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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101 views

Non-Euclidean spaces in Quantum Mechanics

In quantum mechanics, I have been going through basics of the subject. In general the space of quantum states is Hilbert space (which is Euclidean - I presume). Being just curious, are there any ...
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2answers
172 views

No non-trivial UV asymptotically free and IR free

How it could be proven that a non-trivial theory cannot be both asymptotically free and IR free (g=0 both in the UV and IR with some interpolating function in between)? This is of course contrary to ...
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33 views

Mirrored decoupling fermion doublers and a lattice chiral fermion / gauge theory

Nielsen Ninomiya Fermion-doubling problem has known to be a challenge to construct a chiral fermion or chiral gauge theory on the lattice. There is a proposed resolution to use so-called two mirrored ...
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1answer
495 views

Software for calculating Feynman Diagrams

Is there a software (open source preferred) where I would input something like "Ingoing: a fermion $(p1, s1)$ and a photon $(p2, s2)$. Output: A fermion $(k1, r1)$ and a photon $(k2, r2)$" and I would ...
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1answer
223 views

Closed formula for product of gamma matrices

I was asking myself if there is a closed formula for the following product of gamma matrices: $$\gamma_\mu\gamma_\nu \gamma_5.$$ I would like to express this matrix in terms of the basis ...
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59 views

What does it mean that the Higgs has a nonzero vacuum expectation value?

What does it mean that the Higgs has a nonzero vacuum expectation value? Are there any other important field with nonzero VEV? How is this related to the 100-orders magnitude wrong prediction?
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1answer
83 views

Multi-Fermion interactions induced by integrating-out Yukawa-Higgs terms?

Suppose one considers a multi-component free fermions field theory with field $\psi_{q_i}$ with a give global symmetry (such as U(1)). We can say that every component of fermions carry some U(1) ...
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2answers
99 views

Interpretation Klein-Gordon equation

What is the problem if we try to interpret KG equation as a single particle equation? Also I wish to know whether the born interpretation of wavefunction is applicable in relativistic quantum ...
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0answers
105 views

Confusion regarding field operators

Second quantisation of the scalar field leads to an algebra of quantum field operators $$ [\phi(x),\phi(y)] = 0, \ \ [\pi(x), \pi(y)] = 0, \ \ [\phi(x),\pi(y)] = i\hbar \delta(x-y). $$ Where the field ...
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1answer
95 views

Canonical partner of time in QFT and string theory

In analytical mechanics, the Hamiltonian or total energy becomes the conjugate momentum of the time in the symmetric form of the equations. This seems very strange and interesting to me. Does it have ...
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0answers
36 views

Twisted supermultiplets

What is a twisted supermultiplet, in a generic supersymmetric theory? Which ordinary fields belong to one of such twisted supermultiplets? I am confident with the idea of a supermultiplet or a ...
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0answers
72 views

Interesting identity on $SU(3)$

In arXiv:hep-ph/1307.5414 Grabovsky use an interesting identity which is not derived in the paper: ...
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117 views

Srednicki's book chapter 8

Reading first page in chapter 8 of Srednicki's it reads: To employ the $\epsilon$ trick, we multiply $H_0$ with $1-i\epsilon$. The results are equivalent to replacing $m^2$ with $m^2-i\epsilon$. ...
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1answer
148 views

Is the gauge fixing $\partial_\mu A^\mu + \gamma A_\mu A^\mu=0$ used in the literature and does it have a name?

In an exercise for a course on Gauge Theories, I was asked to derive the action of QED with the method by Faddeev and Popov, using the following gauge-fixing function: $$F(A) = \partial_\mu A^\mu + ...
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1answer
470 views

About defining “baryons” and “mesons”

I want to understand the proof of the claims (of the construction as well as of its uniqueness) of gauge singlet states given around equation 2.13 (page 10) of this paper. Also does the listing of ...
2
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1answer
146 views

Problem with Wick's theorem at first order

I've been struggling with a detail in Second Quantization which I really need to clear out of my head. If I expand the S-matrix of a theory with an interaction Hamiltonian $ H_I(x) $ then I have $$ S ...
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1answer
94 views

