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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The derivation of the Belinfante-Rosenfeld tensor

It seems me that there is a "difference" (at least apparently) in how the Belinfante-Rosenfeld tensor is thought of in section 7.4 of Volume 1 of Weinberg's QFT book and in section 2.5.1 of the ...
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1answer
122 views

Which is the coupling between the photon and the SU(2)xU(1) gauginos, before symmetry breaking?

The photon field is the non chiral piece of SU(2)xU(1), independently of symmetry breaking or not, isn't it? But before symmetry breaking, each gauge boson has only a chiral gaugino as ...
3
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1answer
187 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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vote
1answer
443 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
1k views

Lagrangian of Schrodinger field

The usual Schrodinger Lagrangian is $$ \tag 1 i(\psi^{*}\partial_{t}\psi ) + \frac{1}{2m} \psi^{*}(\nabla^2)\psi, $$ which gives the correct equations of motion, with conjugate momentum for $\psi^{*}$ ...
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1answer
481 views

About $\phi^4$ model

In many books the $\phi^4$ model can produce a topological soliton called kink. Are they right? In the case of sine-Gordon model you can have a topological soliton due to you can express the ...
4
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1answer
270 views

String matrix models with c>1

Question 1: What is the status of string random matrix models (~ triangulated random surfaces) with c>1? In my limited search, I have just come across a few papers by Frank Ferrari (in 2000-2002) on ...
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2answers
58 views

Extensions of DHR superselection theory to long range forces

For Haag-Kastler nets $M(O)$ of von-Neumann algebras $M$ indexed by open bounded subsets $O$ of the Minkowski space in AQFT (algebraic quantum field theory) the DHR (Doplicher-Haag-Roberts) ...
3
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1answer
145 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 ...
14
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1answer
205 views

6d Massive Gravity

Massive gravity (with a Fierz-Pauli mass) in 4 dimensions is very well-studied, involving exotic phenomena like the vDVZ discontinuity and the Vainshtein effect that all have an elegant and physically ...
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3answers
205 views

Status of local gauge invariance in axiomatic quantum field theory

In his recent review... Sergio Doplicher, The principle of locality: Effectiveness, fate, and challenges, J. Math. Phys. 51, 015218 (2010), doi ...Sergio Doplicher mentions an important open ...
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2answers
7k views

Why do we not have spin greater than 2?

It is commonly asserted that no consistent, interacting quantum field theory can be constructed with fields that have spin greater than 2 (possibly with some allusion to renormalization). I've also ...
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1answer
381 views

Why is Dirac Lagrangian in Curved Spacetime Weyl Invariant?

Are there any references on the Weyl invariance of the Dirac Lagragian in general spacetime?
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2answers
444 views

Applications of the Feynman-Vernon Influence Functional

I am looking for a reference where the Feynman-Vernon influence functional was defined and used in the context of relativistic quantum field theory. This functional is one method to describe ...
4
votes
1answer
315 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 ...
6
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1answer
1k views

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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1answer
182 views

Instantons and Non Perturbative Amplitudes in Gravity

In perturbative QFT in flat spacetime the perturbation expansion typically does not converge, and estimates of the large order behaviour of perturbative amplitudes reveals ambiguity of the ...
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2answers
489 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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3answers
521 views

Renormalization Group for non-equilibrium

For equilibrium/ground state systems, a (Wilson) renormalization group transformation produces a series of systems (flow of Hamiltonians/couplings $H_{\Lambda}$ where $\Lambda$ is the cut-off) such ...
18
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2answers
365 views

Does 4D N = 3 supersymmetry exist?

Steven Weinberg's book "The Quantum Theory of Fields", volume 3, page 46 gives the following argument against N = 3 supersymmetry: "For global N = 4 supersymmetry there is just one supermultiplet ... ...
17
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1answer
317 views

Models of higher Chern-Simons type

It has long been clear that (the action functional of) Chern-Simons theory has various higher analogs and variations of interest. This includes of course traditional higher dimensional Chern-Simons ...
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2answers
104 views

Significance of the hyperfinite $III_1$ factor for axiomatic quantum field theory

Using a form of the Haag-Kastler axioms for quantum field theory (see AQFT on the nLab for more details), it is possible in quite general contexts to prove that all local algebras are isomorphic to ...
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2answers
173 views

Can symmetry generators be used for quantization?

