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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't Hooft limit of coupling fundamental fermions to Chern-Simons theory

This question is in reference to this paper: arXiv:1110.4386 [hep-th]. I would like to know what is the derivation or a reference to the proof of their crucial equation 2.3 (page 12). In their ...
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The Lagrangian in Scalar Field Theory

This is perhaps a naive question, but why do we write down the Lagrangian $$\mathcal{L}=\frac{1}{2}\eta^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi - \frac{1}{2}m^2\phi^2$$ as the simplest ...
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1answer
340 views

Number of Grassmann generators for Dirac field?

How many Grassmann generators are sufficient for the description of a Dirac spinor in 4 dimensions? i.e. The Dirac field is a map to $\Lambda_N$, the space of supernumbers with $N$ real Grassmann ...
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195 views

Coverage of Quantum Electrodynamics (QED) in introductory Quantum Field Theory (QFT) books [closed]

Which QFT books also cover QED? I am not very familiar with QED, so I am looking for QFT books which cover QED too (I know they cover Quantum Chromodynamics (QCD).).
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123 views

What are relativistic and radiative effects (in quantum simulation)?

I'm reading about Quantum Monte Carlo, and I see that some people are trying to calculate hydrogen and helium energies as accurately as possible. QMC with Green's function or Diffusion QMC seem to be ...
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402 views

Negative probability and spin-0 scalar field in Klein-Gordon equation

Klein-Gordon equation in quantum field theory is known to suffer from the possibility of negative probability. So, the question is, despite this, Klein-Gordon describes spin-zero field. So, how can ...
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Grassmann paradox weirdness

I'm running into an annoying problem I am unable to resolve, although a friend has given me some guidance as to how the resolution might come about. Hopefully someone on here knows the answer. It is ...
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1answer
296 views

How quantum field transforms in case of some particular spin

Except when a particle is spin-0, field of all particles transforms when frame of reference is changed, and this defines what spin is. The question is, specifically how does the quantum field ...
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423 views

An equation that describes massless spin-1 particle

Proca action/equation describes massive spin-1 particle, but I was unable to find an equation that describes massless spin-1 particle. Can anyone tell me what the name of this equation is?
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824 views

How does one derive the Lamb shift for the Hydrogen atom?

I've been perusing my copies of Srednicki and Peskin & Schroeder, and I can't seem to find an explanation of how one derives the Lamb shift that I can follow. How does one derive the Lamb shift? ...
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3k views

Why would Klein-Gordon describe spin-0 scalar field while Dirac describe spin-1/2?

The derivation of both Klein-Gordon equation and Dirac equation is due the need of quantum mechanics (or to say more correctly, quantum field theory) to adhere to special relativity. However, excpet ...
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423 views

Matrix and exponential term problem

We know the Schrodinger equation for free Hamiltonian is : $$ i\hbar\frac{\partial\psi}{\partial t} = H_f \psi $$ the wave function could be written as $$ \psi(x,t)=\hat{S}(t) \psi(x,0) $$ $$ ...
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Would a spin-2 particle necessarily have to be a graviton?

I'm reading often that a possible reason to explain why the Nobel committee is coping out from making the physics Nobel related to the higgs could be among other things the fact that the spin of the ...
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1answer
172 views

Problem in Hamiltonian

I need to elaborate the equation ,and need to know what is the physical significance and how matrices will manipulate in the equation $$ \hat{H} = (\hat{\tau_3}+i\hat{\tau_2})\frac{\hat{p}^2}{2m_0}+ ...
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1answer
93 views

Bogolubov coefficient identities

Along the lines of Birrell and Davies, which contrary to Mukhanov-Winitzki (which is actually my level) gives a quite general but short account on Bogolubov transformations, I tried to follow the ...
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113 views

Is Hyperbolic Space $H3$ the best representation space for momenta, in momentum-scale invariant theories?

The motivation is the following: For each particle of mass m, we could write : $- (E/m)^2 + (p_x/m)^2 + (p_y/m)^2 + (p_z/m)^2 = -1$, which is nothing than a equation for a point in the ...
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344 views

Newton's gravitational constant $G$, the reduced Planck constant $\hbar$, the speed of light $c$: the Dream Team of moderators?

The three great constants of Nature are well known: the speed of light $c$ (special relativity), the reduced Planck constant $\hbar$ (quantum mechanics), Newton's ...
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1answer
199 views

Definition of CFT

A standard QFT cannot be defined as a set of Poincare-invariant correlation functions because this does not take into account the possibility of non-perturbative effects (e.g. instantons) Can we ...
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190 views

Dark matter: degrees of freedom

I'm afraid this question could sound a little too vague. I don't even know if dark matter (DM) can be genuinely described by quantum field theory, or if quantum field theory should be somehow ...
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306 views

Particle sources and particle detectors in quantum field theory

I am looking for a resource that clearly exposes the concepts of a particle source and a particle detector in the context of Quantum Field theory. I want to understand Irreversibility in this context. ...
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3answers
968 views

Creation of particle anti-particle pairs

I was reading some QFT notes and there is one point that I don't understand, they are justifying why we need QFT saying that the number of particles is not preserved once we consider special ...
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0answers
70 views

Books dealing with Quantum field theory [duplicate]

Possible Duplicate: What is a complete book for quantum field theory? I am looking for good books that deal with Quantum Field theory starting from basics. Please suggest something that ...
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573 views

How can perturbativity survive renormalization?

