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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Does the 4/3 problem of classical electromagnetism remain in quantum mechanics?

In Volume II Chapter 28 of the Feymann Lectures on Physics, Feynman discusses the infamous 4/3 problem of classical electromagnetism. Suppose you have a charged particle of radius $a$ and charge $q$ (...
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67 views

Parity transformations and massless Dirac spinors

I am having a bit of a trouble understanding how a parity transformation acts on Dirac spinors with a well-defined chirality and, in particular, the (intuitively correct, since chirality is related to ...
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54 views

Spectral density and Green's function

this is a basic question but from what I can see it has not been asked before. I am reading Nolting's "Fundamentals of Many-Body Physics". He speaks about the spectral density in characterising the ...
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295 views

How can dimensional regularization “analytically continue” from a discrete set?

The procedure of dimensional regularization for UV-divergent integrals is generally described as first evaluating the integral in dimensions low enough for it to converge, then "analytically ...
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39 views

What is a “Scalar Manifold”?

I'm trying to understand a recent paper working within the context of $\mathcal{N}=8$ gauged supergravity with gauge group $\rm{SO}(6)$. There are a number of statements along the lines of: "...the ...
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36 views

Obtaining wave function from field equation

The Dirac field $\Psi(x)$ satisfies the Dirac equation $$(i\gamma^\mu\partial_\mu-m)\Psi(x)=0$$ When we quantize, each of the four components of the Dirac field becomes an operator that creates or ...
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Why do physicists say that elementary particles are point particles?

For example, an electron, it has mass and charge, but is considered to have point mass and point charge, but why? Why are they assumed to have charge and mass in a single infinitely small point in ...
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36 views

Rotations acting on quantum states

Suppose I have a free relativistic massive particle described by a state $|p,\sigma\rangle,$, with $p^\mu=(p^0,0,0,p^3)$, so that $P^3|p\rangle=p^3 |p,\sigma\rangle$ and $J_3|p,\sigma\rangle=\sigma|p,\...
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Irreducible Representations Of Lorentz Group

In Weinberg's The Theory of Quantum Fields Volume 1, he considers classification one-particle states under inhomogeneous Lorentz group. My question only considers pages 62-64. He define states as $P^{...
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78 views

What type of fields are continuous spin representations?

Continuous spin representations (infinite dimensional representations of the Lorentz group) are pretty rarely discussed, and usually not in that much mathematical details. And usually it is done in a ...
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1answer
42 views

Spread of the energy levels and sharp energy eigenvalues of the Schrodinger equation of the H-atom

Solving the Schroedinger equation for the H-atom (or any other system, say a particle in a box, or harmonic oscillator or anything), we obtain the energy eigenvalues are sharp with no spread. However, ...
3
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38 views

Supersymmetry algebra convention?

As derived for instance in this review (page 23-24), the supersymmetry algebra involving grassmann valued generators $Q_\alpha$ and ${\bar Q}_{\dot\alpha}$ is given by: $$[Q_\alpha,M^{\mu\nu}]=(\...
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51 views

Can nonrelativistic QM, as used in bound states, be derived from QFT? [duplicate]

Nonrelativistic QM can be applied to bound states like a hydrogen atom. QFT is used for free particles (whatever one means by particles) that shortly interact with each other and are free again after ...
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Do virtual particles actually physically exist?

I have heard virtual particles pop in and out of existence all the time, most notable being the pairs that pop out beside black holes and while one gets pulled away. But wouldn't this actually violate ...
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3answers
683 views

What does Weinberg–Witten theorem want to express?

Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin $j > 1/2$ cannot carry a Lorentz-covariant current, while massless particles with spin $j > 1$ ...
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59 views

Where is the BRST symmetry?

When quantizing YM we start from the gauge fixed path integral (to remove redundancy of integrating over Gauge symmetric configurations) $$\int \mathcal{D}A \delta(G(A)) \text{det} \Delta_{FP}e^{i\int ...
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28 views

Longitudinal Polarization and Spin-0 for Massive Vector Fields

I was wondering if anybody would be willing to explain how a plane wave solution of the form $\vec{B^\mu}=\epsilon^\mu{e^{k_0ct+\vec{k}.\vec{x}}}$ for a massive vector field's equations, say for ...
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1answer
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Anomalies and determinant bundle curvature

I heard that anomalies and curvature of determinant bundle are related. Namely, curvature of determinant bundle is related to Chern-Simons form (which are involved in description of gauge anomalies). ...
3
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2answers
269 views

From the viewpoint of field theory and Derrick's theorem, what's the classical field configuration corresponding to particle? Is it a wavepacket?

In the framework of QM, we have known that particle, like electron, cannot be a wavepacket, because if it is a wavepacket then it will become "fatter" due to dispersion and it's impossible. However ...
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66 views

Logarithms in Renormalization

I am learning renormalization in Quantum field theory and following mainly Schwartz (Quantum field theory and standard model) for it. While explaining Renormalization group equations it says it mainly ...
4
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1answer
452 views

Lorentz-invariant phase space of a three-body decay process

I am not following the use of delta function in the 3-body decay process. In $\gamma^* \to gq\bar{q}$ process, with $\gamma^*$ being a virtual photon, we have a phase space factor $$d^9R_3 = \frac{d^...
0
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1answer
29 views

Conformational Analysis of Ethane and Butane

How does a condensed matter theorist explain conformations of Ethane and Butane using tools from Quantum field theory? If they don't how do they calculate energy differences and predict differences ...
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What is meant by “Nothing” in Physics/Quantum Physics?

I am not a phycisist, so please forgive my ignorance. This is related to my posts and this. I am trying to understand what is meant by the term "Nothing" in physics or Quantum Field Theory (QFT) since ...
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31 views

Symmetry breaking with adjoint matter, departing from vacuum in different way

$$L=-\frac{1}{4}TrF_{\mu\nu}F^{\mu\nu}+\frac{1}{2}D_\mu\phi D^\mu \phi -\lambda V(\phi)$$ Say we have a potential $V(\phi)=(|\phi|^2-v^2)^2$, and 3-component real scalar field $\phi=(\phi_1, \phi_2, \...
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23 views

Interesting question regarding stimulated emission

why is outgoing photon emitted during stimulated emission in phase with the incoming photon? I can't see why this is so because the two photons may be out of phase yet conserving momentum and energy.
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Functional Gaussian Integral Involving Gradient Square with non-trivial Kernel

I have been trying to solve the following functional gaussian integral. I've had problem finding the inverse kernel. $f(x)$ and $\rho(x)$ are two known scalar fields and they do vanish at infinity. $...
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23 views

The seesaw mechanism and block-diagonalization

I encounter a description about the diagonization in seesaw mechanism. I think it is somewhat elementary in linear algebra, but I can not understand it well. The description is as follows. In the ...
4
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1answer
190 views

Why can we not choose the stress tensor in a CFT to be identically symmetric?

The stress tensor for a conformal field theory (or any quantum field theory) can be derived from the action $S$ by the functional derivative $$T^{\mu \nu} ~=~ -\frac{2}{\sqrt{|g|}}\frac{\delta S}{\...
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1answer
62 views

Issues of normalization & differential final state momenta in analysis of normalized differential quantum-field-theoretic probability of scattering

The normalized differential quantum-field-theoretic probability $dP$ of scattering is given by $$dP=\frac{|\langle f |S|i\rangle|^{2}}{\langle f|f\rangle\langle i|i\rangle}d\Pi,$$ where $|i\rangle$ ...
0
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1answer
45 views

Information that can be extracted from the time-ordered correlation function

The time-ordered correlation function can be very complicated and encodes a tremendous amount of information. For example, the LSZ formula can be used to extract S-matrix elements from the time-...
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0answers
31 views

Comparison of vacua and annihilation operators of Klein-Gordon theory and phi-fourth theory

The ground state or vacuum of an interacting theory is, in general, different from the ground state or vacuum of a free theory. In what cases are the two vacuums the same as each other? Can an ...
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1answer
43 views

Alternatives to scattering experiments

Scattering experiments have been a fruitful and efficient way to determine the particles that exist in nature and how they interact. What are some of the other experimental techniques used to ...
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2answers
78 views

Interacting Hamiltonian commutes with momentum operator?

