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)

9
votes
1answer
814 views

Representations of Lorentz Group

I'd be grateful if someone could check that my exposition here is correct, and then venture an answer to the question at the end! $SO(3)$ has a fundamental representation (spin-1), and tensor product ...
6
votes
2answers
751 views

Number of Components of a Spinor

I'm trying to develop my understanding of spinors. In quantum field theory I've learned that a spinor is a 4 component complex vector field on Minkowski space which transforms under the chiral ...
6
votes
0answers
346 views

An use of the Schwinger-Dyson equation

I was confused as to how the equation 10 on page 7 or equation 21 on page 8 of this paper http://arxiv.org/abs/1211.1866 was derived. Can someone explain from where does this come and what do the "...
1
vote
2answers
239 views

Causality in a gedanken experiment on the hydrogen atom

Consider a gedanken(=thought) experiment where I am tracking the motion of the electron in a hydrogen atom with a time resolution of (say) $\Delta t = 10^{-20}$ seconds. Further assume (for simplicity)...
1
vote
1answer
156 views

What are all the approaches that have been tried for a theory of quantum gravity? [closed]

I am aware that that the most researched approach is that of string theory. I have also heard about quantum loop gravity. What other approaches are there to unify gravity and QFT? Also, please include ...
3
votes
0answers
127 views

Asymptotic limit of the two kink solution of the sine-gordon equation

I am reading a paper on the sine-gordon model. The solution for a two kink solution is given as: $$\phi=4\arctan\left(\frac{\sinh\frac{1}{2}(\theta_1-\theta_2)}{(a_{12})^\frac{1}{2}\cosh\frac{1}{2}(\...
3
votes
1answer
391 views

What is non-Abelian about non-Abelian Chern-Simons' theory?

One is aware that in the axial gauge (say the light-cone gauge $A_{-}=0$) non-supersymmetric Chern-Simons' theory is a quadratic theory. Hence in this gauge there are no gauge-gauge interactions. Then ...
2
votes
3answers
2k views

Fermi's Golden Rule and Density of States

I know Fermi's Golden Rule in the form $$\Gamma_{fi} ~=~ \sum_{f}\frac{2\pi}{\hbar}\delta (E_f - E_i)|M_{fi}|^2$$ where $\Gamma_{fi}$ is the probability transition rate, $M_{fi}$ are the transition ...
1
vote
0answers
52 views

Conservation laws in mSUGRA model

Can somebody list all the quantum numbers (beside R-parity) that are conserved in vertex for SUSY particles in mSUGRA model?
15
votes
3answers
659 views

Quantum field theories with asymptotic freedom

QCD is the best-known example of theories with negtive beta function, i.e., coupling constant decreases when increasing energy scale. I have two questions about it: (1) Are there other theories with ...
5
votes
2answers
342 views

Do all the particles acquire mass in the Standard Model due to the Higgs mechanism only?

I know that a mass term for an intermediate boson is not compatible with the gauge symmetry. But in principle a mass term for the electron field does not violate a gauge symmetry. However to build an ...
2
votes
0answers
793 views

Definitions of the Normal Ordering Operator in CFTs and QFTs

Recall the normal ordering of bosonic operators in QFT is defined by a re-arrangement of operators to put creation operators to the left of annihilation operators in the product. This is designed to ...
2
votes
0answers
203 views

What's the most efficient way to study physics? [duplicate]

I'm CS major trying to learn QFT on my own . I'm trying to make an efficient study plan .The problem is that I've never read any textbook from cover to cover and solved all the problems .What of the ...
0
votes
0answers
74 views

How many particles are created in the strong electromagnetic field?

Consider a vacuum of charged massless scalar field. Then the uniform and isotropic electric field $E$ is turned on for a time interval $\tau$. The question is, how many scalar particles are created?
2
votes
1answer
363 views

Scalar Field Theory Decay/Scattering

I have a few questions related to the following interaction Lagrangian (no use of crossing symmetry in the following) involving the uncharged scalar $\chi$ and the charged scalar $\phi$: $$\tag{1}\...
5
votes
1answer
301 views

Expectation value calculation for a weird operator

In the paper Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups.- E weinberg I am not being able to see one of the calculation. The author states (eqn 3.26) $$\langle ...
3
votes
0answers
86 views

Divergence calculation of a lie algebra valued quantity having spinor indices

I am reading this paper by E. Weinberg - Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups. I am having a problem with a calculation. I don't have much experience ...
8
votes
3answers
2k views

