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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Local number operators in quantum field theory

Redhead claims in his paper "More ado about nothing" that number operators associated with different space points (at fixed time) fail to commute, and hence are not physically meaningful. However, ...
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Does this photograph portray double muon impact with nanogold atoms?

1PHOTO 1: Macro-photograph of an NIH/FDA TEM of a nanogold dark stained biological sample projected onto Silver Halide (AgX) photographic gel paper. On June 10 I questioned if PHOTO 1 ...
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Does yukawa potential of two particles have effect on each other?

Okay,a novice here.Suppose two particle interact with Higgs field.Does The Yukawa potential created by each of them affect each other or the interaction in any way.If so,what is it physical ...
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Calculating Tr(log($\Delta_F$))

I am stuck with this problem for quite sometime. I have a propagator in the momentum representation (from this question), which looks like $$ \widetilde\Delta_F(p) = ...
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59 views

What is the source of Quantum fields [duplicate]

In the beginning of "Quantum Field Theory for the Gifted Amateur," there is the statement: Every particle and every wave in the Universe is simply an excitation of a quantum field that is defined ...
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The gauge invariance and the tree unitarity

Recently I have decided to study EM processes with massive spin-1 boson represented by a field $\hat {W}_{\mu}$. At the first time I have used minimally modified lagrangian: $$ \tag 1 \hat {L} = ...
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683 views

Dirac spinor and Weyl spinor

How can it be shown that the Dirac spinor is the direct sum of a right handed Weyl spinor and a left handed Weyl spinor? EDIT:- Let $\psi_L$ and $\psi_R$ be 2 component left-handed and right-handed ...
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48 views

Importance of the Higgs field being formulated in quantum gauge theory

As far as my knowledge goes, Higgs field is only currently formulated in term of classical gauge theory. What is the importance of Higgs field being formulated in term of quantum gauge theory? In ...
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104 views

Is quantum field operator $\psi$ same as quantum field $\psi$?

So in QFT, quantum field operator $\psi$ is there. $\psi$ seems to take the role of wavefunction in QM, which now acts upon vacuum state. Then, in lagrangian of various quantum field theories, $\psi$ ...
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Why do we need to prove the gauge invariance of QED (or all of the gauge theories) on the Feynman diagrams language?

Let's have the QED lagrangian. It has explicit gauge invariance, so, by the naive thinking, all of the EM processes must satisfy the property of gauge invariance. So why do we need to recheck of gauge ...
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74 views

What is physical meaning of $|\phi|^2$ in quantum field theory and pedagogical spontaneous symmetry breaking?

If wavefunction is $\phi$, we know that $|\phi (x)|^2$ represents probability of finding a particle at $x$. Now let us talk about some pedagogical example in spontaneous symmetry breaking in QFT, ...
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Complex dirac field in antiparticle description

I understand that the Dirac equation has negative and positive sets of solutions and this contributes to its quantization by a superposition of two fourier modes represented as creation and ...
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$U(1)$ abelian/axial/chiral anomaly in 4D

I am reading $U(1)$ abelian/axial/chiral anomaly in 3+1 dimensions using the path integral method (Fujikawa). Am I wrong in assuming that the anomaly can be cancelled by introducing a counter term in ...
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104 views

Self-adjointness

I know I have posted this question before some time ago. But no one could help so I decided to put my problem in another background. The Schrödinger equation of a free scalar field is given by ...
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102 views

Entanglement in single particle state

Is it possible that we have entanglement in different degrees of freedom of a singe particle. like spin and linear momentum .
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297 views

Time-ordering in QFT

In Srednicki QFT page 37. In the derivation of LSZ reduction formula, he introduces the time-order operator $T$, so no time-dependent creation/annihilation operators are left in the transition ...
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(A,B)-Representation of Lorentz Group: Coefficient functions of fields

I have a question regarding the construction of general causal fields in Weinberg's book on quantum field theory. In his conventions a field that transforms according to the irreducible (A,B) ...
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52 views

If non-zero cosmological constant interpreted as a repulsive field, what would be the properties of this field's quanta?

