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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Massless limit of the Klein-Gordon propagator

I am working with the propagator associated to the Klein-Gordon equation, as derived in "Quantum Physics a functional integral point of view", James Glimm, Arthur Jaffe or as derived here: http://www....
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409 views

What do I call the inverse of a propagator?

Let's suppose I have a theory described by a Lagrangian as follows: $ \mathcal{L} = A_\mu \underbrace{\left( \partial^2 g^{\mu\nu} - \partial^\mu \partial^\nu + m^2 g^{\mu \nu} \right)}_{K^{\mu \nu}} ...
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Ward Takahashi identities from Z invariance

I'm trying to get Ward-Takahashi identities using the approach used in Ryder's book (pages 263-266). I like that he starts from demanding gauge invariance of Z in a explicit way and them explores the ...
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What´s the importance of the normalization of the Kinetic term?

It´s usual to read in QFT books of how it is "easier" to have a canonically normalized kinetic term. So, for instance: $${\cal L} = {1 \over 2 }\partial_{\mu} \phi \partial^{\mu}\phi - {1 \over 2 } ...
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Relation between statistical mechanics and quantum field theory

I was talking with a friend of mine, he is a student of theoretical particle physics, and he told me that lots of his topics have their foundations in statistical mechanics. However I thought that the ...
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Spin polarization of decay products

A relativistic moving particle, e.g. muon $\mu^+$, described by its four-momentum vector $p_\mu$, charge $e$ and with a given spin polarization, ${\bf S}=(S_x,S_y,S_z)$, decays into three particles, e....
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Could one transmit a signal with equally-tuned casimir plates across the quantum field?

It seems, one could exploit the Casimir effect to send messages across arbitrarily-large distances with carefully-tuned Casimir plates. Obviously, relativity would preclude FTL information transfer, ...
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supressing certain decay paths and enhancing others with interference

In a scattering reaction, there are many possible final states for the products, each with different production rates. Question: Is there a way in which we could in general supress certain rates ...
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Aharonov-Bohm Effect and Flux Quantization in superconductors

Why is the magnetic flux not quantized in a standard Aharonov-Bohm (infinite) solenoid setup, whereas in a superconductor setting, flux is quantized?
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For nonabelian Yang-Mills in the Coulomb phase, can soft gluons render the charge orientation of charged particles indefinite?

For nonabelian Yang-Mills in the Coulomb phase, can soft gluons render the charge orientation of charged particles indefinite? Let's say the gauge group is a nonabelian simple Lie group G. Suppose ...
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If gauge symmetries are fake, then why do we care if they are anomalous?

My understanding is that gauge symmetries are fake in that they are only redundancies of our description of the system that we put in (either knowingly or unknowingly) see Gauge symmetry is not a ...
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498 views

When do one-point functions vanish?

I have read in many places that one point functions, like the one below: $$\langle \Omega|\phi(x) |\Omega \rangle$$ are equal to zero ( $|\Omega \rangle$ is the vacuum of some interacting theory, $\...
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Equivalent definitions of primary fields in CFT

I have come across two similar definitions of primary fields in conformal field theory. Depending on what I am doing each definition has its own usefulness. I expect both definitions to be compatible ...
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485 views

Very basic question about QFT at finite density

This must be the first question everyone asks when starting to study field theory at finite density and zero temperature. To introduce a finite density one adds a Lagrange multiplier which fixes the ...
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QFTs which are pure constraint

I am interested in (typically topological) field theories arising from Lagrangians of the form. $f(\Phi) \lambda$, where $\lambda$ is a Lagrange multiplier field not appearing in $f(\Phi)$. ...
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203 views

Acting the Hamiltonian operator on a function

I have just a little confusion on some formalism in QM. I have a Hamiltonian density function, $h(x)$, where the regular Hamiltonian is given by $$ H(x) = \int d^{3} \vec{x} \ h(x) $$ I'm wondering,...
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How to show the oblique parameters S, T, and U are coefficients of d=6 operators

In Morii, Lim, Mukherjee, The Physics of the Standard Model and Beyond. 2004, ch. 8, they claim that the Peskin–Takeuchi oblique parameters S, T and U are in fact Wilson coefficients of certain ...
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Reflection positivity in general

In the Euclidean QFT obtained by "Wick-rotating" a unitary QFT, the correlation functions satisfy a property called reflection positivity, see e.g. this Wikipedia article for the case of a scalar ...
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What makes *electric* charge special (wrt. CPT theorem)?

I'm wondering why the 'C' in CPT - charge conjugation - refers specifically to electric charge. Of course you could say that C is just defined as $e^+ \leftrightarrow e^-$... but there has to be ...
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Two-loop regularization

Working out some quantum field theory computations, I have to find out the value of the two-loop Feynman integral $$ I(p)=\int\frac{d^4p_1}{(2\pi)^4}\frac{d^4p_2}{(2\pi)^4}\frac{1}{(p_1^2+m_1^2)(...
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Some questions about flavour and R-symmetry in $2+1$ ${\cal N}=3$ theory

I have heard this fact that for ${\cal N}=3$ theories in $2+1$ with $N_f$ ${\cal N}=3$ matter fields the flavour symmetry group is $USp(N_f)$, $U(N_f)$ or $SO(2N_f)$ depending on whether the gauge ...
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What's the role of field equation in QFT?

For free field theory, it seems the solutions of a field equation are used to give a representation of Poincare group, and the field equation is still satisfied after quantization. However for an ...
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What really goes on in a vacuum?

I've been told that a vacuum isn't actually empty space, rather that it consists of antiparticle pairs spontaneously materialising then quickly annihilating, which leads me to a few questions. ...
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Charge Analog of the Higgs Boson?