Take the Poincaré group for example. The conservation of rest-mass $m_0$ is generated by the invariance with respect to $p^2 = -\partial_\mu\partial^\mu$. Now if one simply claims The state where ...
11
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1answer
160 views

Limitations in using FLEX as a DMFT solver

When using the fluctuating exchange approximation (FLEX) as a dynamical mean field theory (DMFT) solver, Kotliar, et al. (p. 898) suggest that it is only reliable for when the interaction strength, ...
21
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1answer
474 views

Vasiliev Higher Spin Theory and Supersymmetry

Recently there is renewed interest in the ideas of Vasiliev, Fradkin and others on generalizing gravity theories on deSitter or Anti-deSitter spaces to include higher spin fields (utilizing known ...
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3answers
601 views

Continuum theory from lattice theory

I am looking for references on how to obtain continuum theories from lattice theories. There are basically a few questions that I am interested in, but any references are welcome. For example, you can ...
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1answer
358 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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3answers
2k views

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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4answers
358 views

AQFT and the Standard Model

The German physicist Rudolf Haag presented a new approach to QFT that centralizes the role of an algebra of observables in his book "Local Quantum Physics". The mathematical objects known as operator ...
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1answer
141 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
419 views

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 ...
3
votes
2answers
425 views

When is many-body perturbation theory valid?

I'm calculating expectation values (thermal, time-independent) using many-body perturbation theory, but I'm unsure how to work out what values the parameter I'm expanding the perturbation series in ...
22
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3answers
3k views

Good reading on the Keldysh formalism

I'd like some suggestions for good reading materials on the Keldysh formalism in a condensed matter context. I'm familiar with the imaginary time, coherent state, and path integral formalisms, but ...
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1answer
682 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 = ...
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votes
5answers
7k views

Gauge symmetry is not a symmetry?

I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate ...
5
votes
2answers
539 views

Behavior of Correlation functions/partition functions during phase transitions

can somebody explain to me what happens or how do the correlation functions/partition functions in general behave (if such general answer/behavior exists and if not then why not) during a first and ...
1
vote
1answer
325 views

“Classical” limit of Quantum Hall Effect

Imagine a partially filled $\nu=1$ state of the integer quantum Hall effect (IQHE). One way to think about it is to imagine a gas of electrons where each particle is locked to the lowest quantum state ...
15
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1answer
700 views

A reading list to build up to the spin statistics theorem

Wikipedia's article on the spin-statistics theorem sums it up thusly: In quantum mechanics, the spin-statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin ...
2
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1answer
165 views

Relativistic equation with arbitrary spin

can anyone give me some good references on how to obtain the relativistic equation of particles with arbitrary spin?
8
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1answer
884 views

What is a quark condensate?

What is a quark condensate? is it a bound state between 2 quarks? can we have 3(or more)-quarks condensate? What mediates the interaction between the constituents of the condensate? Are the ...
1
vote
1answer
775 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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votes
3answers
1k views

Left and Right-handed fermions

Is there a simple intuitive way to understand the difference between left-handed and right-handed fermions (electrons say)? How to experimentally distinguish between them?
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vote
2answers
347 views

Reeh–Schlieder theorem in QFT and entanglement in biological systems

Context: There have been a few papers out recently which mention how photosynthesis in plants might have connections to entanglement, or even perhaps that entanglement is causing photosynthetic ...
6
votes
3answers
400 views

GUT that includes all 3 particle families into a large group?

Explaining SU(5) GUTs (using the first particle family as an example) in the last SUSY lecture 10, Lenny Susskind mentioned that there are at present no ideas how to combine simultaneously all 3 ...
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3answers
2k views
7
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1answer
570 views

Is Bose-Einstein condensate a good example of a classical massive boson field?

Physically, we know that a BEC has formed if a macroscopic number of bosons occupy a single quantum state. The wave-function $\Psi(x)$ of the latter, normalized to the total number of condensed atoms ...
7
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1answer
247 views

To construct an action from a given two-point function

This is really a basic question whose answer I guess may have to do with the way we construct Feynman rules and diagrams. The question is: Suppose I have been given a two-point function (found in some ...
3
votes
1answer
175 views

Particle Indistinguishability Scale Limit

QFT says that all particles are indistinguishable from one-another [1]. That is, take a proton from cosmic ray from a supernova a billion light-yeas away, and compare it to a proton that just got ...
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1answer
599 views

Online lecture videos on QCD? [duplicate]

I would like to know if there are any online collections of lecture videos on QCD or non-Abelian QFT at a graduate level (at the level of volume 2 of Weinberg's QFT books?) For example: In String ...
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1answer
270 views

How to quantize the free electro-magnetic field in 2d?

I am wondering how one can quantize the free electro-magnetic field in the two dimensional space-time. The standard method of fixing the Coulomb gauge in 4d does not seem to generalize immediately to ...