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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Penrose's Zig-Zag Model and Conservation of Momentum

I was reading through Penrose's Road to Reality when I saw his interesting description of the Dirac electron (Chapter 25, Section 2). He points out that in the two-spinor formalism, Dirac's one ...
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76 views

What is ``thermal" about a thermal quotient of EdS and EAds?

This is in continuation of my previous question and is in reference to this paper. I guess that the authors are interested in $S^n$ and $\mathbb{H}^n$ since these are the Euclideanized versions of $...
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1answer
320 views

What are the details of the renormalization of Chern-Simons theory?

What is a good, simple argument as to why Chern-Simons theory' is renormalisable? Any good books/references dealing with this effectively? Why does the $\beta$-function vanish? Thanks!
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2answers
229 views

Space translation of operators, states, and particle densities

In Sidney Coleman's Lectures he talked about space translations such that $$\tag{1} e^{ia P}\rho(x) e^{-ia P} ~=~ \rho(x-a),$$ but when I expanded the exponentials and used the commutation relation ...
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1answer
322 views

Fine-Tuning, the Hiearchy Problem, and Mass in the Standard Model

In Chapter 1 of his book String Theory in a Nutshell, Kiritsis states the following. The [Standard M]odel is unstable as we increase the energy (hierarchy problem of mass scales) and the theory ...
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1answer
242 views

Dimension analysis in Derrick theorem

The following image is taken from p. 85 in the textbook Topological Solitons by N. Manton and P.M. Sutcliffe: What I don't understand from the above statement: why $e(\mu)$ has minimum ...
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1answer
413 views

Defining Euclidean global AdS

How does one see that that the Euclidean AdS is the same as the hyperbolic space at the same dimension ie $EAdS_n = \mathbb{H}_n = SO_0(n,1)/SO(n)$? Or is this to be seen as the definition of ...
3
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1answer
692 views

Symmetric transverse traceless tensors of rank $s$ and $(s,0,0,..,0)$ representations of $SO(n)$

Can someone help see this connection as to why a spin $s$ (an Integer) particle is to be thought of as a symmetric transverse traceless tensor of rank $s$ and that they lie in the $(s,0,0,..,0)$ ...
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1answer
447 views

Perturbation theory

I am puzzled with perturbation theory when studying quantum mechanics and solid theory. What I learn about perturbation is, from my ignorant point of view, just mathematics, or even simpler, matrix ...
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1answer
230 views

What is the the Ehrenfest-Oppenheimer rule on the statistics of composite systems?

Ehrenfest 1931 gives an argument to the effect that the application of the spin-statistics theorem to composite systems is valid, but only as an approximation and under certain conditions. ...
3
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1answer
265 views

Connection between particles and fields and spinor representation of the Poincare group

Let's have a definition of massive particle as an irreucible representation of the Poincare group. Then, let's have a spinor field $\psi_{\alpha \alpha_{1}...\alpha_{n - 1}\dot {\beta} \dot {\beta}_{1}...
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2answers
623 views

In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play?

Isham & Doering have written a series of papers exploring how to ground physics in topoi. Now the internal logic of topoi is higher order typed intuitionistic logic. In their theory what role is ...
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1answer
943 views

What is the meaning of Non-Relativistic theory in Condensed Matter Physics?

I an attempt to evade the Goldstone Theorem, it is argued in Gilbert and Klein and Lee's paper that in a non-relativistic field there exists a preferred direction which can be used to evade Goldstone'...
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1answer
519 views

Evaluation of QED amplitude with 1 external photon

I'm trying to compute the exact QED amplitude with one external photon. Suppose that the photon has 4-momentum $q$ and polarization $\varepsilon^\mu$. Peskin and Schroeder (p318) claim that ignoring ...
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2answers
411 views

Physical consequences of non-abelian non-trivial holonomy

The Aharonov-Bohm effect (http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect#Significance) can be well described and explained in terms of holonomy of the $U(1)$ connection of the ...
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178 views

Finding difficulties in taking continuum limit in nonlinear sigma model

I am learning nonlinear sigma model from Assa Auerbach's book "Interacting Electrons and Quantum Magnetism" and getting some difficulties in taking continuum limit. I am following chapter 12: The ...
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1answer
530 views