Since mass can be given to particles via the interaction with the Higgs Field could there be a "Charger Field" that supplies particles with charge? Possibly this would require two different "charger ...
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what is the relationship between these two sorts of anomalies?

Recently there has been a few questions about anomalies in QFTs: Why do some anomalies (only) lead to inconsistent quantum field theories Classical and quantum anomalies In these, people have been ...
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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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How is the 'cluster decomposition principle' implemented in holographic theories?

Since holographic theories are non-local by definition, how is this principle implemented? Naively, it seems to me it is not, at least, in some sense. I would appreciate an explanation as simple ...
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Constraining two-point functions of boundary operators on the disk

I'm trying to understand the constraints on the disk CFT correlation function $\langle O_1(y_1)O_2(y_2)\rangle$, where the $O_i$'s are boundary operators that are not necessarily primary. It's a well-...
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273 views

The electron jumps and lets loose photons

Where is the source of the photon. If the photon propagates from within the electrons transit does this point to some sort of field? Does the energy come from a boundary being broken in laymens ...
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189 views

What is the Principle of Maximum Conformality?

I'm trying to understand this article about an advance in the theoretical understanding of QCD which centers on the Principal of Maximum Conformality. What is this Principle? In other words, what is ...
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814 views

Ghosts in Pauli Villars Regularization

I'm trying to understand how Pauli Villars Regularization works. I know we add ghost particles, but I want to see more precisely. To do this, we'll work with $\phi^3$ theory. The Lagrangian is $$ {\...
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What does the concept of phase space mean in particle physics?

I came across the concept of phase space in statistical mechanics. How does this concept come about in particle physics? Why was it introduced and how is it used? What does it mean when ...
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Is eternal inflation Lorentz invariant?

Start without general relativity. Consider a metastable vacuum over good ol'-fashioned Minkowski space. It decays. A bubble forms and the domain wall expands. The domain wall is timelike, and ...
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Derivation of the enhancement of U(1)$_L$ x U(1)$_R$ to SU(2)$_L$ x SU(2)$_R$ at the self-dual radius

Towards the end of the paragraph with the title String theory's added value 2: enhanced non-Abelian symmetries at self-dual radii and abstract C with current algebras of this article, it is explained ...
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Particle as a representation of the Lorentz group

In QFT one may refer to a particle as a representation of the Lorentz group (LG). More accurately - every particle is a quantum of some field $\phi(x)$ that belongs to some representation of the LG. I ...
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What would the universe be like if Electroweak symmetry were unbroken? [duplicate]

Possible Duplicate: What happens to matter in a standard model with zero Higgs VEV? What if the Higgs did not have a "Mexican hat" potential and the therefore it's vacuum expectation value ...
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Wilson loops and gauge invariant operators (Part 2)

These questions are sort of a continuation of this previous question. I would like to know of the proof/reference to the fact that in a pure gauge theory Wilson loops are all the possible gauge ...
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1answer
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Calculating conductivity from Green's functions

I am trying to calculate the conductivity in the linear response regime of a disordered electron gas. (or eventually of a mean field Heavy fermion system with known one particle green's functions). I ...
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Must all symmetries have consequences?

Must all symmetries have consequences? We know that transnational invariance, for example, leads to momentum conservation, etc, cf. Noether's Theorem. Is it possible for a theory or a model to have ...
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Hypothetical very massive particles

I'm looking for a table or compilation of hypothetical very massive ($m\gtrsim 1$ TeV) particles and their expected masses (or bounds on them or relation with other scales). All I know is (please, ...
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Quantum Zeno effect and unstable particles

Is it possible to increase indefinitely the lifetime of unstable particles by applying the quantum Zeno effect? Is there a bound from theoretical principles about the maximum extension one can get in ...
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What's the relation between perturbative and nonperturbative QFT?

In case of any miscommunication let me describe my understanding of the meaning of "perturbative" and "non-perturbative", and correct me if something is wrong: In a perturbatively defined QFT the ...
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Classical and quantum anomalies

I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or points of view: Anomalies are due to the fact that quantum field ...
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Why $\lambda\phi^4$ theory, where $\lambda>0$, is not bounded from below?

Why the following interaction, in QFT, $$\displaystyle{\cal L}_{\rm int} ~=~\frac{\lambda}{4!}\phi^4$$ where $\lambda$ is positive, represents a theory that is unstable (or unbounded from below as it ...
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Relation among anomaly, unitarity bound and renormalizability

There is something I'm not sure about that has come up in a comment to other question: Why do we not have spin greater than 2? It's a good question--- the violation of renormalizability is linked ...
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311 views

Lepton masses in the Standard Model

Some simple questions regarding leptonic masses in the Standard Model (SM): Why there is not an explicit mass term in addition to the effective mass term that arises from the Yukawa terms after ...
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Pedagogic reference for calculation of 2-loop anomalous dimension (supersymmetric)

I want to know of pedagogic references which teach how to compute anomalous dimensions (..wave-function renormalization..) at lets say 2-loops. I guess there might be specialized techniques for ...
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Gauge fixing choice for the gauge field $A_0$

In many situations, I have seen that the the author makes a gauge choice $A_0=0$, e.g. Manton in his paper on the force between the 't Hooft Polyakov monopole. Please can you provide me a ...
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Dual Resonance Model: Fermions

I am going through Ramond's 1971 paper Dual Theory for Free Fermions Phys Rev D3 10, 2415 where he first attempts to introduce fermions into the conventional dual resonance model. I get the 'gist' of ...
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Coupling of vector gauge and a massive tensor field

I was reviewing the paper-Coupling of a vector gauge field to a massive tensor field In the calculation I found the term $ 2\mu^2 \varepsilon^{ijk} \dfrac{\partial_j}{\partial^2}B_k\dot{B}$ which ...