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 ...

learn more… | top users | synonyms (1)

2
votes
0answers
109 views

Neglecting mass at asymptotic spacelike momenta

What is the rational/reason for neglecting masses at asymptotic non-exceptional space-like momenta. I have come across this as a first fix for being able to extract information from the ...
7
votes
1answer
282 views

Integral in $n$−dimensional euclidean space

I've asked this question in Mathematics Stack Exchange, but unfortunately there is no answer yet. I repost it because this integral comes from QFT and maybe someone here did it before or could help ...
9
votes
2answers
1k views

Does anyone take the Wightman axioms seriously?

Does anyone take the Wightman axioms seriously? Mainly with respect to quantum gravity or gauge theores, abelian or non-abelian? Anyone doing any research on axiomatization of QFTs in some way?
4
votes
1answer
312 views

Is $\hat{\phi}^{-}\hat{\phi}^{+}$ a well defined observable in the Quantum field theory of a scalar field?

Is the Hermitian operator $\hat{\mathcal{O}}=\hat{\phi}^{-}(x)\hat{\phi}^{+}(x)$, where $\hat{\phi}^{+}(x)$ is positive frequency part of the scalar field operator, a well defined observable in QFT? ...
3
votes
1answer
151 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 ...
4
votes
0answers
58 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 ...
6
votes
0answers
115 views

d=2 O(3) sigma model becomes “conformal antiferromagnet”

In Advanced topic in quantum field theory / M. Shifman on page 251 the author discusses the fact that the theta term is topological and does not affect the equations of motion. Then he said: "In ...
0
votes
0answers
156 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?
9
votes
1answer
240 views

Complex Representation of a gauge group and a Chiral Gauge Theory

In this John Preskill et al paper, a statement is made in page 1: We will refer to a gauge theory with fermions transforming as a complex representation of the gauge group as a chiral gauge ...
15
votes
1answer
2k 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 ...
0
votes
2answers
176 views

What are the problems in trying to interpret the Klein-Gordon equation as a single particle 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 ...
3
votes
1answer
200 views

Quantum Field Theory and antiparticles vs particles

Does a particle and its antiparticle share the same field in QFT? If an electron is an energized spot in the electron field, is a positron a less energized spot or even a spot of negative energy (if ...
5
votes
0answers
160 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 ...
3
votes
1answer
931 views

Weinberg dimension 5 operator

How to prove that the $\Delta L=2,$ dimension=5 Weinberg operator $LLHH$ is the unique operator which violates lepton number by two units, without derivative couplings, etc.??
3
votes
1answer
161 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) ...
16
votes
2answers
2k views

What does a $SU(2)$ doublet really mean?

What do we really mean when we say that the neutron and proton wavefunctions together form an $SU(2)$ doublet? What is the significance of this? What does this transformation really doing to the ...
1
vote
1answer
570 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 ...
2
votes
0answers
37 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 ...
6
votes
1answer
169 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 $m^2-i\epsilon$. ...
2
votes
0answers
80 views

Interesting identity on $SU(3)$

In arXiv:hep-ph/1307.5414 Grabovsky use an interesting identity which is not derived in the paper: ...
1
vote
1answer
128 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 ...
2
votes
1answer
527 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 ...
4
votes
1answer
705 views

About Boltzmann H-theorem

What is the assumption for Boltzmann H-theorem? One can derive it just from the unitarity of quantum mechanics, so this should be generally true, does it imply a closed system will always thermalize ...
4
votes
2answers
198 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 ...
4
votes
1answer
196 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 ...
2
votes
1answer
102 views

Under what conditions is a vector-spinor gamma trace free

I came upon the concept of irreducible vector-spinors while trying to simplify an expression involving the gravitino field. It is claimed that an irredicible vector-spinor is gamma-traceless, i.e. $$ ...
7
votes
1answer
465 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? ...
3
votes
1answer
216 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 ...
3
votes
1answer
96 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 ...
2
votes
2answers
629 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.
6
votes
2answers
261 views

Mass generation by Chern-Simons theory

Why the mass generation via a Higgs mechanism is different from that of Chern-Simons theory? I haven't done any formal course in Quantum field theory,so how do I understand this just having some basic ...
3
votes
3answers
1k views

EQUAL TIME commutation relations

Why is equal time commutation relation used in canonical quantization of free fields?
1
vote
1answer
238 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 ...
4
votes
2answers
776 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 ...
6
votes
1answer
197 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 + ...
4
votes
1answer
258 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 ...
4
votes
1answer
622 views

Components of the Weyl spinor field

In the Weyl basis we can separate the spinor field into 2 components: the right-chiral spinor and the left-chiral spinor. Each of these fields has again 2 components which are coupled. What is the ...
4
votes
1answer
261 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
2k 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 ...
2
votes
2answers
331 views

Dimensional aspects of the imaginary unit $i$ in physics [duplicate]

From a real world perspective each dimension in the 3-D Cartesian System can be represented by an axis that is perpendicular to 2 other axes. I read somewhere else that the effect of ${i}$ is to ...
5
votes
3answers
2k views

Dirac spinor and Weyl spinor

How can it be shown that the Dirac spinor is the direct sum of a right handed Weyl spinor and a left handed Weyl spinor? EDIT:- Let $\psi_L$ and $\psi_R$ be 2 component left-handed and right-handed ...
2
votes
1answer
647 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 ...
3
votes
2answers
163 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), ...
4
votes
4answers
705 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 ...
0
votes
2answers
189 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 ...
3
votes
1answer
103 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 ...
3
votes
1answer
589 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 ...
1
vote
1answer
192 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 ...
2
votes
1answer
631 views

What is meant by a local Lagrangian density?

What is meant by a local Lagrangian density? How will a non-local Lagrangian look like? What is the problem that we do not consider such Lagrangian densities?
6
votes
1answer
273 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 ...