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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Question regarding operators and cylindrical coordinates

I have the following problem in my hand: I need to arrive from the Cartesian expression $$x_{j}{\partial_{k}}x_{j}{\partial_{k}}-x_{j}{\partial_{k}}x_{k}{\partial_{j}}$$ to this expression: ...
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2answers
177 views

Question on the Hagedorn tower in Type I string theory

In a previous question (Mass spectrum of Type I string theory), I had asked about the mass spectrum of Type I string theory. I got a response saying that it is a Hagedorn tower. However, my source ...
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1answer
369 views

Setting of renormalization scale in field theory calculations

In dimensional regularization an arbitrary mass parameter $\mu$ must be introduced in going to $4-\epsilon$ dimensions. I am trying to understand to what extent this parameter can be eliminated from ...
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1answer
145 views

Flavour diagonal SUSY breaking

Because there is a single Yukawa matrix for the SM leptons, the lepton mass and flavour states can be aligned, by diagonalization, even if the Yukawa matrix had off-diagonal elements. SUSY breaking, ...
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3answers
477 views

Many photons, one quantum field?

If a photon can be described as an excitation in a quantum field, is this the same field for all photons, or does each photon exist in its own field?
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1answer
150 views

Why doesn't one-photon-irreducible function have any pole at $q^2=0$?

I'm reading the QFT textbook by Weinberg. In volume one chapter 10 page 451, at the lower part of the page he says, Now, because $\Pi^*_{\mu\nu}(q)$ receives contributions only from ...
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1answer
321 views

For mesons, or baryons, do sea quarks contribute to the angular momentum of the bound state?

The total angular momentum of a bound state of quarks, such as a meson say, can be done by studying the spin and orbital angular momentum of the 2 valence quarks. What about the sea quarks why they ...
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69 views

About deriving the multi-trace index in terms of the single-trace index

This question is in reference to this paper Combining their equations 5.2, 5.3, 5.6 and 5.7 one seems to be looking at the integral/partition function, $Z(x) = \prod_{n=1}^{n =\infty}\left [ \int ...
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1answer
174 views

Parametrization of $U(N)$ non-linear sigma model

The motivation of this question actually comes from this (really old) paper of Weinberg. He considers a theory of massless pions. They have a chiral $SU(2)_{L} \times SU(2)_{R}$ symmetry. The pions ...
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2answers
290 views

How to prove that the generator of proper vertices is the Legendre transform of $W(j) = \log \frac{Z[j]}{Z[0]}$

I'm studying QFT from Le Bellac's book, but I can't understand very well his proof for the generator of proper vertices. Can someone give a more readable and/or understandable proof?
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1answer
168 views

Spectra of the Type II String theories

The spectrum of the Type II string theory (both IIA and IIB) is given by: \begin{array}{*{20}{c}} \hline & {{\text{Sector}}}& & {{\text{Spectrum}}}& & {{\text{Massless Fields}}} ...
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1answer
229 views

Four-gauge-boson vertex in non-Abelian gauge theories

In Peskin & Schroeder's book page 524, the following diagram is calculated for the gauge boson self-energy in order $g^2$: In dimensional regularization, its contribution is given by ...
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2answers
160 views

$\langle B|A \rangle$ expressed in terms of the Partition Function

Say you have an electron departing from point A and reaching poing B after a time t. According to some helping friend, the Partition Function for that electron going from point A to B can be written ...
5
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1answer
345 views

Can Divergences in Nonrenormalizable Theories Always Be Absorbed by (An Infinite Number of) Counterterms?

For example, consider the $\phi^3$ theory in $d=8$, with Lagrangian: $\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^{2}\phi^{2}-\frac{1}{3!}\lambda_{3}\phi^{3}$. In 8 ...
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1answer
324 views

Energy eigeinstates written in the field operator eigenstates basis

For an harmonic oscillator we can write the Hamiltonian eigenvalues in the basis of the amplitude eigenvalues : for example the ground state is a gaussian : $⟨x|0⟩=a.e^{-b.x^{2}}$. I was wondering ...
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197 views

quantization of Dirac field

The general solution to the Dirac equation is a sum of plane wave solutions $$ \psi(x) \sim \int d^3k \sum_r b_r(k) u_r(k)e^{-ikx} + d^\dagger_r(k) v_r(k)e^{+ikx} $$ The basis spinors $u_r$ and $v_r$ ...
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1answer
278 views

Is conservation of statistics logically independent of spin?

