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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Decay Amplitudes Notation

This question is mostly about how to interpret notation used in Particle Physics. I am given that at lowest order the rate of $b\rightarrow s\gamma$ is proportional to $\langle B_p|b^\dagger ...
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How is the double slit experiment modeled in contemporary physical theories?

Suppose I have the following double split experiment set up: a monochromatic electron source of low intensity, which we can model as emitting a single electron at a time with energy $T$. a ...
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Why is there extra minus sign in Feynman's rules for every closed fermionic loop?

I know this is connected to the fact that fermions are represented by anticommuting operators, but I still cannot find the way to get this minus in Feynman rules.
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Why are interacting noncommutative quantum field theories with space-time noncommutativity unitary?

Can anyone explain in a simple manner why interacting noncommutative quantum field theories with space-time noncommutativity of the Moyal bracket sort are unitary? Thanks.
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A question from Ticcati's red QFT textbook.

From Ticcati's textbook, he asks to show that from the axioms of position operator we get that: $$ \text{e}^{-ia\cdot P} |x\rangle = |x+a\rangle $$ where the axioms are: $$ X=X^{\dagger} $$ If ...
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Can the Lamb shift be expressed in more-or-less closed form in terms of the renormalized 2-, 3-,…,n-point VEVs of QED?

I see here that there are three contributions to the Lamb shift, from vacuum polarization (-27 MHz), from electron mass renormalization(+1017 MHz), and from the anomalous magnetic moment (+68 MHz). ...
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Seeking chiral anomaly EFT example

If an effective field theory has a chiral anomaly it means that chiral symmetry isn't a symmetry of the underlying theory which has been cut off to make the EFT. My question is whether there's a good ...
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1answer
114 views

Spinors in more dimensions and new degeneracies?

As you more than probably know spinors dimensions go as $2^{\frac{D}2}$ in D spacetime dimensions. If we look at the peculiar case of D=2*4, spinors have 4 components and we usually say that's related ...
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261 views

If LHC searches of a Higgs boson won't be a success, what consequences for the theory of electroweak interaction it can bear?

Whether it is necessary to search still for variants of an explanation of spontaneously breaking gauge symmetry, giving masses for a W, Z-bosons? Goldstone bosons are bosons that appear necessarily ...
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2answers
884 views

Who first realized the uncertainty principle allows for virtual particle pair production?

For all I've read about Quantum Field Theory I've never seen the concept of the living vacuum accredited to someone in particular. Given the importance of this very application of the uncertainty ...
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624 views

Find equations of motion from given Lagrangian density [closed]

Could someone help me solve this probably not very hard problem? Given Lagrangian Density: $\mathcal ...
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413 views

Proca theory and renormalization

What is the simplest physical argument to claim that Proca theory (involving a massive spin-1 boson) is not renormalizable?
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375 views

Non-minimal coupling of electromagnetic field

For a massless scalar field the equation of motion in a general curved Space time is $\frac{1}{\sqrt{g}}\partial_\mu(\sqrt{g}g^{\mu\nu}\partial_\nu\phi)=0$. Though, in the action, we can by hand ...
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2answers
203 views

An integral related to QFT

How to show $$\displaystyle\int\int\int f(p,p')e^{ip\cdot x-ip'\cdot x}d^3pd^3p'd^3x=(2\pi)^3\int f(p,p)d^3p$$ ? I have $p\cdot x=Et-\bf p\cdot x$
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666 views

Explanation of Cardy's “a theorem”

There seems to have been some discussion of Cardy's "a-theorem" recently: “It is shown that, for d even, the one-point function of the trace of the stress tensor on the sphere, Sd, when suitably ...
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1answer
303 views

Why *should* the mass of elementary particles theoretically be of the magnitude of the Planck mass?

Why should the mass of elementary particles be theoretically of the magnitude of the Planck mass? I've read that already a few times but I don't understand why it should be that way. For example: ...
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1answer
319 views

Propagators from integral representations of Green`s functions

I'm working on an article about propagators from int. representations of Green`s functions for several N-dimensional potential(all this is done in an N-dimensional Euclidian space). Potentials like ...
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198 views

What happens to a Luttinger liquid under time reversal?

