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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Can i Wick contract terms with derivatives with terms without derivatives?

Consider for example the QCD three point vertex, can i contract a gluon field with the gluon field with a derivative in the vertex?
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36 views

Is there any $SU(\infty)$ gauge theory in quantum field theory?

The groups $U(N)$ and $SU(N)$ are the most important Lie groups in quantum field theory. The most popular are the $U(1),SU(2),SU(3)$ groups (these gauge groups form the Standard model). But is there ...
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29 views

QED+Classical Background Renormalization

I would like to ask a question related to quantum corrections and renormalization in QED. We have the QED vertex $\overline{\psi}[-ie \gamma^{\mu}(B_{\mu}+A_{\mu})]\psi,$ being $B_{\mu}$ a classical ...
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41 views

Klein-Gordon Field Angular Momentum Operator in Terms of Creation and Annihilation Operators

I am computing the angular momentum operator for real Klein-Gordon field (essentially question six of here (though please note this is not a homework question, I am following through Tong's course via ...
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13 views

If we considered chiral perturbation theory with coplex $\phi$-s, wold the next lo leading order renormalization $\gamma$-s change?

The Lagrangian of chiral perturbation theory (with two quark flavors) is written using the following matrix $U$ $$U=e^{i\sigma^i\phi_i/f}$$ where $\sigma^i$ are the Pauli matrices, $\phi_i$ are three ...
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24 views

Distinction of Dirac monopole and Polyakov t'hooft monopole

Can anybody explain the physical difference between Dirac monopole and Polyakov monopole? First, let me write down what i know briefly. Dirac monopole It comes from the symmetry of Maxwell ...
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33 views

how could the sun photons be the source of light to our vision? [on hold]

if the atom has 99.99% empty space and the photon has no mass while our universe is 2dimensional flat so how could the sun photons be the source of our vision? how could photons be reflected by ...
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1answer
42 views

A question to gauge fixing in nonabelian gauge theories

In quantum gauge theories it is usual to fix the gauge with the equation $\partial^\mu A_\mu = 0$ where $A_\mu$ is the gauge connection. From this gauge fixing condition the remaining gauge degree of ...
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25 views

Covariant projection method - Meson bound states

I have seen many papers that discuss the production or decay of mesons ( quark bound states ) to make use of the covariant projection method where the product $\upsilon\bar{u}$ of the quark spinors ...
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15 views

How to let pythia to output the complete event record in LHEF or StDHep format?

I am currently using Pythia 6.4 to simulate some processes (I do not have the intention to upgrade to 8). Now, I need Pythia to output its event record in the format of LHEF or StDHeP. I accidently ...
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2answers
57 views

Compact QED and Non-compact QED - Polyakov textbook

This question is related with Polyakov, "Gauge Fields and Strings" section 4.3 Firstly, Polyakov define a QED on a lattice Compact QED \begin{align} S = \frac{1}{2} \sum_{x, \alpha, \beta} ...
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1answer
33 views

Do contractions with Dirac matrices involve a metric?

When figuring out where the spacetime metric enters an equation it is often useful to write all vector indices as covariant indices and write out the inverse metrics that are needed to contract them, ...
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1answer
88 views

Strange use of complex analysis in Weinberg QFT 1?

In the beginning of chapter 3 on scattering theory in Weinberg's QFT book there is a use of the Cauchy residual theorem that I just cannot get. First some notation, we are looking at states that are ...
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36 views

Textbooks for nonequilibrium quantum field theory

What are good textbooks for nonequilibrium quantum field theory? Please answer by naming quality books and a short description and review about each one that you have personally read or benefited ...
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0answers
47 views

Negative interaction energies for relativistic bound states

I guess that bound states are treated as poles with infinite lifetime, i.e. precise determination for energy eigenvalues. But what's left with negative interaction energies, which are connected to ...
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1answer
91 views

Is the Dirac equation equivalent to the Klein-Gordon equation for its left handed component?

The Dirac equation $$(i\gamma^a\partial_a - m)\psi=0\tag{0}$$ is given by a first order operator acting on a Dirac spinor, which is the direct sum of a left handed spinor and a right handed spinor. ...
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100 views

Has Sen quantized superstring fields?