If the number of fermions is $n$, we expect the quantity $(-1)^n$ to be conserved, i.e., $n$ never changes between even and odd. This is known as conservation of statistics. In the normal context of ...
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522 views

Calculating the branching ratio of higgs for decay to two photons? [closed]

I need to use the three lowest order Feynman diagrams to first calculate the squared matrix element to put into Fermi's golden rule formula and then from there get the branching ratio of higgs decays ...
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1answer
264 views

Renormalizibility by power counting

When testing a theory for its renormalizability, in practice one always calculates the mass dimension of the coupling constants $g_i$. If $[g_i]>0$ for any $i$ the theory is not renormalizable. I ...
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2answers
877 views

Renormalization condition: why must be the residue of the propagator be 1

In on-shell scheme, one of the renormalization conditions is that the propagator, say, a scalar theory $$\frac{1}{p^2+m^2-\Sigma(p^2)-i\epsilon}$$ must have a unit residue at the pole of ...
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1answer
551 views

Yang-Mills instanton

How can instanton solution to Yang-Mills theory with gauge group $SU(3)$ or $SU(N)$ be obtained? For $SU(2)$ it is explained in textbooks but what about more general color gauge groups? EDIT: How ...
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46 views

Is there anything connecting concrete connecting evaluating of non perturbative field theory correlation functions and solitons/instantons?

I keep reading about instantons and solitons being non-perturbative effects. Well it does make sense that mass of solitons goes inversly as coupling constants so their effects would not be seen in ...
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2answers
1k views

Irreducible Representations Of Lorentz Group

In Weinberg's The Theory of Quantum Fields Volume 1, he considers classification one-particle states under inhomogeneous Lorentz group. My question only considers pages 62-64. He define states as ...
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1answer
175 views

Plane waves in QFT

Suppose we work in the metric $(-1,+1)$. How do we describe an incoming particle with a plane wave; $\exp(-\mathrm ikx)$ or $\exp(+\mathrm ikx)$? What's the difference? Does it change if we work in ...
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89 views

``integrated vertex operators" in 1-loop open/closed bosonic string amplitude

This question is in reference to the first ~15 minutes of this String Theory lecture by Prof.Shiraz Minwalla, http://theory.tifr.res.in/Videos/strings28_24sep08.mp4 Can one give a reference ...
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137 views

A particlar normal ordering problem [duplicate]

Say we have an expression of the form: $$ \left<0\right|:\phi(x)^2: : \phi(y)^2:\left|0\right>, $$ where $\phi$ is some scalar field. I have heard the claim several times, that in evaluating ...
7
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2answers
492 views

What is the exact relationship between on-shell amplitudes and off-shell correlators in AdS/CFT?

In this answer to a question, it is mentioned that in the AdS/CFT correspondence, on-shell amplitudes on the AdS side are related to off-shell correlators on the CFT side. Can somebody explain this ...
3
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1answer
195 views

What is the math showing that the time reversed version of an electron is a positron? (+general time reversal question)

As in Wheeler's One Electron Universe idea, how do you show that electrons and positrons are time-reversed versions of each other? Do you just apply time reversal to an electron and out pops a ...
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1answer
547 views

QED photon propagator to one-loop order gets different answers

I'm a self-studying 14-year-old who has a passion for particle physics. I'm currently trying to calculate the QED photon propagator to one loop. However, in all the places I've looked, even with the ...
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2answers
3k views

Definition of Casimir operator and its properties

I'm not sure which is the exact definition of a Casimir operator. In some texts it is defined as the product of generators of the form: $$X^2=\sum X_iX^i$$ But in other parts it is defined as an ...
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1answer
84 views

Casimir force using Pauli-Villars regularization

In Zee's Quantum field theory in a nutshell, 2nd edition, p. 74 he claims that: $$ \sum_a c_a \Lambda_a \sum_n \frac{\omega_n}{\omega_n + \Lambda_a} = - \sum_a c_a \Lambda_a \sum_n ...
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2answers
111 views

Independent systems and Lagrangians

Definition 1: The notion of independent systems has a precise meaning in probabilities. It states that the (joint) probability or finding the system ($S_1S_2$) in the configuration ($C_1C_2$) is ...
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3answers
361 views

Bound State of Only Massless Particles? Follows a Time-Like Trajectory?

