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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Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
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167 views

Second quantization of Klein Gordon field

Does the second quantization of the Klein Gordon field which involves using the harmonic oscillator paradigm ultimately lead to the conclusion that electromagnetic field is nothing but photons(bosons) ...
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37 views

Is the real scalar remained real after analytical continuation in imaginary time formulation?

I am studying thermal field theory. I am being confused while studying analytical continuation of time coordinate made in the real scalar field theory at finite temperature. Apparently it occurs to me ...
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75 views

Generalized Unitarity cut of Scalar One-loop Box integral

How does one perform the integrals in four particle cuts in generalized unitarity? It would be helpful how one finds solutions to the simplest case, the fully determined box integral given by: ...
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189 views

Can we have a physical interpretation for a time independent Schrodinger equation of this form?

I am interested in a time independent Schrodinger equation of this form. $$F*\psi - \frac{\hbar^2}{2m} \frac{\partial^2{\psi}}{\partial{x^2}} = E\psi$$ Here the product $V\psi$ is replaced by the ...
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97 views

Can we make usable energy from subnuclear particles?

I understand mass and energy are the same, but in this question I will be talking about mass being turned into usable energy (electricity/heat/etc). We can make our energy through chemical reactions ...
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1answer
197 views

Vacuum expectation value in QFT

In QFT, one writes the VEV of a field $\psi$ as $\langle0|\psi|0\rangle$. But as I understand it, the fields in QFT are not operators, but just some functions which we use to calculate cross-sections. ...
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1k 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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1answer
97 views

Normalization for QFT single particle destruction operator

I don't understand a particular statement in the QFT book by Klauber. The particular page I'm having difficulty on is page 67 of chapter 3 (PDF link). The big picture is that the author wishes to ...
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1answer
139 views

Loop corrections to propagator (QFT of Srednicki)

Perhaps this is a very basic question. In chapter 14 of Srednicki's QFT textbook (2007), $O(g^2)$ loop corrections to the propagator of $\phi^3$ theory is discussed. However, I don't know how to ...
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212 views

Derivation of Lagrangian density for an infinite classical dielectric in interaction with the EM field

I am tasked with reading and reproducing all the steps in J.J. Hopfield's 1958 paper "Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals". Embarrassingly I am stuck ...
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68 views

A question about polarization in quantum mechanics

We start our question we a definition A subbundle $P\subset TM^{\mathbf{C}}$ of the complexified tangent bundle is called a complex polarization if \ $P$ is Lagrangian P involutive dim$P\cap\bar ...
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139 views

Equations of motion from the Standard Model

For some time now I have been wondering if you could not derive any sort of equations of motion from the Standard Model: ...
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11answers
5k views

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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1answer
342 views

Is Conformal Symmetry Local or Global?

I'm just brushing up on a bit of CFT, and I'm trying to understand whether conformal symmetry is local or global in the physics sense. Obviously when the metric is viewed as dynamical then the ...
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1answer
156 views

How does the electron electric dipole moment (EDM) depend on supersymmetry?

I have read a recent paper that says that limit on the EDM of the electron has now been measured to 12 times better accuracy. According to that paper, as I understood, there should be a difference in ...
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1answer
71 views

How can I integrate in $\mathrm{d}t$ the cube of the harmonic oscillator propagator?

I'm redoing the calculations of "Point Canonical Transformations in the path integral", by Gervais and Jevicki; while doing so I stumbled in integrals like $$ \int \mathrm{d}t \, \Delta_F^3(t) = ...
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263 views

Calculating the branching ratio of higgs for decay to two photons? [closed]

I need to use the three lowest order Feynman diagrams to first calculate the squared matrix element to put into Fermi's golden rule formula and then from there get the branching ratio of higgs decays ...
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2answers
5k views

What is a complete book for quantum field theory?

I am searching for a complete and comprehensive book for QFT. What is, in your opinion, a good one?
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753 views

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 ...
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57 views

Lecture Notes to Learn Quantum Field Theory [duplicate]

What are some good lecture notes to learn quantum field theory from, available online?
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109 views

Why Liouville theory is interesting? [closed]

What makes Liouville theory subject to relatively intense research field?
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2answers
765 views

What does second quantization mean in the context of string theory?

String field theory (in which string theory undergoes "second quantization") seems to reside in the backwaters of discussions of string theory. What does second quantization mean in the context of a ...
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2answers
1k views

Why do neutrino oscillations imply nonzero neutrino masses?

Neutrinos can pass from one family to another (that is, change in flavor) in a process known as neutrino oscillation. The oscillation between the different families occurs randomly, and the likelihood ...
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1answer
127 views

minimizing the Higgs potential equivalent to finding the minimum?

When my advisor tells me to "minimize the Higgs potential", is she asking me to find the minimum (take the derivative of the potential and set it equal to zero)?
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1answer
253 views

Quantum Field Theory: why fields are equal to zero on the boundary?

One of the first assumptions, when introducing the Lagrangian and Hamiltonian in an undergraduate course on QFT is $$ \phi(x)=0\,\text{on the boundary} $$ and this is widely used in many situations ...
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2answers
252 views

Is the Dirac Lagrangian Hermitian?

I'm wondering of the Dirac Lagrangian density $$\mathcal{L} =\overline{\psi}(-i\gamma^\mu \partial_\mu +m)\psi $$ is an hermitian operator, since upon complex conjugating one gets ...
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909 views

What does a nucleus look like?

It's a Christmas time and so I hope I'll be pardoned for asking a question which probably doesn't make much sense :-) In standard undergraduate nuclear physics course one learns about models such as ...
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1answer
128 views

Supersymmetric generalisation of the bosonic $\sigma$ model in QM

I am reading some lecture notes which demonstrate how various models in SUSY QM can be used to obtain topological invariants such as the Euler characteristic from the Witten Index. The following ...
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1answer
76 views

3-point correlation function for a massive scalar field

I am a little bit perplexed as to how to compute the three-point correlation function for a massive scalar field, I know that it should be equal to zero. I need to show that: $\lim_{T\rightarrow ...
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315 views

Where does the divergence in the $g\phi^3$ $d=4$ 3 point one loop diagram (three external legs) come from?

$g\phi^3$ , $d=4$ , 3 point One loop diagram (three external legs) Divergence I am trying to find where the divergence factor/pole is on the following diagram in 4 dimensions so that I can use ...
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1answer
106 views

Ground states of Chiral Boson Theory with tunneling

I am reading this paper(pdf) and on page 11, the chiral boson theory on a cylinder is studied when both edges of the cylinder are brought in close proximity so that electron is allowed. Why is it ...
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1answer
118 views

What is a supermultiplet?

In Quantum field theory by Lewis H. Ryder, a supermultiplet is mentioned with no explanation as to what one is.
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1answer
307 views

Quantum Field Theory and the Hartree-Fock approximation

I'm currently reviewing some of my notes on Quantum Field Theory (the version of Greiner) and I was wondering if QFT always works in the Hartree-Fock approximation ? Or at least that's what it seems ...
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1answer
242 views

**Group structure** in Chern-Simons theory?

A non-Abelian Chern-Simons(C-S) has the action $$ S=\int L dt=\int \frac{k}{4\pi}Tr[\big( A \wedge d A + (2/3) A \wedge A \wedge A \big)] $$ We know that the common cases, $A=A^a T^a$ is the ...
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276 views

Virtual Higgs boson?

Can particles emit a virtual Higgs boson in a similar manner to the way a virtual photon is emitted?
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1answer
170 views

Photons traveling backwards in time?

Imagine that two widely separated charged particles $A$ and $B$ exchange a photon. Because they are far apart one can imagine that there is a major contribution to the photon propagator that travels ...
9
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1answer
245 views

Anomalies for not-on-site discrete gauge symmetries

If a symmetry group $G$ (let's say finite for simplicity) acts on a lattice theory by acting only on the vertex variables, I will call it ultralocal. Any ultralocal symmetry can be gauged. However, in ...
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128 views

Calculating Forces via Feynman diagrams?

How would one go about calculating forces that test objects feel using Feynman diagram methods? For example, say we have a massive object in GR so that the metric takes on the standard ...
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82 views

Half-integer Spin and “natural conformal dimension”

If we consider a classical field theory for a massless particle of integer spin $s$, in a curved space-time, one finds that it is "naturally" conformal in a space-time of dimension $2+2s$ For ...
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1answer
161 views

Stress-energy Trace of Massless Klein Gordon Field

I've calculated the trace of the stress-energy for a massless KG field and I keep getting $T = - (\partial \phi)^2$ in 3+1 dimensions. I'm using $$T_{\mu\nu} = \partial_\mu \phi \partial_\nu \phi - ...
5
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1answer
162 views

How do non-transverse photon polarizations cancel in Euclidean QED?

First, recall how to write scattering amplitudes in covariant fashion in Minkowskian QED. One starts by considering some process with an external photon whose momentum is chosen to be ...
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2answers
200 views

$2\pi$ and Feynman Rules

I notice a $2\pi$ term in the $\delta$-function when trying to construct an amplitude using the Feynman Rules. The $2\pi$ also appears as an integration measure to enforce normalisation in the phase ...
6
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1answer
203 views

Basic question about the S-Matrix, Unitarity and Effective Field Theory

Consider scattering some particles in a state collectively denoted by $i$ to a final state denote by $f$. The scattering amplitude, S-matrix is then defined by: $S_{fi}\equiv \langle ...
5
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2answers
670 views

Why is there a minus sign in this wave equation derivation?

My book on quantum mechanics suggests a derivation of the wave equation $$\left(\Delta - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} \right) \psi(\bar{r},t) = 0$$ from the photon energy-impulse ...
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1answer
82 views

are there any “known unknowns” that could affect the possibility of a false vacuum?

(Although Donald Rumsfeld was mocked for talking about "known unknowns" and "unknown unknowns", I think it's an truly important distinction.) Periodically, I hear about how the universe might be in a ...
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92 views

Peskin's book page 334 proof of $Z_1=Z_2$ to all orders in QED perturbation theory

Peskin in his QFT page 334 argued that $Z_1=Z_2$ to all orders in QED perturbation theory, but I couldn't understand his argument: ... With a generalization of the argument given there (section ...
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2answers
204 views

If photons don't interact directly, how can electromagnetic waves interfere?

If photons don't interact directly, how can electromagnetic waves interfere? I know that photons can scatter via higher order mechanisms, but not directly. Does those mechanisms explain the classical ...
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59 views

Matrix integral in multi-matrix model

Though it is a mathematical problem, maybe more physicists know it well. In quiver matrix model which is reviewed DV or CKR, the path integral reduce to the matrix integral $$Z \sim \int ...