Suppose you a have an ordinary Luttinger liquid with $$ H = \int dx \sum _{\eta= \pm 1 , \sigma =\uparrow,\downarrow } \psi^\dagger_{\eta, \sigma} (x) (-i v \eta \partial _x) \psi _{\eta,\sigma} (x). ...
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Convergence and well-definedness of Lorentzian path integrals

Wick rotation of quantum field theories to Euclidean path integrals with a nonnegative measure everywhere is a wonderful tool. Not so with Lorentzian path integrals. Events far separated in ...
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1answer
284 views

WKB approximation to loop diagrams

I'm a bit confused with the terminology here. This paper claimed to use WKB method to calculate the usual loop diagrams. Notice that the vertex is approximated by expanding around the classical ...
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1answer
172 views

Reality constraint

What is the "definition" of a reality constraint and why is it called that way? (I mean how it is used for example in quantum field theory and string theory)
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1answer
784 views

Conservation of quantum Noether current

The Noether current for a set of scalar fields $\varphi_a$ can classically be written as: $$j^\mu(x)=\frac{\delta \mathcal L(x)}{\partial(\partial_{\mu}\varphi_a(x))}\delta \varphi_a(x)$$ The ...
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2answers
862 views

The Energy-Momentum Tensor and the Ward Identity

I have a question regarding a homework problem for my quantum field theory assignment. For the purposes of the question, we can just assume the Lagrangian is that of a real scalar field: ...
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What is the 2-point correlation function of the electron field in QED?

The Feynman propagator for the free electron field is the Fourier transform w.r.t. $y$ of the time-ordered 2-point VEV $\left<0\right|\mathcal{T}[\hat\psi(x)\hat\psi(x+y)]\left|0\right>$, taking ...
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2answers
431 views

Can I couple a chiral fermion to electrodynamics?

Or, perhaps, the question is in which circumstances can I couple it, and of these, which are the simplest. For instance, I think that you can not have a massive Dirac fermion and just couple the ...
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3answers
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What is a antiunitary operator?

In field theory one can define a time reversal operator T such that $T^{-1} \phi (x) T = \phi (\mathcal T x)$. It is then proved that T must be antiunitary: $T^{-1} i T = -i$. How is this equation ...
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512 views

Canonical quantization of quantum field

The canonical quantization of a quantum field prescribes that given a lagrangian, one can quantize the theory by imposing the commutation relations between the field operators and their conjugated ...
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786 views

Hyperfine structure vs Lamb shift in the hydrogen atom

The hyperfine structure of the energy levels of the hydrogen atom refers to the shifts in the evergy levels due to the magnetic moments of the nucleus and of the electron. This is an effect of ...
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4answers
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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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1answer
401 views

Integers powers of fields in a QFT Lagrangian

Why can we not have non-integer powers of fields in a QFT Lagrangian, eg. $\phi^{5/2}$? Or if we wanted a charged $\phi^3$ theory, could we not have a $(\phi^*\phi)^{3/2}$ term?
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480 views

Boundary terms involving fields at infinity

In trying to prove that $[P^\mu,P^\nu]=0$ for a real quantized scalar field, where $P^\mu$ is the 4-momentum operator obtained from $T^{\mu\nu}$, I had to have my fields and/or their derivatives ...
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2answers
2k views

What's the relation between virtual photons and electromagnetic potentials?

Given that: 1) virtual photons mediate the electric and magnetic force fields 2) the magnetic field is the curl of the magnetic vector potential 3) the electric field is the negative gradient of ...
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1answer
300 views

Mathematical definition of Bogomol'nyi–Prasad–Sommerfield (BPS) states

What is the mathematical definition of Bogomol'nyi–Prasad–Sommerfield (BPS) states, independent of any specific physical theory.
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To what extent is the “minimal substitution” or “minimal coupling” for the EM vector potential valid?

In all text books (and papers for that matter) about QFT and the classical limit of relativistic equations, one comes across the "minimal substitution" to introduce the magnetic potential into the ...
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558 views

Is microcausality *necessary* for no-signaling?