Recipe for computing vertex factors in Feynman diagrams

I am currently studying quantum field theory from Srednicki. In class we have covered till chapter 14 and then skipped to IR divergences. So my knowledge of quantum field theory is limited to those ...
3
votes
1answer
229 views

The state of Indefinite metric in Quantum Electrodynamics

I faced difficulties to grasp why indefinite metric is introduced from no where in QED, after searching internet I found that this is a problem in QED, because one needs it to preserve theory's ...
7
votes
1answer
789 views

Lagrangian of 2D square lattice of point masses connected by springs

Zee's QFT book mentions the Lagrangian of a square 2D horizontal lattice of point masses, connected by springs, and considering only vertical displacements $q_{i}$, as $ L = \frac{1}{2} \sum\limits_{...
1
vote
3answers
1k views

Why can't light escape from inside event horizon of Black Holes?

The simple answer: Its because Gravity of Black Hole there doesn't allow it. See also this and this Phys.SE posts. Isn't it a classical answer? When we're unable to connect Gravity with Quantum ...
3
votes
2answers
403 views

Instructional examples of QFT

Where can one find some concrete physical problems (with solutions) that illustrates the uselfullness and power of QFT? These must not be solvable by QM or SR alone. It would be good if the problem ...
4
votes
1answer
1k views

Is the Lagrangian density in field theory real?

As the Lagrangian in classical mechanics corresponds to energy, it must be real. But is that the case in quantum field theory? I mean, it should still correspond to some sort of energy, but what about ...
1
vote
1answer
2k views

Is it possible that the Big Bang was caused by virtual particle creation?

As far as I understand, it is understood that throughout the universe there exists, what is known as, a quantum field from which, due to its fluctuations, temporary (pairs of) virtual particles ...
0
votes
2answers
406 views

Harmonic oscillator and Lorentz symmetry

There is a analog between harmonic oscillator $x=\frac{1}{\sqrt{2\omega}}(a+a^\dagger)$ and quantum field $\phi=\int dp^3\frac{1}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}(a_p e^{ipx}+a^\dagger e^{-ipx})$, ...
5
votes
1answer
885 views

Spontaneous symmetry breaking in SU(5) GUT?

At the end of this video lecture about grand unified theories, Prof. Susskind explains that there should be some kind of an additional Higgs mechanism at work, to break the symmetry between the $SU(2)$...
5
votes
0answers
592 views

Gaussian Integrals : Functional determinant expressed as a trace

Be $A_{ij}$ a symmetric matrix. Then I can easily write $$ \int \exp\left(-\frac{1}{2}\sum_{i,j}x_i A_{ij} x_j+\sum_{i} B_i x_i\right)\; d^nx= \sqrt{(2\pi)^n}\exp\left\{-\frac{1}{2}\mathrm{Tr}\log A\...
37
votes
9answers
6k views

Is the wave-particle duality a real duality?

I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. I most recently heard this in this video. However, I wonder; is this actually a duality? ...
5
votes
1answer
505 views

Higher dimension operator in free Dirac Lagrangian

When discussing higher dimensional operators in a theory with fermions, why do I never see anyone ever talk about the dimension five operator $\partial_\mu\bar\psi\partial^\mu\psi$? How does the ...
8
votes
2answers
733 views

Wavefunction collapse and gravity

If gravity can be thought of as both a wave (the gravitational wave, as predicted to exist by Albert Einstein and certain calculations) and a particle (the graviton), would it make sense to apply ...
2
votes
1answer
328 views

Tachyon vertex operator (Polchinski's book)

I would like to know how does Polchinski in his book "derive" what is the "tachyon vertex operator" (..as say stated in equation 3.6.25, 6.2.11..) I can't locate a "derivation" of the fact that $:e^{...
7
votes
1answer
362 views

Are the Møller wave operators $\Omega_\pm$ related to $\lim_{t\rightarrow\infty}U(t)$ from field theory?

When we want to compute correlation functions $\langle\Omega|\,T\hat{\phi}(x_1)\ldots|\Omega\rangle$ in an interacting quantum field theory, we relate it to the free-field objects $|0\rangle$ and $\...
11
votes
3answers
1k views

Evaluating propagator without the epsilon trick

Consider the Klein–Gordon equation and its propagator: $$G(x,y) = \frac{1}{(2\pi)^4}\int d^4 p \frac{e^{-i p.(x-y)}}{p^2 - m^2} \; .$$ I'd like to see a method of evaluating explicit form of $G$ ...
3
votes
4answers
819 views

Why the Hamiltonian and the Lagrangian are used interchangeably in QFT perturbation calculations

Whenever one needs to calculate correlation functions in QFT using perturbations one encounters the following expression: $\langle 0| some\ operators \times \exp(iS_{(t)}) |0\rangle$ where, ...
2
votes
1answer
202 views

Other Gross-Neveu like theories?