If non-zero cosmological constant interpreted as a repulsive field, what would be the properties of the excitation of such field, i.e. the particle which serves as the field's quantum? What would be ...
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2 entangled electrons in QFT

In field theory, by quantizing a dirac field, we can obtain a creation operator for a single electron of definite momentum, of definite spin up or down, these respectively are: ...
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417 views

What is the meaning of Non-Relativistic theory in Condensed Matter Physics?

I an attempt to evade the Goldstone Theorem, it is argued in Gilbert and Klein and Lee's paper that in a non-relativistic field there exists a preferred direction which can be used to evade ...
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What is the physical interpretation of the fermion field Hamilton?

I am still unclear what the hamilitonian of a quantized field is, but what I do know is the hamilitonian of the boson field is defined as \begin{align} H_{\text{boson}} &=& ...
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CPT invariance of Dirac equation

We know that Dirac equation is \begin{equation} ( i \partial _\mu \gamma ^\mu - m ) \psi ~=~0. \end{equation} How can we show that Dirac equation is invariant under CPT transformation?
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How to calculate the 2-point function of gravitons?

I'm curious about how to calculate the 2-point function of graviton, but there are no textbooks of general relativity covering this problem. So how to calculate it? In which book can I find the ...
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310 views

How does the nature of nuclear force change between attractive or repulsive based on distance?

I know that the nuclear force is responsible for binding the protons and neutrons together in the nucleus. The force is powerfully attractive at small separations and rapidly decreases as the distance ...
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What is the most general definition of a bosonic Gaussian state?

I am reading this paper where the definition of the bosonic state is mentioned on page 2 here :- http://arxiv.org/pdf/0806.1625.pdf . From a general definition of any density operator in terms of ...
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126 views

Lorentz group representations in QFT: what's the vector space?

In QFT, a representation of the Lorentz group is specified as follows: $$ U^\dagger(\Lambda)\phi(x) U(\Lambda)= R(\Lambda)~\phi(\Lambda^{-1}x) $$ Where $\Lambda$ is an element of the Lorentz group, ...
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Why does the action have to be hermitian?

The hermiticity of operators of observables, e.g. the Hamiltonian, in QM is usually justified by saying that the eigenvalues must be real valued. I know that the Lagrangian is just a Legendre ...
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Research Topics In Theoretical Physics [on hold]

Could someone with a broader overview of the subject, and with more academic experience list research topics in Theoretical Physics? I'm a third year undergrad thinking about future research. I don't ...
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86 views

A Spin up particle in QFT

This appears like a question that is rarely addressed in field theory pedagogy (perhaps because the answer is obvious): how does one describe a particle of definite spin in quantum field theory? For ...
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Error in Standard Textbook “An Introduction to Quantum Field Theory” of Peskin and Schroeder?

On page 191 there is a equation for $D$ given by $$D=x(k^2-m^2)+y(k'^2-m^2)+z(k-p)^2+(x+y+z)i\epsilon. \tag{6.43}$$ With $k'=k+q$ and the constraint $x+y+z=1$. Also $p^2=p'^2=m^2$ and maybe $q=p'-p$. ...
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Quantum Energy Teleportation and Stress-Energy tensor divergence

This question is about a paper from last year about Quantum Energy Teleportation. If I understand the main assertion of what QET is supposed to involve, basically you are teleporting energy as ...
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647 views

Symmetries of the Standard Model: exact, anomalous, spontaneously broken

There are a number of possible symmetries in fundamental physics, such as: Lorentz invariance (or actually, Poincaré invariance, which can itself be broken down into translation invariance and ...
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How do instantons cause vacuum decay?