In Peskin's textbook chapter 7 Radiative Corrections: some formal developments (page 212 second paragraph), he describes two-point functions and chooses states to be eigenstates of the full ...
0
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1answer
46 views

Why is $\sqrt{v_1+v_2+\ldots} =246$ GeV in multi-Higgs models?

Where does the condition come from that in models with several electroweak breaking doublets the square root of the squared sum of the VEVs should yield $246$ GeV?
3
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1answer
64 views

Can a symmetry breaking VEV lie far above the “symmetry breaking scale?”

The scale where some symmetry gets broken can be computed using the renormalization group equations for the gauge couplings. If there is only one Higgs VEV responsible for some breaking, can this VEV ...
5
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1answer
82 views

How to understand the idea of functional renormalization group?

I have been looking at how to use the functional RG method in many-body systems, but I don't quiet get the idea of it, it look different from Wilson's RG approach (eg. why shall we integrate out the ...
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25 views

What are the Higgs masses for $SU(2) \times U(1)$ goes to $U(1)$ symmetry breaking with a complex triplet?

Consider an $SU(2)\times U(1)_Y\rightarrow U(1)_{EM}$ theory that is broken via a complex triplet with hypercharge 2. The potential is of the form \begin{align} V(\Phi) = -m^2\Phi^\dagger\Phi + \...
5
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1answer
84 views

Why is the $D^0$ oscillation so different from the $K^0$ and $B^0$?

I have looked for this answer into many articles and books but I am not able to figure out why $D^0\to\bar{D}^0$ is so highly suppressed if compared to the $B^0 \to \bar{B}^0$ and $K^0 \to \bar{K}^0$ ...
0
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0answers
93 views

Why are photons massless (quantum field theory) [duplicate]

I'm really trying to understand Quantum field theory and gauge in-variance, I'd like to ask a question about this to aid my understanding. The QED lagrangian as below has a kinetic term for this gauge ...
1
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0answers
46 views

What is a good mathematical introduction to QFT [duplicate]

I've noticed that, any time I try to pick up Peskin and Schroeder, the main stumbling block it the leap in mathematical constructs from QM. Is there a good textbook that could teach me some of the ...
3
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2answers
45 views

Momentum conserving delta-function in the transfer matrix of quantum-field-theoretic scattering theory

The $S$-matrix vanishes unless the initial and final states have the same total $4$-momentum, so it is helpful to factor an overall momentum-conserving $\delta$-function: $$\mathcal{T}=(2\pi)^{4}\...
3
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1answer
100 views

Can I catch a particle (such as electron) and say it's left hand

Why is only the left hand electron coupled to weak interaction? How can I tell the chirality of an electron?
3
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1answer
72 views

Why doesn't the four-gluon vertex give mass to gluons?

We have a four-gluon vertex and a gluon vacuum condensate. Why doesn't this provide us with gluon masses, as in the NJL model where the condensate gives rise to an effective mass term?
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11answers
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Quantum Field Theory from a mathematical point of view

I'm a student of mathematics with not much background in physics. I'm interested in learning Quantum field theory from a mathematical point of view. Are there any good books or other reference ...
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Applying AdS-CFT to traversable wormholes? [closed]

ER=EPR recently brought up the connection between non-traversable wormholes and entanglements. What about traversable wormholes? Can we apply AdS/CFT to traversable wormholes?
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Why do people say that the Higgs mechanism gives mass to the gauge bosons without mentioning the fermions?

Many presentations of the Higgs mechanism only explain it as giving mass to the $W$ and $Z$ gauge bosons, but don't mention the quarks or charged leptons. For example: https://en.wikipedia.org/wiki/...
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Why use coherent state path integral? What is its motivation or goal?

In almost all textbooks of quantum field theory for high energy, they insert the position and momentum eigenstate to formulate the path integral. While in condensed matter field theory, they insert ...
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Antiunitary operators in the tenfold way

In the classification of free fermion systems in condensed matter, physicists usually divide the systems into ten symmetry classes, first discovered by Altland and Zirnbauer. In their classification, ...
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4answers
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Decay of massless particles

We don't normally consider the possibility that massless particles could undergo radioactive decay. There are elementary arguments that make it sound implausible. (A bunch of the following is ...