By "Gross-Neveu like" I mean non-supersymmetric QFTs whose partition function/beta-function (or any n-point function) is somehow exactly solvable in the large $N_c$ or $N_f$ or 't Hooft limit. (.....
11
votes
4answers
727 views

Why do we study the scalar field in QFT when there is no such thing in nature?

The Klein-Gordan equation describing a spinless scalar field is one of the first things one studies in a QFT course, but there are no elementary spin-0 fields in nature. Is the scalar field to QFT ...
2
votes
1answer
538 views

Is proper time renormalization gauge invariant?

Proper Time Renormalization is achieved by putting: $$ \int_0^\infty e^{iat} dt = {1\over ia} $$ Is it true that this is the only kind of normalization that is gauge invariant? If so, why do famous ...
14
votes
1answer
830 views

Multi-loop beta function of gauge theory (*without* Feynman diagrams)

I would like to point to the beautiful section 4.3 (page 42) of these lecture notes. I think this is the most educative exposition I have ever seen anywhere about Yang-Mill's beta function. What I ...
2
votes
0answers
407 views

Question on the Gell-Mann Low equation

Question on the Gell-Mann Low Equation. In this paper, http://arxiv.org/abs/1205.3365, page 21, the author argues that if: t →∞(1-iϵ), all the terms in equation (193) goes to zero, except the first ...
2
votes
3answers
1k views

Scalar Field Redefinition and Scattering Amplitude

Consider a field redefinition $$ \phi \rightarrow \phi' = \phi+\lambda \phi^2 $$ Find the Feynman rules for this theory and work out the $2\rightarrow 2$ scattering amplitude at tree level (The result ...
2
votes
1answer
271 views

Relationship between local and global scaling (Weyl) symmetry

Theorem 5.1 on page 80 of this paper says that Assuming that the matter fields satisfy their equations of motion, the matter field action is locally Weyl invariant if and only if the corresponding ...
2
votes
2answers
860 views

What is the expectation value of the number operator when the vacuum has a VEV?

The number operator N applied to a field whose vacuum has zero VEV gives $N|0>=0$. What if we apply it to the Higgs field? The background of this question is that in popular scientific accounts, ...
6
votes
0answers
162 views

Gauge-invariance of pole mass using Ward Identity

I am able to explicitly verify to one-loop order that pole masses are independent of the choice of gauge paramter. But how do I use the Ward-Identity/Taylor-Slavnov identity show that the position of ...
2
votes
1answer
154 views

A problem with supersymmetry transformation invariance

Consider the following transformation of the integration measure $dX d\psi_1 d\psi_2$: where $\psi_1$ $\psi_2$,$\varepsilon^1$, and $\varepsilon^2$ are Grassman variables. $\delta_\varepsilon X= \...
16
votes
2answers
3k views

What is the physical interpretation of the S-matrix in QFT?

A few closely related questions regarding the physical interpretation of the S-matrix in QFT: I am interested in both heuristic and mathematically precise answers. Given a quantum field theory when ...
12
votes
1answer
436 views

Hawking Radiation as Tunneling

Firstly, I'm aware that Hawking radiation can be derived in the "normal" way using the Bogoliubov transformation. However, I was intrigued by the heuristic explanation in terms of tunneling. The ...
2
votes
2answers
346 views

A step in the derivation of the magnetic moment of the electron in Zee's QFT book

In chapter III.6 of his Quantum Field Theory in a Nutshell, A. Zee sets out to derive the magnetic moment of an electron in quantum electrodynamics. He starts by replacing in the Dirac equation the ...
0
votes
1answer
222 views

About interchange phase of identical particles in Weinberg's QFT book

In Weinberg's textbook on QFT(google book preview), he discussed the phase acquired after interchanging particle labels in the last paragraph of page 171 and the footnote of page 172. It seems he's ...
1
vote
2answers
699 views

Proca equation question

i'm having trouble understanding the Proca equation $$(g_{\mu\nu}(\Box+\mu^2)-\partial_{\mu}\partial_{\nu})\varphi^{\nu}=0$$ where $g_{\mu\nu}$ is the metric and $\mu$ is a parameter. Where is the ...
0
votes
1answer
103 views

What does Friedrichs mean by “Myriotic fields”?

I came across K. O. Friedrichs' very old book (1953) "Mathematical Apsects of the Quantum Theory of Fields", and hardly any of it makes sense to me. One of the strange things that he refers to are "...