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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Understanding CP-violation from a toy model of two fermions and a scalar boson

Consider a field theory given by the following Lagrangian $$\mathcal{L}_{int}=y\overline{\psi_1}\psi_2\phi+y^*\overline{\psi}_2\psi_1\phi^\dagger$$ where $\phi$ is a complex scalar field, and $\psi_1,\...
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614 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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30 views

constraints on quartic interaction coefficients in double scalar field Lagrangian

Consider the 4-dimensional Lagrangian density with two real scalar fields $\phi_1$ and $\phi_2$: $$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi_1 \partial^{\mu}\phi_1 + \frac{1}{2}\partial_{\mu}\phi_2 \...
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Is it possible that the Big Bang was caused by virtual particle creation?

As far as I understand, it is understood that throughout the universe there exists, what is known as, a quantum field from which, due to its fluctuations, temporary (pairs of) virtual particles ...
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733 views

Conservation of Energy and Quantum Fluctuations

Regarding conservation of mass-energy Wikipedia says: "this is an exact law, or more precisely, has never been shown to be violated." However, regarding quantum fluctuations, Wikipedia says here: "...
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64 views

What is the matrix representation of the momentum operator (generator of translations) that is used in the commutators of the Poincaré Group?

So the commutators of the Poincareé group are given by \begin{eqnarray} [J_{i},P_{j}]=i\epsilon_{ijk}P_{k}, \quad [J_{i},J_{j}]=i\epsilon_{ijk}J_{k}, \quad [J_{i},K_{j}]=i\epsilon_{ijk}K_{k}, \quad [...
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30 views

Construction of vector bundles of relativistic fields by Mackey's method of induced representation

I recently stumbled on Sternberg's book on group theory and physics. The ideas expressed in the book are really great, but the detailed reasoning is very hard to follow, I find. I am kind of stuck ...
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75 views

Does the Flavor symmetry forbid $uu\rightarrow cc,ss$?

This question comes from the reading of this paper. They suppose a flavor symmetry group $G_F = U(3)_q\times U(3)_{d} \times U(2)_{d}$ which acts on the three LH quarks $q_L$, three RH quarks $u_R$ ...
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46 views

Defining Thermodynamic beta in unit of second

If I define Thermodynamic beta in unit of second. Does this mean that: Boltzmann constant $k$ is unit-less? $T$ is in units of frequency (Hz) or Kelvin $K$? In this case, is defining Thermodynamic ...
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308 views

Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
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21 views

Is the reduction of tensor loop integrals to scalar integrals using Passarino Veltman Functions, theory dependent?

While reducing the tensor integrals to scalar integrals all that we use are Lorentz covariance and the physical interpretation of the result. Thus I think that the Pa Ve Reduction of Tensor integrals ...
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517 views

How to compute the normal ordered angular momentum of a Klein-Gordon real scalar in terms of ladder operators?

I'm trying to compute the angular momentum $$Q_i=-2\epsilon_{ijk}\int{d^3x}\,x^kT^{0j}\tag{1}$$ where ${T^\mu}_\nu=\frac{\partial\mathcal{L}}{\partial(\partial_\mu\phi)}\partial_\nu\phi-{\delta^\mu}_\...
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150 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 ...
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42 views

Interpretation of the mass of the field

Before QFT I had never thought if a field should or should not have any mass. Now it turns out that either case is possible. It might be naive to think this way, but I picture the mass of the field in ...
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36 views

Why must the Vacuum Manifold contain the quotient group?

For a symmetry breaking pattern $G \rightarrow H$, the vacuum manifold must contain the quotient space $G/H$. In most cases, we take the vacuum manifold to be the quotient space. My question is, Is ...
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2k views

Why do some anomalies (only) lead to inconsistent quantum field theories

In connection with Classical and quantum anomalies, I'd like to ask for a simple explanation why some anomalies lead to valid quantum field theories while some others (happily absent in the standard ...
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52 views

If you reverse the velocity of all elementary particles, is time moving backwards? [on hold]

Imagine that you reverse the velocity of all elementary particles. Does this mean that time is running backwards, and that it´s the only way to physically realise the past?
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Is my understanding of creation/annihilation operators' functional dependency correct?

I am trying to gain a little intuition about second quantisation, specifically about creation/annihilation operators. Lets say you quantise the free EM field (in 1d) and end up with the usual: $H=\...
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4answers
843 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, ...
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194 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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52 views

Euler-Lagrange Equation in Quantum Field Theory

The quantum fields are operator valued distributions. In some sloppy books like Peskin and Schroeder the Euler-Lagrange equation are used to get the equations of motion. What does it mean to take a ...
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522 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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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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162 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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74 views

One particle states in an interacting theory

Question: What is the general definition of one particle states $|\vec p\rangle$ in an interacting QFT? By general I mean non-perturbative and non-asymptotic. Context. 1) For example, in Weigand'...
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109 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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95 views

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

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
50 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 ...
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28 views

Virtual Particles in QCD Vacuum [on hold]

I would like to ask what are the virtual particles in the QCD vacuum. Are they QCD bound states or they are just quarks? In fact, I am puzzled by the logics explained in Peskin and Schroeder book, ...
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1answer
67 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-...
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198 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 ...
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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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43 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
238 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 ...
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1answer
153 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 ...
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2answers
116 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
451 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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407 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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23 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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48 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 $\...
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1answer
70 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 ...
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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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62 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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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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274 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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Generalisation of a particle in QFT

In classical mechanics, we assumed a particle to have a definite momentum and a definite position. Afterwards, with Quantum mechanics, we gave up the concept of a time-dependend position and momentum, ...
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179 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? ...
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2answers
54 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
105 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{...