Two Loop ultraviolet divergence of $\phi^4$ theory

During the renormalization procedure of a massive $\phi^4$ theory at two loop level, one finds that the quantity $K_{\Lambda}(k^2,m^2)-K_{\Lambda}(0,m^2)$ that appears in the bare $\Gamma^{(2)}$ ...
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71 views

Wavefuntion for Wigner Crystal

Quantum wavefunctions of infinite variables can be written that describe certain Fractional Quantum Halls states, such as the Laughlin family of wavefucntions $ \Pi_{i<j} (z_i-z_j)^k $ that ...
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56 views

Casimir Effect and polarization of photons

I have read Casimir's derivation of the Casimir fore between 2 parallel plates and have been told that in reality, the Casimir force should be twice as large due to the 2 polarization states of ...
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142 views

experimental bounds on microcausality violation

In "The Great Soviet Encyclopedia", 3rd Edition from 1970-1979, (evidently an old book), some V. I. Grigor’ev has a well-written little note on microcausality. Towards the end he states an ...
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1answer
406 views

Problem of Klein-gordon Equation

Ryder in his QFT book writes in eqn (2.20): Probability density, $\rho = \frac{i\hbar}{2m}(\phi^*\frac{\partial \phi}{\partial t} - \phi \frac{\partial \phi^*}{\partial t})$ Then in the next ...
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1answer
592 views

The Einstein-Klein-Gordon (EKG) equations

I am a little confused about a few papers I read on the Einstein-Klein-Gordon (EKG) equations. From what I understood one takes the energy-stress-tensor of the scalar field: $$T_{\mu\nu } = −\...
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1answer
49 views

Differences the nonlinerarties

I want to comparison between oscillons based on non-linearities. Can someone elaborate it with the reason behind it : When the sinusoidal vibrations are of the correct amplitude and frequency and ...
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1answer
697 views

A curious issue about Dyson-Schwinger equation(DSE): why does it work so well?

This question comes out of my other question "Time ordering and time derivative in path integral formalism and operator formalism", especially from the discussion with drake. The original post is ...
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2answers
621 views

Nambu-Goldstone bosons from a quantum anomaly symmetry breaking?

We know that: Nambu-Goldstone bosons come from Goldstone theorem: a spontaneous (continuous)-symmetry breaking of the system leads to massless scalar modes. quantum anomaly: is the anomalous ...
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2answers
2k views

Why does the classical Noether charge become the quantum symmetry generator?

It is often said that the classical charge $Q$ becomes the quantum generator $X$ after quantization. Indeed this is certainly the case for simple examples of energy and momentum. But why should this ...
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471 views

What is the algebraic property that corresponds to a topological term?

Warning: This question will be fairly ill-posed. I have spent a lot of time trying to make it better posed without success, so please bear with me. A single $SU(2)$ spin may be represented by the $0+...
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2answers
340 views

Quantum Anomalies in Non-Gauge Theories?

I'm reading about quantum anomalies in QFT and all the examples seem to arise in gauge theories. Is it true that theories without a local gauge invariance don't have quantum anomalies? I can't think ...
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1answer
285 views

Can one prove the full spin-statistics theorem from the spin 0, 1/2 and 1 cases?

Using second quantization for scalar field, spinor field and vector fields, we can get commutation and anticommutation relations for the birth and destruction operators of the fields, which leads us ...
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1answer
750 views

Is reparameterization invariance some kind of gauge symmetry?

On page 116 of this book it is said, that reparameterization invariance of the string action is analogous to the gauge invariance in electrodynamices. Whereas Maxwell's equations are symmetric under ...
2
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1answer
247 views

Justification for smeared fields in the Wightman axioms?

I just started reading PCT, Spin and Statistics, and All That. Can someone explain why we use operator valued distributions to describe fields? I read somewhere that it would take infinite energy to ...
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228 views

Heat kernel expansion for entanglement entropy

Can somebody please let me know where I can find a reference for calculating heat kernel coefficients on a manifold with conical singularities? I am trying to compute the entanglement entropy for ...
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61 views

How to determine that the renormalization constant $Z_3$ must depend only on $g$ and $\Lambda/m$

In Le Bellac's book, Quantum and Statistical Field Theory, the renormalization constant $Z_3$ is introduced with the equation $$ \Gamma^{(2)}_R(k^2, m^2, g) = Z_3 \Gamma^{(2)}(k^2, m_0^2, g_0; \Lambda)...
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1answer
348 views

Anomalies for not-on-site discrete gauge symmetries

If a symmetry group $G$ (let's say finite for simplicity) acts on a lattice theory by acting only on the vertex variables, I will call it ultralocal. Any ultralocal symmetry can be gauged. However, in ...
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1answer
581 views

Why is renormalization necessary in finite theories?