Spinor and Scalar Bose-Einstein condensate

I read about an order paramater that describes a Bose-Einstein condensate. But I don't understand, the classification into "scalar" condensate and "spinor" one. Is it linked with spin of atoms that ...
6
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1answer
225 views

Light Front Dynamics and Infinite Momentum Frame

What is the the relationship between Light Front Dynamics (One of the forms of dynamics pioneered by Dirac), and the infinite momentum frame? In the literature, it is claimed that the two are very ...
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3answers
256 views

EQUAL TIME commutation relations

Why is equal time commutation relation used in canonical quantization of free fields?
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1answer
164 views

Divergent bare parameters/couplings: what is the physical meaning of it? Do this have any relation with wilson's renormalization group approach?

I understand that bare parameters in the Lagrangian are different from the physical one that you measure in an experiment. I'm wondering if the fact that they are divergent has any physical meaning? ...
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2answers
99 views

How does QFT help with defining measurement in Quantum Mechanics?

I learned that a quantum system has an "overall state", a vector in a Hilbert space. That Hilbert space can be decomposed in a basis of "basic states". For example if in the Universe there is only a ...
3
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1answer
93 views

Equation 7.22 in Peskin & Schroeder: writing the Fourier transform of a two-point function as a series of 1PI diagrams

In Peskin and Schroeder's QFT book, on page 219, there is the following equation: The heading to the equation is: "The Fourier transform of the two-point function can now be written as". Could ...
21
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1answer
378 views

Anomalous target space diffeomorphisms for one-loop world-line integrals

The Schwinger effect can be calculated in the world-line formalism by coupling the particle to the target space potential $A$. My question relates to how this calculation might extend to computing ...
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2answers
265 views

Does the existence of dualities imply a more fundamental structure?

I was wondering if the existence of some kind of duality in physics always implies the existence of some underlying more fundamental structure/concept? Let me give a few example from history: ...
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1answer
183 views

Why must SUSY be broken?

Background One usually claims that supersymmetry must be spontaneously broken. The reasoning is roughly the following: Since $M^2=P^{\mu}P_{\mu}$ is a casimir operator of the supersymmetry algebra, ...
3
votes
1answer
57 views

A coincident stack of D3 branes vs a shell of them

I would in general like to understand how to derive the low energy metrics to describe D-brane configurations. Any pedagogic reference which explains the method? In particular I have in mind these ...
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0answers
92 views

Large gauge transformations for higher p-form gauge fields

Question: What is the large gauge transformations for higher p-form gauge field on a spatial d-dimensional torus $T^d$ or a generic (compact) manifold $M$? for p=1,2,3, etc or any other integers. Is ...
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2answers
264 views

Why does a Lorentz scalar field transform as $U^{-1}(\Lambda)\phi(x)U(\Lambda) = \phi(\Lambda^{-1}x)$?

This problem is from Srednicki page 19. Why $U^{-1}(\Lambda)\phi(x)U(\Lambda) = \phi(\Lambda^{-1}x)$? Can anyone derive this? $\phi$ is a scalar and $\Lambda$ Lorentz transformation.
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1answer
168 views

Properties of Lorentz transformation generator?

In chapter 2 of Srednicki, the author defines: $$ U(1+\delta \omega) = I +\frac{i}{2h}\delta \omega_{\mu \nu} M^{\mu \nu} $$ where the $M^{\mu\nu}$s are hermitian operators and are the generators of ...
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1answer
109 views

Global SU(2) invariance of QED Lagrangian

I'm having problems seeing the global SU(2) invariance of the QED Lagrangian. My specific problem is seeing why \begin{equation} e^{-i a_i \sigma_i} \gamma_\mu e^{i a_i \sigma_i} = \gamma_\mu ...
2
votes
1answer
118 views

How to find a particular representation for the gamma matrices?

