron + positron. Interaction Hamiltonian is given by (ignoring the positive and real constants) $\mathcal{H} = \bar{\psi} \...
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0answers
106 views

Are strings in string theory actually little black holes? [closed]

I sometimes read that strings in string theory are actually little black holes, or can be interpreted that way. Is this true? How is that consistent with that the particle that a string represents ...
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1answer
65 views

What is the difference between worldsheet supersymmetry and spacetime supersymmetry?

What is the difference between worldsheet supersymmetry and spacetime supersymmetry? For worldline formulation of fermions quantum mechanics, there is a supersymmetry. But the corresponding spacetime ...
2
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1answer
73 views

R-matrix and S-matrix in QFT

In the study of quantum field theory, one may encounter S-matrix a lot. Recently, in the study of integrability, I encountered R-matrix formulation which I am not familiar with. First of all, the S-...
2
votes
3answers
208 views

Complex scalar field theory

For the complex scalar field theory $$L = -\partial_{\mu}\phi^{*}\partial_{\mu}\phi - m^{2}\phi^{*}\phi + J\phi^{*}+J^{*}\phi,$$ Why is there no factor of 1/2 in the lagrangian like in the real ...
106
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2answers
12k views

Why do we not have spin greater than 2?

It is commonly asserted that no consistent, interacting quantum field theory can be constructed with fields that have spin greater than 2 (possibly with some allusion to renormalization). I've also ...
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1answer
50 views

Vacuum persistance amplitude

E. Fradkin's Field Theories in Condensed Matter Physics formulas 3.57 and 3.58: I feel really sad about it, but all my tries of getting from formula $$ Z = \operatorname{tr} \hat{T} \prod_{j=1}^{...
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3answers
247 views

Are there Gauge fields that are not 4-vectors?

In my understanding Gauge fields are fields that have some kind of redundancy, i.e. a transformation that does not change the physical state. As far as I can see all the Gauge fields in the Standard ...
3
votes
1answer
155 views

S-matrix in Weinberg QFT

I'm a bit confused by Weinberg's discussion of scattering. He defined the in and out states $|\Psi^{\pm}_\alpha\rangle$ with particle content $\alpha$ as states that transform under the Poincare group ...
2
votes
2answers
128 views

What is the meaning of the size of an elementary particle in QFT? What is the meaning of a point particle? [duplicate]

I have often seen people refer to the size of a particle being at most a given value, or a particle being a point particle, in the context of quantum field theory. Examples are the Wikipedia entry on ...
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2answers
460 views

How are the field operator and quantum state after a beam splitter and a polarizing beam splitter individually?

How are the field operator $\hat{a}$, $\hat{a}^\dagger$ and the quantum state (like coherent state $|\alpha>$, Fock state $|n>$) changed after a beam splitter and a polarizing beam splitter ...
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votes
1answer
412 views

Momentum Space Renormalization of $\phi ^6 $ Model

I'm trying to find the RG flow to lowest order in $\epsilon = 3 -d $ for the energy functional: $$ f=\frac{1}{2} \phi ^2 +u \phi ^6 +\frac{c}{2} (\nabla \phi ) ^2 $$ where $\ d$ is the dimension we'...
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25 views

Multi-Cut Matrix Models

I have a question pertaining specifically to a one-matrix model with a multi-cut solution. The standard procedure is to take a polynomial superpotential $W(x)$. In the classical limit (analogous to $...
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0answers
53 views

Does Feynman parametrization commute with derivative?

Let $I = \int \frac{d^4k}{(2\pi)^4} \frac{(p+k)\cdot\gamma}{(p+k)^2-m^2+i\epsilon} \frac{1}{k^2+i\epsilon}$ I would like to do two operations on the integral, namely Feynman parametrization and $\...
6
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1answer
78 views

What is the mathematical motivation for complexifying momenta in BCFW?

One of the first steps in obtaining the on-shell BCFW recursion relations is complexifying the momenta of the external particles. Now complexifying things is not unprecedented (the dispersion program ...
4
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1answer
205 views

Temperature in the Hamiltonian limit

There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
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1answer
64 views

Such a huge mass for Higgs boson? And how can it, as a quantum, decay?

With a mass of 126GeV/c2 Higgs boson would have a mass slightly greater than a caesium atom. Isn't it too much? Wouldn't be in this way the ubiquitous Higgs field so dense to cause problems for the ...
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1answer
54 views

How to define the distance between two points in a conformal transformed space?

Consider a particular conformal transformation $x^\mu\rightarrow x'^\mu$, and the metric of a flat space transforms in the following way, $$\eta_{\mu\nu}\rightarrow g'_{\mu\nu}=\Lambda^2(x)\eta_{\mu\...
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1answer
278 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 $$\Delta_{lm}(x,y)=\theta(x-y)P^{(L)}_{lm}\left(-...
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1answer
180 views

Singlet neutrinos decaying to Higgs bosons during leptogenesis

(i) The Lagrangian of electroweak model extended with right-chiral singlet neutrinos $N_{iR}$ contains the Yukawa coupling term+ the bare Majorana mass term $$f_{\alpha i}\overline{l_{L\alpha}}\hat\...
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9answers
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Is the wave-particle duality a real duality?