Michael Brown made the following comment here: The modern understanding of renormalization (due to Kadanoff, Wilson and others) is hardly controversial and has nothing really to do with infinities....
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117 views

Second quantization with qubits

Is "second quantization" means system wich can contain variable, unknown, superposed and otherwise uncertain number of qubits? Can "second quantized" system contain 0.5% of 1 qubit and 95% of 2 ...
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1answer
180 views

Fermion zero modes under 1+1 D Higgs spacetime vortex?

Jackiw and Rossi had a classic paper Zero modes of the vortex-fermion system (1981). In that nice-written paper, they found fermionic zero modes of Dirac operator under nontrivial Higgs vortex in 2D ...
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3answers
2k views

Why is the functional integral of a functional derivative zero?

I'm reading Quantum Field Theory and Critical Phenomena, 4th ed., by Zinn-Justin and on page 154 I came across the statement that the functional integral of a functional derivative is zero, i.e. $$\...
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0answers
959 views

Scattering Amplitude in second Born Approximation for the Yukawa potential

Does anyone know where I can find the analytical expressions of the scattering amplitude in second Born Approximation for the Yukawa potential? I need it for the both cases of the method of partial ...
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2answers
1k views

No magnetic dipole moment for photon

Electrically neutral particles such as neutrinos can have nonvanishing magnetic dipole moments. Spin-1 particles, e.g., deuterium nuclei, can also have dipole moments. Googling seems to show that the ...
6
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1answer
177 views

Does the Fermi surface make sense for “Fermi liquids” with non-uniform charge density?

For a Fermi liquid, the Fermi momentum is determined by the singularity of the Green's function at $\omega=0$, i.e., $G(\omega=0,{\bf k}={\bf k}_F)\to\infty$. Suppose due to an external field or ...
3
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1answer
374 views

Massless fields in curved spacetimes

I read the following statement in one of Penrose's paper zero rest-mass field equations can, with suitable interpretations, be regarded as being conformally invariant. I take this to imply that ...
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1answer
241 views

The basic equation of bosonization

[..quoting from Page 11 of Polchinski Vol2..] Given $1+1$ conformal bosonic fields $H(z)$ one has their OPE as, $H(z)H(0) \sim -ln(z)$ Then from here how do the following identities come? $e^{iH(z)...
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2answers
273 views

Conservation of Energy and CP violation

In classical mechanics there is Noether's theorem: If a system has a certain symmetry there is a related conserved quantity. Energy conservation is a result of a system being time invariant. This is ...
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1answer
187 views

Special relativity and quantum mechanics

I know how the Dirac's equation about the relativistic quantum mechanics works. Can anyone tell me how can one combine special relativity and quantum mechanics as a whole - special relativity is valid ...
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3answers
2k views

If photons carry 1 spin unit, why does visible light seem to have no angular momentum?

Spin 1 silver atoms have a definite spin axis, e.g. up or down along an axis labeled X. This in turn means that they carry angular momentum in an overt, visible fashion. However, spin 1 photons do ...
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1answer
88 views

Nonequilibrium themal QFT

Wick rotation to thermal of QFT in Minkowski space to thermal QFT, which is after this transformation analogue to statistical mechanics, does only describe equilibrium statistical mechanics. On page ...
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1answer
302 views

localization of wave or particles

Nonlinear field theories contain a large number of localized solutions. I have found this text in a article. What I don't understand is "what is localized?". Is it refer defining position of a ...
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1answer
74 views

How does one extract the universal part of entanglement entropy?

I want to know how equation 2.11 (page 9) follows from 2.10 (page 8) in this paper. The two references mentioned just before 2.11 also seem to skip this crucial step. Unless I am missing something ...
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2answers
626 views

topological entanglement entropy for a punctured torus and sphere

Topological entanglement entropy (http://arxiv.org/pdf/cond-mat/0510613.pdf, http://arxiv.org/abs/hep-th/0510092) is usually calculated for surfaces with boundary. How would it look like for compact ...