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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u-Channel Matrix element for electron-positron annihilation

This one is a quantum related question. The calculation relates to the Matrix element for the annhilation of a electron-positron into two photons: $$ e^-e^+\rightarrow\gamma\gamma $$ I've recently ...
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125 views

Zee's Nutshell: Feynman diagrams “baby problem”: Connected vs. Disconnected

On page 47 of A. Zee's QFT in a Nutshell, he explains how disconnected Feynman diagrams can be built from lower-order connected diagrams: I don't know how to understand formula $(6)$. I understand ...
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44 views

QFT with fixed boundary conditions

I am looking for references on the formulation of QFTs with fixed boundary conditions for the fields (typically $\phi(0)=\phi(L)=0$), and especially how to construct the corresponding perturbative ...
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127 views

Is a Feynman diagram depicting a vacuum bubble “that gets real” valid?

In exercise I.7.3 of A. Zee's QFT in a Nutshell, we have to draw all the Feynman diagrams of the scalar theory $$ Z(J) = \int D\varphi e^{i\int d^4x\{\frac ...
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582 views

General Relativity - Einstein field equation and quantum field theory

Einstein field equation has many solutions. Out of them, is there any solution that is incompatible with quantum field theory? Also, what solutions of Einstein field equation would be incompatible ...
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86 views

Topology and Quantum Field Theory

I am interested in finding any one particle state $\left| \Psi \right>$, mostly possibly topological in nature like a kink, such that $$ \left< VAC | R \widetilde{R} | \Psi \right> \neq ...
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2k views

What is the fundamental probabilistic interpretation of Quantum Fields?

In quantum mechanics, particles are described by wave functions, which describe probability amplitudes. In quantum field theory, particles are described by excitations of quantum fields. What is the ...
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154 views

Mathematical proof that $\exp(-1/|g|)$ is always related with formation of bound states through scales?

I know that this function ($g$ means coupling) is non-analytical in $g=0$, so this function is only appreciable under non-perturbative calculations, so is a non-perturbative phenomena. This function ...
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1answer
117 views

Resources for 2 Particle Irreducible (2PI) or Cornwall-Jackiw-Tomboulis (CJT) formalism

I'am currently learning the 2 particle irreducible (2PI) or Cornwall-Jackiw-Tomboulis (CJT) formalism. Does anybody know a textbook or a review that treats this subject? As far I only found the ...
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188 views

Propagator and probability amplitude that a particle propagates

My QFT knowledge has very much rusted and i got confused by these few lines from Peskin and Schroeder: p.27: " [..] the amplitude for a particle to propagate from $y$ to $x$ is $\langle 0| \phi(x) ...
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372 views

Normalization of the real Klein Gordon Field in Peskin and Schroeder chapter 2

In Peskin & Schroeder's QFT, how do you get from equation 2.35 to 2.37? (In particular, how does the invariant normalization of the Klein-Gordon real field imply that ...
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21 views

FESR: Relation Between Total Cross Section and Spectral Function

In the papers I am reading the total cross section of electrons, positron scattering into hadrons can always be written in terms of an integral of a weight function w(s) and the spectral function ...
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1answer
67 views

AQFT: Can test functions obey the Klein-Gordon equation?

In AQFT we can choose test functions with compact support. Can such functions obey a Klein-Gordon equation? I start with a test function $g$ with compact support and I apply the Klein-Gordon ...
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1k views

Majorana zero mode in quantum field theory

Recently, Majorana zero mode becomes very hot in condensed matter physics. I remember there was a lot of study of fermion zero mode in quantum field theory, where advanced math, such as index ...
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3answers
216 views

What is the physical meaning of $a_{\vec{p}} \! \mid \! 0 \rangle$

$a^\dagger_{\vec{p}} \! \mid \! 0 \rangle = \mid \! p \rangle$ is interpreted as a creation of a particle with momentum $p$ from the vacuum. $a_{\vec{p}} \! \mid \! p \rangle = \mid \! 0 \rangle$ is ...
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70 views

Books dealing with Quantum field theory [duplicate]

Possible Duplicate: What is a complete book for quantum field theory? I am looking for good books that deal with Quantum Field theory starting from basics. Please suggest something that ...
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33 views

Book for quantum field theory similar to Ballentine's quantum mechanics book [duplicate]

I have been studying quantum mechanics from Ballentine's book. I enjoy such books. I want somebody here to recommendation a book for qft with similar approach.
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81 views

Non-symmetry of a lagrangian

If a transformation $\Phi \rightarrow \Phi + \alpha \partial \Phi/ \partial \alpha$ is not a symmetry of the Lagrangian, then the Noether current is no longer conserved, but rather ...
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Does Bose-Statistics mean that we are only allowed to write symmetric tensor products of Higgs fields in the Lagrangian?

