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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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, ...
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1answer
433 views

Path integral with zero energy modes

Consider the field integral for the partition function of a free non-relativistic electron in a condensed matter setting, i.e. $$ Z = ∫D\bar\psi D\psi \exp\left(-\sum_{k,ω} \bar\psi_{k,ω} (-iω + ...
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2answers
2k views

Lorentz invariance of the integration measure

This is regards to the lorentz invariance of a classical scalar field theory. We assume that the action which is $S= \int d^4 x \mathcal{L}$, is invariant under a Lorentz transformation. How do you ...
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1k views

Why do many people say vector fields describe spin-1 particle but omit the spin-0 part?

We know a vector field is a $(\frac{1}{2},\frac{1}{2})$ representation of Lorentz group, which should describe both spin-1 and spin-0 particles. However many of the articles(mostly lecture notes) I've ...
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1answer
278 views

Equivalent Representations of Clifford Algebra

I'm reviewing David Tong's excellent QFT lecture notes here and am a little confused by something he writes on page 94. We've considered the standard chiral representation of the Clifford Algebra, ...
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52 views

Linear combination of anomalous dimensions in effective potential on pseudomoduli space

In the paper of Intriligator, Seiberg, and Shih from 2007, they give an expression for the effective potential on the pseudo-moduli space $X$, estimated at large $X$ (equation 1.3). In this equation, ...
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0answers
106 views

The asymptotic behavior of the propagator of a field

In Steven Weinberg's book "The Quantum Theory of Fields" vol. I, Section 12.1, page 500, it writes: "We will write the asymptotic behavior of the propagator $\Delta_f(k)$ of a field of type $f$ in ...
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1answer
75 views

How does quantum entropy scales with the size of the sample?

Suppose i have a 3D bulk of physical matter with no black holes enclosed in a sphere of radius $R$. What is the scaling law of all quantum entropy in function of $R$? If the scaling is not $R^2$, in ...
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1answer
381 views

Lorentz Invariant Equation of Motion for Scalar Field

I'm trying to understand why you can't write down a first order equation of motion for a scalar field in special relativity. Suppose $\phi(x)$ a scalar field, $v^{\mu}$ a 4-vector. According to my ...
4
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1answer
171 views

QED Commutation Relations Implications

In Brian Hatfield's book on QFT and Strings there is the following quote: In particular $$ [A_i (x,t), E_j(y,t)] = -i \delta_{ij}\delta(x-y) $$ implies that $$ [A_i(x,t),\nabla \cdot E(y,t)] = ...
9
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1answer
770 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
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2answers
723 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
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0answers
333 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 ...
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2answers
234 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 ...
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1answer
152 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
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122 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: ...
3
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1answer
371 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
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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 ...
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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?
14
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3answers
638 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
334 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
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0answers
692 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 ...
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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 ...
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0answers
70 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
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1answer
334 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 $\phi$: ...
5
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1answer
292 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 ...
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0answers
83 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 ...
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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
212 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
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1answer
739 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} ...
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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
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2answers
390 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
997 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 ...
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1answer
1k 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
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2answers
387 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 $\phi=\int dp^3\frac{1}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}(a_p e^{ipx}+a^\dagger e^{-ipx})$, ...
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0answers
131 views

Does the attached “poster” work as a hook into the arXiv paper cited, “Nonlinear Wightman fields”? [closed]

"Nonlinear Wightman fields" are my current response to a wish to do interacting quantum field theory differently, no matter how successful what we currently do may be. The following image of a single ...
5
votes
1answer
813 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 ...
5
votes
0answers
535 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 ...
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9answers
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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
466 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
642 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
301 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 ...
6
votes
1answer
327 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
793 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
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1answer
196 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. ...
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4answers
704 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
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1answer
468 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
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1answer
774 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
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0answers
356 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 ...