Today I saw a paper by Ashoke Sen titled "BV Master Action for Heterotic and Type II String Field Theories". Is it really the "quantization" of superstring fields for the first time? What can be its ...
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39 views

correlation functions [on hold]

What is the physical meaning of following correlation functions in one-dimensional correlated electron systems: 1. density-density correlation function, 2. spin-spin correlation function, 3. ...
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38 views

How can the stress tensor components of a worldsheet CFT in general background be (anti)-holomorphic?

In all textbooks/lecture notes on string theory (e.g. Polchinski, page 43 at the bottom) it is proven that, as the stress tensor is traceless and conserved, $T^a_a=\partial^a T_{ab}=0$, we have ...
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66 views

Are we teleporting? [on hold]

First of all - i'd like to declare that i'm a complete and utter noob when it comes to anything physics or mathematics involved.So please be patient with me and explain everything to me in layman's ...
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0answers
55 views

Singularity in the context of the Quantum mechanics [on hold]

In the TV program , Professor Michio Kaku had told that singularity can be defined as the rotation of the neutron . I'm searching whether the insist was right or wrong . How does the quantum mechanics ...
3
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1answer
66 views

State space of interacting theories

Haag's theorem states that in general, an interacting quantum field and the corresponding free field have unitary-inequivalent state space representations. I would like to have an example of a state ...
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48 views

Peskin eqn 7.2 contradiction

They state $\langle\Omega|\phi(x)|\lambda_p\rangle=\langle\Omega|e^{iP\cdot x}\phi(0)e^{-iP\cdot x}|\lambda_p\rangle$ where $|\lambda_p\rangle$ is a state of momentum $\textbf{p}$. They then rewrite ...
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38 views

Wightman axioms always imply triviality in 4D?

Someone mentioned to me in passing that it had been proven that the Wightman axioms are over-restrictive in four dimensions and provably always result in trivial correlators (or maybe a trivial ...
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2answers
241 views

Are there any inventions/applications in our world based on QFT?

Are there nowadays any actual devices or experimental applications which are based on the quantum field theory and if so, how are they related to QFT? I could not find any similar question besides ...
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48 views

Free probability in Physics

Recently I have started reading some materials on non-commutative probability. IN this area mathematicians sometimes consider quantum theory as a non-commutative version of classical probability, with ...
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3answers
81 views

How many fields that we know of permiate the universe?

The Higgs field, as I understand it reading layman's articles, permeated the entire universe only a fraction of a second after the big bang. Are there any other fields that they know about or ...
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1answer
20 views

What justifies the perturbative expansion in chiral perturbation theory?

The Lagrangian of chiral perturbation theory is ordered following a momenta power counting scheme, having terms at leading order (which is two 2 $O(p^2)$) next to leading order ($O(p^4)$) and so on. ...
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52 views

Quantizing Klein-Gordon via Lie Groups [on hold]

I'm trying to understand second quantization of the Klein-Gordon equation, as explained in, say, standard books like Peskin and Schroder, but using the language of Lie (representation) theory. In a ...
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23 views

QFT Normalization of multi-particle states

Peskin 7.2 states that the identity operator for the entire Hilbert space is given by ...
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1answer
59 views

New “oscillator basis” of gamma matrices?

It was mentioned in http://kclpure.kcl.ac.uk/portal/files/12371620/Studentthesis-Mehmet_Akyol_2013.pdf page 28, a new concept "oscillator basis" or more precisely the author defines gamma matrices of ...
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1answer
79 views

How does one make sense of a delta function of a scalar field?

Disclaimer: Originally posted on math SE, but thought that it was better in physics SE, so deleted my post on math SE and posted here. In the classic review summary of stochastic quantization here, ...
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18 views

Do operator bases in Lagrangians have a vector space structure?

In effective field theories we deal with bases of operators. I wonder in which sense is this similar to bases of a vector space. We can change bases and write the Lagrangian in another basis, just as ...
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513 views

Two definitions of Green's function

In literature, usually two types of definition exist for Green's function. $\hat{L}G=\delta(x-x')$. This equation states that Green's function is a solution to an ODE assuming the source is a delta ...
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108 views
+50

Why are the quantum observables defined on opens sets a presheaf and not a sheaf?