Is there any way in which a bound state could consist only of massless particles? If yes, would this "atom" of massless particles travel on a light-like trajectory, or would the interaction energy ...
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74 views

Holomorphic coupling as a source for gaugino condensation

On the top of page 23 of hep-th/03061119, it is pointed out that treating the holomorphic gauge coupling $\tau$ as a background (spurion) superfield allows one to think of its $F$-term, $F_\tau$ as ...
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1answer
320 views

Difference between vector and pseudo-scalar

In physics, a pseudo-scalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion such as improper rotations while a true scalar does not. Can someone show me ...
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1answer
665 views

Different representations of the Lorentz algebra

I've found many definitions of Lorentz generators that satisfy the Lorentz algebra: ...
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3answers
164 views

Problem involving Dirac's equation

I'm stuck in an equation derivation of Ryder's QFT book. Starting with Dirac's equation: $$(i\gamma^\mu\partial_\mu-m)\psi=0$$ If I multiply by $i\gamma^\nu\partial_\nu$, I get: ...
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2answers
314 views

Infrared-free QED and Higgsless standard model phenomenology

This is one of those "what if" fantasy world type questions. I like hard sci-fi so please no "well, you changed one thing about the world so now anything goes." :) What if the Higgs had no vev? That ...
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0answers
65 views

Standard Quantum Mechanics representation as a constrained 2 + 1 space-time (membrane) theory?

Could a particular Standard Quantum Mechanics representation be a constrained 2 + 1 space-time theory (membrane theory) ? (i) This question is motivated by a possible (approximative) analogy with ...
5
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1answer
191 views

physical importance of regularization in QFT?

The standard lore in QFT is that one must work with renormalised fields, mass, interaction etc. So we must work with "physical" or renormalised quantities and all our ignorance with respect to its ...
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1answer
160 views

Creating a state of definite momentum and position(within uncertainty limit)

claim: $a^{\dagger}$= $\int d^{3}kf_{1}(k)a^{\dagger}(k)$ Creates a state with Localized momentum $k_{1}$and localized position near origin; where $f_{1}(k)$ $\propto ...
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1answer
182 views

Vortex in D dimensions soliton

let us consider the two-dimensional configuration shown in Fig. 3.1a. The lengths of the arrows represent the magnitude of φ, while their directions indicate the orientation in the $φ_1 -φ_2$ plane. ...
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1answer
531 views

sine-Gordon equation

I have derived a solition equation (2 dimensions) from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{1}$$ and also I have got sine-Gordon equation for solition ...
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0answers
288 views

Domain wall and kink solutions from solitions equations

A general solition equation can be obtaion from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{92.6}$$ where $x_0$ is a constant of integration when we drived this ...
5
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1answer
364 views

Determinant for a coupled fluctuation Lagrangian

Lets consider a bosonic physical system in variables $t, x$ and $y(x)$ ($x$ dependent) with a classical Lagrangian $L$. To first order in fluctuations $x \to x+\xi_1$ and $y \to y+\xi_2$ the ...
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4answers
4k views

Trace and adjoint representation of $SU(N)$

In the adjoint representation of $SU(N)$, the generators $t^a_G$ are chosen as $$ (t^a_G)_{bc}=-if^{abc} $$ The following identity can be found in Taizo Muta's book "Foundations of Quantum ...
3
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1answer
178 views

Supersymmetry and non-compact $R$-symmetry group?

The $R$-symmetry for $N$ supercharges is $U(N)$. Is it possible to generalize $R$-symmetry [let's take $U(4)$) to be something like $U(2,2)$ (maybe analogous to Wick rotation of $SO(3,1)$ to ...
2
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0answers
104 views

How does this paper relate to standard QED?

This paper proposes a microscopic mechanism for generating the values of $c, \epsilon_0, \mu_0$. They state that their vacuum is assumed to contain ephemeral (meaning existing within the limits of ...
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1answer
270 views

Significance of Poles of Correlation Function in QFT

In QFT, specifically in scattering processes, what is the physical significance of the poles / residues of the $N$-point correlation function? And why?
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1answer
660 views

Questions about angular momentum and 3-dimensional(3D) space?

Q1: As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ ...