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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What is the relationship between the Higgs field and quarks?

I have some difficulty considering the relative size of each and the meaning behind the shape of Higgs boson. I ask relating to the structures of both the Higgs field and quarks. How is it that the ...
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1k views

What is the difference between manifest Lorentz invariance and canonical Lorentz invariance?

I often read that the Lorentz symmetry is manifest in the path integral formulation but is not in the canonical quantization - what does this really mean?
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411 views

quantum field theoretic models of decoherence

I am interested in whether there is a field theoretic description (there is, so what is it?) of the tensor product (aka density matrix) model of open quantum systems. In particular, I am interested in ...
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497 views

Does string theory provide a physical regulator for Standard Model divergencies?

In other question, Ron Maimon says that he thinks string theory is the physical regulator. I did not know that string theory regularize divergencies. So, Q1: How does string theory regularize the ...
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331 views

Relativistic contraction for a wave packet and uncertainty on momentum

Consider an electron described by a wave packet of extension $\Delta x$ for experimentalist A in the lab. Now assume experimentalist B is flying at a very high speed with regard to A and observes the ...
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3k views

Gentle introduction to twistors

When reading about the twistor uprising or trying to follow a corresponding Nima talk, it always annoys me that I have no clue about how twistor space, the twistor formalism, or twistor theory works. ...
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561 views

What's the differences between pseudospin and spin?

It seems that they both transform as an U(2) group, but I've been told that the three components of real spin change signs under inversion while it is not the case for pseudospin. Could someone name ...
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1k views

About calculation of anomalous dimension in Peskin and Schroeder's book.

This question is in reference to question 13.2 in the QFT book by Peskin and Schroeder. To put it in general - I would like to know how does one define "anomalous dimensions" if one is given the ...
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916 views

Intuition for gauge parallel transport (Wilson loops)

I'm looking for a geometrical interpretation of the statement that "Wilson loop is a gauge parallel transport". I have seen QFT notes describe U(x,y) as "transporting the gauge transformation", and ...
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148 views

Showing that electron and positrons have the same absolute charge

In Zee's quantum field theory in a nutshell, 2nd edition, pg 551 he has the charge of a Dirac field written as $Q=\int {d^3p \over (2\pi)^3(E_p/m)} \sum_s ...
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Self energy, 1PI, and tadpoles

I'm having a hard time reconciling the following discrepancy: Recall that in passing to the effective action via a Legendre transformation, we interpret the effective action $\Gamma[\phi_c]$ to be ...
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170 views

Charge and the Dirac field

In Zee's quantum field theory in a nutshell, 2nd edition, pg 550 he has $Q=\int {d^3p \over (2\pi)^3(E_p/m)} \sum_s \{b^\dagger(p,s)b(p,s)-d^\dagger(p,s)d(p,s)\}$ showing clearly that $b$ ...
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321 views

Validity of Cutkosky cutting rules for fermions

It is rather obvious for me that the generalized optical theorem (see e.g. Peskin&Schroeder) must hold for S-matrix elements for fermions as it is directly related to the unitarity of the ...
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163 views

Relating theta_QCD to neutron EDM

How do I relate the topological $\theta_\text{QCD}$ parameter to the electric dipole moment (EDM) of the neutron? I am very familiar with chiral perturbation theory. I just need to know how to take ...
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683 views

How can we define BF theory on a general 4-manifold?

(I have rewritten the question some, with new understanding) 4d BF theory is classically presented as the TFT arising from the Lagrangian $B\wedge F$, where $B$ is an abelian 2-connection (locally ...
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197 views

Calculation of Commutation in constraint analysis

During analysis the constraint from a theory, suppose my canonical Hamiltonian is $$H_c=P^A\dot{A}+P^B\dot{B}-L$$ where $P^A=\frac{\partial L}{\partial \dot A}$ and $P^B=\frac{\partial L}{\partial ...
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587 views

Spontaneous radiation

The usual explanation of spontaneous radiation is that the energy eigenstates are perturbed by QED interaction, so that the eigenstates obtained from single-particle QM are no longer eigenstates of ...
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457 views

Mathematical concept of supersymmetry

I wish to study supersymmetry in field theory(sometime in december). However, I am quite not sure what is needed for its study. In supersymmetry, I just want to get the mathematical idea, such as its ...
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160 views

Eq. (5.3.20) Weinberg Volume 1, p. 209

Weinberg claims that it is obvious that the $\sigma = 0$ component of $u^\mu$ at zero spatial momentum points in the 3-direction. This is supposed to follow from (5.3.6). Unfortunately I am not seeing ...
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158 views

Calculating equation of motion using path integral

Suppose my action integral is $S=\int d^4x(\nabla \times A)^2$ and $\delta S$ gives $\delta S =\int d^4x [2(\nabla \times A).(\nabla \times \delta A)]$ I would like to calculate the coefficient of ...
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1k views

How does the Feynman's $i\epsilon$-prescription make the Feynman propagator causal?

The Feynman propagator is non-vanishing outside the light cone, but still manages to be in accord with causality. How is this achieved? What does the $i\epsilon$-prescription have to do with this?
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441 views

Hidden particles in higher derivative field theories

Given a higher derivative classical/quantum field theory with say one scalar field, particularly the Lee-Wick standard model. It has been shown that such a field theory encompasses two kinds of ...
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348 views

When can a classical field theory be quantized?

Given a classical field theory can it be always quantized? Put in another way, Does there necessarily need to exist a particle excitation given a generic classical field theory? By generic I mean all ...
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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: ...
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401 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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251 views

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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169 views

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, ...
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285 views

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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196 views

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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222 views

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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2answers
616 views

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 ...
3
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1answer
477 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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507 views

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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479 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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1answer
166 views

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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3answers
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 ...
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331 views

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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1answer
328 views

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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1answer
293 views

Two-loop regularization

Working out some quantum field theory computations, I have to find out the value of the two-loop Feynman integral $$ ...
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100 views

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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1answer
271 views

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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3answers
957 views

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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322 views

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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400 views

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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1answer
487 views

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 ...