There are proofs in the literature that QFT including microcausality is sufficient for it not to be possible to send signals by making quantum mechanical measurements associated with regions of ...
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1answer
142 views

diffusion by an external potential in quantum field theory

I'm studying quantum field theory and I encountered some problems of diffusion of particles by an external potential. Until now I have to do with diffusion of the type particle-particle obtaining the ...
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1answer
189 views

Question about the parity of the ghost number operator in BRST quantization

Given a Lie algebra $[K_i,K_j]=f_{ij}^k K_k$, and ghost fields satisfying the anticommutation relations $\{c^i,b_j\}=\delta_j^i$, the ghost number operator is then $U=c^ib_i$ (duplicate indices are ...
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1answer
453 views

How is the operation of a Goldleaf Electroscope explained in terms of virtual particles?

If an electroscope is charged negatively the electrons on the leaves will repell each other and stand apart. It is clear than there is a steady force between the leaves that counters gravity. How is ...
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1answer
151 views

$\frac{1}{(1-x)_+}$ type distributions and parton distribution functions

I am trying to get to grips with Altarelli-Parisi-type equations. In chapter 17 of Peskin/Schroeder, they first develop the equations for a similar problem in QED. Equation $(17.123)$ introduces the ...
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1answer
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What is a chiral field?

I have not found a clear definition of this. A teacher told me that it was a field having some constrains but that is not very convincing for me. He told me also that some examples could be skyrme ...
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515 views

Trouble with constrained quantization (Dirac bracket)

Consider the following peculiar Lagrangian with two degrees of freedom $q_1$ and $q_2$ $$ L = \dot q_1 q_2 + q_1\dot q_2 -\frac12(q_1^2 + q_2^2) $$ and the goal is to properly quantize it, following ...
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1answer
227 views

About unitarity and R-charge in 2+1 superconformal field theory

How does unitarity require that every scalar operator in a $2+1$ SCFT will have to have a scaling dimension $\geq \frac{1}{2}$ ? Why is an operator with scaling dimension exactly equal to ...
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1answer
797 views

Transverse-plus, transverse minus, and longitudinal polarization of spin 1 particle

What is difference in transverse-plus, transverse minus, and longitudinal polarization of spin 1 particle, and how are this related to its three spin projections states? What is difference in spin 1/2 ...
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Equivalence of canonical quantization and path integral quantization

Consider the real scalar field $\phi(x,t)$ on 1+1 dimensional space-time with some action, for instance $$ S[\phi] = \frac{1}{4\pi\nu} \int dx\,dt\, (v(\partial_x \phi)^2 - \partial_x\phi\partial_t ...
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1answer
369 views

Why does gravity forbid local observables?

I heard in a conference that gravity forbids to construct local gauge invariants like $\mathrm{Tr}\left\{−\frac{1}{4} F_{μν}^{a}F_{a}^{μν}\right\}$ and only allows non-local gauge invariant quantities ...
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Why should the Standard Model be renormalizable?

Effective theories like Little Higgs models or Nambu-Jona-Lasinio model are non-renormalizable and there is no problem with it, since an effective theory does not need to be renormalizable. These ...
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251 views

Is there literature on a continuous mass spectrum for the Higgs field?

Various masses for the Higgs field are compatible with experiment, but is it possible that the Higgs field is not observable because it has a continuous mass spectrum? Work in the 60s and 70s on free ...
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375 views

What happens to a single quark in lattice QCD simulations?

I understand that if a pair quark/antiquark, out of the vacuum, tries to separate then the energy increases, another pair is produced, and we finish with two mesons or generically two hadron jets. But ...
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Representations of gamma matrices

I have to do this exercise for homework. Find a representation of the gamma matrices unitarily connected to the standard representation for wich the spinors $u(p)$ that satisfy the equation $(p_\mu ...
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1answer
697 views

How do you obtain the commutation relations at non-equal times (for the edge of a fractional quantum Hall state)?

The edge of a fractional quantum Hall state is an example of a chiral Luttinger liquid. Take, for the sake of simplicity, the edge of the Laughlin state. The Hamiltonian is: $$H = ...