I asked this question as a subquestion in another thread, but got the answer below and thought it deserved a thread of its own. Two well-known representation of the gamma matrices are the Weyl and ...
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2answers
130 views

Propagator and expectation value

Given a propagator of some system, is there a way of finding the expectation value of some operator without knowing the eigenstates involved? For example, if I have the propagator of a particle in a ...
2
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3answers
177 views

How do you find a particular representation for Grassmann numbers?

This question is more general in the sense that I want to know how one finds a particular (say matrix) representation for any object. For the case of Grassmann numbers we have from Wikipedia the ...
3
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1answer
123 views

Lorentz transformation implemented by a non-unitary operator.

One often come across in QFT sentences like the following, for instance: ...under a Lorentz transformation $\Lambda$ implemented by the unitary operator $U(\Lambda)$, a Dirac field transforms ...
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votes
1answer
420 views

Formalism Of Quantum Field Theory vs Quantum Mechanics

How far can we extend the formalisms on quantum mechanics (QM) to quantum field theory (QFT)? In particular, How is a Fock space $\mathcal{F}$ different from a Hilbert space $\mathcal{H}$? Can a ...
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0answers
75 views

Space and time translation of quantum field

In book I am studying, the authors want to calculate the spectral representation of the g-lesser (and g-greater) functions and find a general expression for these. In order to do so they start with ...
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votes
5answers
492 views

What distinguishes time from space in Quantum Field Theory?

Consider the following expression for a general QFT action: $$ S ~=~ \int_0^t\mathrm dt~L ~=~\int_0^t\mathrm dt\int_\mathbb {R^3}\mathrm d^3x~\mathcal L ~=~\int\mathrm d^4x~\mathcal L.$$ Here we ...
4
votes
1answer
727 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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4answers
2k views

Scattering of light by light: experimental status

Scattering of light by light does not occur in the solutions of Maxwell's equations (since they are linear and EM waves obey superposition), but it is a prediction of QED (the most significant Feynman ...
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1answer
199 views

Gaussian Integral over Grassman variables

I need to evaluate two Grassmann integrals, one over "real" Grassmann variable another one over complex variables. Lets start with the real one first : The prototype we have for $n$ real Grassmann ...
6
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2answers
245 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 ...
6
votes
2answers
264 views

Mass gap for photons

I am puzzled by the answers to the question: What is a mass gap? There, Ron Maimon's answer gives a clear-cut definition, which I suppose applies to any quantum field theory with Hamiltonian $H$, ...
3
votes
2answers
76 views

Energy spectrum, mass spectrum, and mass gap

In Arnold Neumaier's nice answer to this question: The energy spectrum in quantum field theory it is remarked that 'If there is a mass gap (i.e., if no representation of tiny positive mass exists), ...
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3answers
322 views

Difference between $SU(2)$ and $SU(2)$ gauge transformations?

I hear this jargon all the time, so what is the difference? (Of course this is nothing special to $SU(2)$, but rather I just took it as an example)
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1answer
6k 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 ...
2
votes
1answer
73 views

Symmetry of Minkowksi Metric -> Conserved Current?

My understanding of the Minkowski Metric is that we have the freedom to choose whether to place the negative sign on the time-component or on the spatial-components. That is, either basis should ...
2
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1answer
214 views

Why must the Dirac equation multiplied by its complex conjugate give the KG equation?

This may be a simple question. I can show this is the case mathematically but cannot explain why it happens. It was only when asked why this happens when I realised I couldn't explain it ...
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1answer
136 views

Higgs maths video Brian Greene

What do you think of the video below? ==> http://www.youtube.com/watch?v=KWj00MCqSxs Is the explanation in this video largely correct, or missing something? Is the mathematical description in the ...
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1answer
131 views

Algebraic formulation of QFT and unbounded operators

In AQFT one specifies the structure of the observables as a $C^*$-algebra. This seems to excludes algebras that don't have a norm, such as the Heisenberg algebra. Fortunately for this case one turns ...
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2answers
461 views

Geometrical interpretation of the Dirac equation

Is there an intuitive geometrical picture behind the Dirac equation, and the gamma matrices that it uses? I know the geometric algebra is a Clifford algebra. Can the properties of geometric algebra, ...