Given Higgs fields, transforming as the representation $R$ of a group $G$. Does the physical fact that scalars=boson commute mean that we are only allowed to write symmetric tensor products of the ...
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26 views

Writing the Interaction Hamiltonian for pions in a different way

$\pi^+$, $\pi^-$ and $\pi^0$ are scalars particles with masses approximately equals. Their interaction is, approximately, given by $H_{int}(x) = g \epsilon^{abe}\epsilon^{cde}(\phi^a\partial_\mu ...
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73 views

What are the cosmological ramifications if we probabilise and continuify the order of differentiation in $F=\frac{d(mv)}{dt}$?

Newton's second law of motion states that $F=\frac{d(mv)}{dt}$. This is a first-order differential equation, in which the order of differentiation of momentum is 1. So we can write it ...
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206 views

Feynman diagrams with classical apparatus on the perturbative region

In QFT, one usually simplifies the interaction between fields and classical apparatus (sources, detectors, etc.) by assuming the classical devices only interact with the asymptotic on-shell states ...
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28 views

Holographic dualities with a QFT with a mass gap

The original holographic duality AdS/CFT points to a conformal field theory in the boundary. CFTs do not have a mass gap and all mass spectra are allowed Are there any existing examples of ...
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102 views

Undergrad in QFT/GR looking to do string theory Ph.D [closed]

I am currently a third year undergrad in physics who is currently taking QFT and GR. I took these classes just out of pure interest in the subjects but I find that my mind is being blown almost every ...
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64 views

Visualizing Instantons?

Solitons (aka kinks) in quantum field theory, in an approximation where their internal structure can be ignored, can be visualized as particles. Namely their world line in a spacetime diagram will be ...
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2k views

Wicks Theorem and Gaussian Integrals

I am trying to complete A. Zee's book QFT in a Nutshell and at page 15 he mentions Wick's theorem and Wick contractions. (apologies for the huge page-snip). Why does he mean by connecting the '$2n$ ...
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26 views

Two point correlator : Dispersion Relation

Does anybody has a reference or an advice on how to derive the following idendity? \begin{equation} \Pi(s) = \frac{1}{\pi} \int_0^\infty \frac{Im \Pi(s')}{s' - s} ds' \end{equation} where $\Pi(s)$ is ...
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3answers
406 views

Why is Planck's constant the same for all particles?

This question came to me while reading Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from? This question has a nice answer that explains that wave number has be ...
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1k views

How does QFT help with entanglement?

I'm a bit confused. QFT is claimed to incorporate both Quantum Mechanics and Special Relativity. Therefore it should address the problem of non-locality caused by entanglement. However when I search ...
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53 views

Proof of periodicity of Floquet Green's function

It is claimed in many papers that the two-time Green's function in time periodic Hamiltonian case is periodic in the average time, i.e. \begin{equation} G(t+T,t'+T)=G(t,t') \end{equation} when ...
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1answer
429 views

Finding the ground state of the toric code Hamiltonian

How do I write by proof, the ground state of the toric code (by Kitaev) Hamiltonian $ H=-\sum_{v}A(v)-\sum_{p}B(p) $ where $A(v)=\sigma_{v,1}^{x}\sigma_{v,2}^{x}\sigma_{v,3}^{x}\sigma_{v,4}^{x}$ and ...
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43 views

Solution of Dirichlet problem for scalar field in Ads

I am reading "Anti de Sitter space and holography" by Witten. In this article he derives the two-point function for CFT from theADS/CFT correspondence for a massless scalar field living in the bulk. ...
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149 views

Gauge symmetry for p-forms

It is well known that the Lorentz invariance of the S-matrix implies gauge redundancy for 1-forms or 'photons'. Does this argument go through to $p$-forms? That is, does Lorentz invariance of the ...
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38 views

Supersymmetry breaking and normalizable zero modes

Why does supersymmetry always lead to normalizable zero modes? For example, it is stated in the paper by Michelson and Kaplan (http://arxiv.org/abs/hep-th/9510053) that we can assume, without loss of ...
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1answer
81 views

Which definition of a quantum field is right?