In local quantum field theory or AQFT one can mathematically describe over each open set $U$ of a spacetime $M$ the quantum states or observables of the theory. This structure is commonly referred as ...
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44 views

QFT background needed for AdS/CFT integrability [closed]

Apologies if this type of question isn't permitted. I'm very interested in integrability in the context of AdS/CFT. I'm starting my Masters soon in a very GATIS-involved institute and would like to ...
1
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1answer
58 views

Does a charged particle propagating in free space have a 'self-energy' like term due to it’s interaction with the fluctuations of the quantum vacuum? [on hold]

Does a charged particle propagating in free space have a 'self-energy' like term due to it’s interaction with the fluctuations of the quantum vacuum? (particle-antiparticle pairs popping into and out ...
2
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1answer
48 views

Ultraviolet behaviour in dimensional regularization

In dimensional regularization, we introduce an arbitrary energy scale $\mu$. Naively, it plays the role of another parameter of the theory that needs to be fixed experimentally, but actually it is not ...
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1answer
73 views

Derivation of eq 6.17, Peskin and Schroeder

I am having trouble following a derivation in Peskin and Schroeder's textbook, namely equation 6.17 on page 182. It seems benign at first, but I am completely stuck. Essentially, we have an expression ...
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35 views

How to handle the infrared divergence of massless $\phi^4$ in scattering

For massless $\phi^4$ theory, if exterior momentums are going to zero, then this diagram will be $$\int \frac{dk^4}{k^4}$$ will suffer from infrared divergence. Because the infrared divergence, ...
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23 views

Holography with wave functionals rather than partition functions

Roughly speaking Gubser-Klebanov-Polyakov Witten's (GKPW) prescription in the context of holography tells us partition function of CFT is "equal" to that of the gravity theory in one higher dimension ...
3
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1answer
65 views

Why is gravity sensitive to absolute energies?

In QFT absolute energies play no role in the physical set-up, only relative energies (i.e. energy differences) are important. However, in general relativity this doesn't appear to be the case, I've ...
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16 views

Bound states and corresponding elementary fields

Let's have some bound state, like positronium or meson. I need to calculate an amplitude of process which involves bound state in in- or out-state. Is it necessary to introduce corresponding ...
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2answers
89 views

Why Kink can not tunnel to vacuum, and is topologically stable?

Why the kink $$\phi(x)=v\tanh(\frac{x}{\xi}) ,$$ can not tunnel into vacuum $+v$ or $-v$ (Spontaneous symmetry breaking vacuum). From the boundary condition ($x\rightarrow \pm\infty, ...
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0answers
36 views

How can the VEV of a field be a function of spacetime?

Often in the discussion of effective action and effective potential (say, in the context of $\phi^4-$theory )the one-point function in presence of source is defined as \begin{equation} \frac{\delta ...
3
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1answer
35 views

One-point function and VEV in $\phi^4$-theory

Why is it that the one-point function in the $\phi^4-$theory, for example calculated from the generating functional, always gives zero value in absence of external source i.e., $J=0$? If there is ...
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44 views

Riemannian generalization of Weierstrass transform

As it has been written on this Wikipedia page, one can define the Weierstrass transform on any Riemannian manifold. Even though, I couldn't find any references guess that the Weierstrass transform on ...
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1answer
67 views

Derivation of the Lorentz algebra explicity [closed]

I need the complete proof for commutation relation of the Lorentz group generators. The proof of Lorentz algebra using this commutation relation.
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29 views

Can we have supersymmetry using real scalar instead of complex scalars?

I am aware that a suersymmetric theories containing a complex scalar a Weyl fermion and an auxiliary field exist. I was wondering if we can have something analogous using real and not complex scalar ...
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26 views

Path integral for boson vs fermion (soft derivation + use )

I have been looking around for a soft derivation with a bit of detail for boson and fermion path integrals that I could understand. I have a passing knowledge generally of what a path integral is in ...