I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. I most recently heard this in this video. However, I wonder; is this actually a duality? ...
2
votes
2answers
55 views

Does QFT modifies Quantum Mechanics? [duplicate]

The basis of Quantum Mechanics is contained in the postulates which tell us how to describe quantum systems (below I disconsider possibly degenerate spectra just for simplicity): To describe a ...
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1answer
110 views

A question from A. Zee's book

On page 463, it writes in eq. (3) $$4H=\Sigma_\alpha(Q_\alpha Q^\dagger_\alpha+Q^\dagger_\alpha Q_\alpha).\tag 3$$ And then it writes that this is followed by eq.(4) as $$\langle S| H|S\rangle=\frac{...
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0answers
38 views

Is it possible in this Universe to communicate a bit of information with energy that scales sub-linearly with distance?

If we look at all the ways that people do communicate information, they all seem to have a cost "at least linear in distance." For example, communicating over a wire has attenutation, so the energy ...
4
votes
1answer
86 views

Is the usage of the Fock space a postulate in QFT?

In this question, when I write Fock space, I mean "the direct sum of the symmetric or antisymmetric tensors in the tensor powers of a single-particle Hilbert space H", as it is described by Wikipedia. ...
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1answer
54 views

Connection between “classical” Grassmann variables and Heisenberg Equation of motion

I have been reading di Francesco et al's textbook on Conformal Field theory, and am confused by a particular statement they make on pg 22. Let $\{\psi_i\}$ be a set of Grassmann variables. Starting ...
3
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1answer
41 views

Experimental observation of non-perturbative effects

Many quantum field theories come with non-perturbative objects such as solitons and instantons, and non-perturbative effects such as the Schwinger effect. However, it is hard to find any review on ...
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0answers
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What is a method of finding minima of the one-loop effective potential?

Say you have a theory with an arbitrary number of real scalars, and you wants to find their Vevs in the global one-loop vacuum. How is this accomplished?
4
votes
1answer
45 views

Polarization vectors in Quantum Electric Field

The quantum electric field is written as, \begin{equation} \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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0answers
71 views

How do we compute correlation function in the Schrodinger picture?

From concreteness' sake consider $\phi^4$ theory with a real scalar (even though the choice of the theory has nothing to do in principle with what I am going to ask). Consider thefollowing ...
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5answers
521 views

Why Does Renormalized Perturbation Theory Work?

I've read about renormalization of $\phi^4$ theory, ie. $\mathcal{L}=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-m^2\phi^2-\frac{\lambda}{4!}\phi^4\,,$ particularly from Ryder's book. But I am ...
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0answers
50 views

A few questions concerning one loop corrections to the action

When we perform a Legendre transform on the connected generate functional $W[J]$ we get the quantum action (or 1PI action) $ \Gamma[\phi] = W[J(\phi)] - \int\mathrm{d}^4x\,\phi J,\quad\phi(J)=\frac{\...
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1answer
205 views

Wilsonian vs 1PI

As a follow up to Difference between 1PI effective action and Wilsonian effective action, where can I find pedagogical material that highlights the similarities and differences between the 1PI and ...
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0answers
22 views

Gaussian Model scaling fields

last week one of my lectures mentioned the "scaling fields" for the 2D Gaussian Model, $\Phi = e^{\pm ip\phi}$ but did not give any further explanation what that means or where that comes from. ...
0
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1answer
59 views

Solving a step in the derivation of the anomalous magnetic moment of the electron

In the book An Introduction to Quantum Field Theory by Peskin and Schroeder there is a derivation of the anomalous magnetic moment of the electron. The Feynman diagram to be solved is this one: and ...
21
votes
7answers
3k views

Reading list in topological QFT

I'm interested in learning about topological QFT including Chern Simons theory, Jones polynomial, Donaldson theory and Floer homology - basically the kind of things Witten worked on in the 80s. I'm ...
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2answers
942 views

History of the names “Feynman-gauge” & “Landau-gauge”. How arised & how settled?

Edit: Use this PO.org question instead. Warning: Students, stay away from antiquities. The aim to learn is to survive. Hi. Today the nomenclatures Feynman gauge and Landau gauge seem established, ...
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0answers
83 views

Wilsonian Renormalisation — Peskin & Schroder Sect. 12.1

I'm working my way through Peskin & Schroeder, but some of the details of the calculations done in their introduction to the renormalisation group are slipping past me. For concreteness, the ...
0
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0answers
44 views

Fine Structure and Fine Structure Constant - intuitive relation?

How does the fine structure and fine structure constant relate to each other, intuitively? I've seen $\alpha$ extrapolated as a term in energy calculations for fine structure, but is there a ...
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0answers
41 views

Doubts about the theta angle and the ground state energy density in Euclidean Yang-Mills theory

I am reading the following notes https://munsal.files.wordpress.com/2014/10/marino-lectures2014.pdf. On section 4.3 the euclidean Yang-Mills theory is considered. It is said that renormalizability and ...
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2answers
254 views

From Quantum Mechanics to Quantum field theory to String theory?

Today during a very "unique" study session, I might have internalized why Quantum mechanics was not enough, and Quantum field theory makes sense. It seems the reasons are that When a potential is ...
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1answer
62 views

About the non-locality of gravitational energy 2

Gravitational energy is non-local which is essentially because of the equivalence principle. The equivalence principle says that you can always transform your frame so that you feel like in a ...
2
votes
2answers
163 views

Quantum Operators: An Identity

I came across the following neat property: For an operator $\hat{A}$ which is a linear combination of creation and annihilation operators, we have: $$ \langle e^{\hat{A}} \rangle = e^{\langle \...
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1answer
84 views

Wick renormalization

I'm trying to understand the Wick renormalization in the framework of the Ito integral. I saw the Wick theorem as presented on Wikipedia in a QFT course and I would like to understand how that is ...