In introductory quantum field theory, I was taught that, given a single-particle Hilbert space $\mathcal H$, the quantum field operator for that type of particle was a mapping $\varphi(x)$ from ...
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2answers
1k views

Does anyone take the Wightman axioms seriously?

Does anyone take the Wightman axioms seriously? Mainly with respect to quantum gravity or gauge theores, abelian or non-abelian? Anyone doing any research on axiomatization of QFTs in some way?
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53 views

Simple question about vacuum fluctuations

Let's say I have an electron traveling alone in the vacuum, when a vacuum disturbance (fluctuation) occurs nearby. If the disturbance has the correct form, say, an electron-position pair, could the ...
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71 views

How are tree-level calculations related to the classical theory?

I've read the answers (and linked notes) to another question (Tree level QFT and classical fields/particles) and I understand them. They seem to explain how to organise a perturbative calculation of ...
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3answers
115 views

Any suggestion for a book that includes quantum mechanics principles and smoothly introduces you to QED (quantum electrodynamics)?

I am not a physicist but I am into quantum mechanics and statistical mechanics. In my department, the quantum mechanics we do include only Schroedinger's equation and problems, some approximation ...
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126 views

Feynman Diagrams Integral Calculation

Are there any easy tricks to calculate integrals of the form: $$\int d^4x \ e^{ikx} \dfrac{1}{x^2} \ \ (\text{ans:} \ i\dfrac{4\pi^4}{k^2}) \ \ \text{and} \ \ \int d^4x \ \mu^2 \dfrac{\ln ...
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1answer
150 views

What is the QFT picture of a static electric field?

Accelerating charge generates electromagnetic waves and loses energy, in QFT terms it emits photons that carry it away. What of a static charge? Moving photons are usually associated with waves, which ...
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1answer
1k views

How can we speak use the notion of “particle” in LHC, given that we live in a curved spacetime?

I understood from lectures that the metric of a spacetime was absolute: It does not depend upon the test charge we put inside. Indeed, all the calculation our professor carried out were independent of ...
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4answers
583 views

Why gauge theories have such a success?

[This question was inspired by a identical question asked on a other forum] Note that we may morally include general relativity in the gauge theories. We may have several (some are deliberately ...
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1answer
82 views

Explicit derivation of the Feynman amplitude of $e^+e^-\rightarrow\mu^+\mu^-$

I'm trying to compute the Feynman amplitude of the process $$ e^+(p_1,s_1)e^-(p_2,s_2)\rightarrow \mu^+(q_1,r_1)\mu^-(q_2,r_2), $$ considering as interaction Lagrangian $$ ...
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1answer
396 views

Källén–Lehmann spectral representation for massless particle?

Is it possible to write down a KL-like formula for massless particles (in particular, the photon)? The usual proof of the theorem assumes (see ...
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49 views

Chiral multiplet : Fundamental and adjoint representation and its Lagrangian

In supersymmetry theory, consider $4d$ $N=1$ theory, we know that chiral superfield (In fundamental representation $\Phi \rightarrow e^{i\alpha} \Phi$) $\Phi$ and its lagrangian is given as ...
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110 views

How do instantons look in real time/spacetime?

Instantons, as I understand it, are mathematical constructions in Eucledean spacetime. Does it imply that instantons do not exist in real spacetime or instanton tunneling effects are does not have ...
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72 views

How do I derive Feynman rules for vectors involving derivatives?

Suppose I have a term in the Lagrangian: $$\cal{L} \equiv (\partial_\mu B^+_\nu) B^{-\mu} A^\nu $$, where $B^\pm$ are charged massive vector particles and $A$ is photon. Now, how can we derive the ...
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33 views

Massless Dirac Field Chirality and CP

I have some very basic questions about Quantum Field Theory. So let's assume we have massless fermions. In 4 spacetime dimensions, due to the Group Structure of $SO(3,1)$ there exists the famous ...