From what I read about on instantons (Zee, QFT in a Nutshell, pg 309-310), an instanton is a vacuum solution that maps $S^3 \rightarrow S^3$ (the boundary of Euclideanized spacetime), which comes from ...
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Cluster Expansion vs Cluster Decomposition

Are the cluster expansion (which we encounter in Statistical Physics), and cluster decomposition (in Quantum Field Theory) related to each other? (I have a reason to believe they are)
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106 views

geometric quantization of the moduli space of abelian Chern-Simons theory

I wish to understand the statement in this paper more precisely: (1). Any 3d Topological quantum field theories(TQFT) associates an inner-product vector space $H_{\Sigma}$ to a Riemann surface ...
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465 views

Path integral and geometric quantization

I was wondering how one obtains geometric quantization from a path integral. It's often assumed that something like this is possible, for example, when working with Chern-Simons theory, but rarely ...
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339 views

Understanding Cherns-Simons-Witten Theory

I want to read about Wittens work, on Cherns-Simons theory, and relations to knots and jones polynomials. I am extremely motivated to read his paper: Quantum Field Theory and Jones polynomial. What ...
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Mass generation by Chern-Simons theory

Why the mass generation via a Higgs mechanism is different from that of Chern-Simons theory? I haven't done any formal course in Quantum field theory,so how do I understand this just having some basic ...
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558 views

The Chern-Simons/WZW correspondence

Can someone tell me a reference which proves this? - as to how does the bulk partition function of Chern-Simons' theory get completely determined by the WZW theory (its conformal blocks) on its ...
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Yang-Mills CP violation

Why does a term proportional to $\left(F,\,\tilde{F}\right)\propto Tr\left[ F_{\mu\nu}\tilde{F}^{\mu\nu}\right]$ in the Lagrangian of the pure Yang-Mills theory violate CP?
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Noncommutative Field Quantization

I'm studying noncommutative (quantum) field theory, and I have confusion need to be clear. I'm reading Szabo's and Douglas's .pdf of noncommutative QFT. As I understand, in the book they just ...
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What is the analogy of $|x\rangle$ in quantum field theory?

Let me start from path integral formulation in quantum mechanics and quantum field theory. In QM, we have $$ U(x_b,x_a;T) = \langle x_b | U(T) |x_a \rangle= \int \mathcal{D}q e^{iS} \tag{1} $$ ...
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113 views

Where does this delta of zero come from?

It is common when evaluating the partition function for a $O(N)$ non-linear sigma model to enforce the confinement to the $N$-sphere with a delta functional, so that $$ Z ~=~ \int d[\pi] d[\sigma] ~ ...
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63 views

How non-abelian gauge coupling runs below confinement or QCD scale?

I know the famous beta function of asymptotic free, but that seems describe the running coupling beyond confinement/QCD scale so that a perturbative analysis can apply. But how coupling runs below ...
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I want to decompose a tensor product using Littlewood-Richardson rule, How do I find the component of this in each irreducible space?

Let me set up the notation I am using. $(abc,de)$ denotes the standard Young tableau where the first row is $abc$ and the second row is $de$. Each young tableau corresponds to the young symmetriser, ...
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608 views

Why is the functional integral of a functional derivative zero?

I'm reading Quantum Field Theory and Critical Phenomena, 4th ed., by Zinn-Justin and on page 154 I came across the statement that the functional integral of a functional derivative is zero, i.e. ...
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S-Matrix Generating Functional (Problem 4.1 in Weinberg)

I'm currently working through Weinberg's QFT book, but I'm somewhat stuck at problem 4.1, which states: Define generating functionals for the S-matrix and its connected part: \begin{equation} ...
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160 views

Coleman-Weinberg potential: resum at 2 loops?

Say we want to compute the Coleman-Weinberg potential at 2 loops. The general strategy as we know is to expand the field $\phi$ around some background classical field $\phi \rightarrow \phi_b + ...
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567 views

Analytic continuation of imaginary time Greens function in the time domain

Consider the imaginary time Greens function of a fermion field $\Psi(x,τ)$ at zero temperature $$ G^τ = -\langle \theta(τ)\Psi(x,τ)\Psi^\dagger(0,0) - \theta(-τ)\Psi^\dagger(0,0)\Psi(x,τ) \rangle $$ ...
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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 $\bar{l}_1\sigma_{\mu\nu} r_2 \bar{r}_3 \sigma^{\mu\nu} l_4 =$ $ ...