The most usual way to renormalize quantum field theories is by re-writing the Lagrangian in terms of physical (finite) parameters plus counter-terms. Take $\lambda \phi^4$ theory for instance: $$ ...
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Do strong and weak interactions have classical force fields as their limits?

Electromagnetic interaction has classical electromagnetism as its classical limit. Is it possible to similarly describe strong and weak interactions classically?
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793 views

Gauge fixing and equations of motion

Consider an action that is gauge invariant. Do we obtain the same information from the following: Find the equations of motion, and then fix the gauge? Fix the gauge in the action, and then find the ...
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2answers
303 views

Fermion Field of Standard Model

Why fermion field is treated as anti-commuting and boson field as truly classical in standard model?
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How to obtain Dirac equation from Schrodinger equation and special relativity?

I'm reading the Wikipedia page for the Dirac equation: The Dirac equation is superficially similar to the Schrödinger equation for a free massive particle: A) ...
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1k views

How to construct the charge conjugation matrix for any given dimension?

Generally, Gamma matrices could be constructed based on the Clifford algebra. \begin{equation} \gamma^{i}\gamma^{j}+\gamma^{j}\gamma^{i}=2h^{ij}, \end{equation} My question is how to generally ...
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3answers
244 views

Odd number of second class constraints (!)

For my thesis, I have calculated the constraints for a system using Dirac method of constraint analysis. The problem is I got odd number of second class constraints (!), which gives me unusual numbers ...
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1answer
383 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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324 views

momentum four vector and dirac matrices

$$c\left(\alpha _i\right.{\cdot P + \beta mc) \psi = E \psi } $$ From the above dirac equation it can be shown for zero momenta that spin and antimatter are associated with $\beta $. On the other ...
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3answers
209 views

Quantizing first-class constraints for open algebras: can Hermiticity and noncommutativity coexist?

An open algebra for a collection of first-class constraints, $G_a$, $a=1,\cdots, r$, is given by the Poisson bracket $\{ G_a, G_b \} = {f_{ab}}^c[\phi] G_c$ classically, where the structure constants ...
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1answer
125 views

Is matrix picture of quantum mechnics further used in QFT and superstring theories?

Just curious: is matrix picture of quantum mechnaics further used in QFT and superstring theories? It seems like not....
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Calculating the commutator of Pauli-Lubanski operator and generators of Lorentz group

The Pauli-Lubanski operator is defined as $${W^\alpha } = \frac{1}{2}{\varepsilon ^{\alpha \beta \mu \nu }}{P_\beta}{M_{\mu \nu }},\qquad ({\varepsilon ^{0123}} = + 1,\;{\varepsilon _{0123}} = - ...
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2answers
307 views

Ordering Ambiguity in Quantum Hamiltonian

While dealing with General Sigma models (See e.g. Ref. 1) $$\tag{10.67} S ~=~ \frac{1}{2}\int \! dt ~g_{ij}(X) \dot{X^i} \dot{X^j}, $$ where the Riemann metric can be expanded as, $$\tag{10.68} ...
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1answer
3k views

Proof of Yang's theorem

Yang's theorem states that a massive spin-1 particle cannot decay into a pair of identical massless spin-1 particles. The proof starts by going to the rest frame of the decaying particle, and relies ...
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499 views

Why is fractional statistics and non-Abelian common for fractional charges?

Why non integer spins obey Fermi statistics? Why is fractional statistics and non-Abelian common for fractional charges?
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Lagrangian to Hamiltonian in Quantum Field Theory

While deriving Hamiltonian from Lagrangian density, we use the formula $$\mathcal{H} ~=~ \pi \dot{\phi} - \mathcal{L}.$$ But since we are considering space and time as parameters, why the formula ...
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2answers
465 views

2D Ghost CFT and two-point functions

For some reason I am suddenly confused over something which should be quit elementary. In two-dimensional CFT's the two-point functions of quasi-primary fields are fixed by global $SL(2,\mathbb ...
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1answer
557 views

Interpretation of field operator

Consider a real scalar field operator $\varphi$. It can be written in terms of creation and anihilation operators as $$\varphi(\textbf{x})=\int \tilde{dk}[ ...
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1answer
289 views

Importance of phase in probability amplitude in QFT

I have started teaching myself QFT from the textbook by A. Zee. From reading that book, my idea of a path integral in field theory is the probability amplitude to go from a given field configuration ...
3
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1answer
306 views

scattering singularity

In QFT when one works out the cross section between two colliding electrons one gets a formula which is proportional to $\theta^{-4}$ where $\theta$ is the scattering angle which is due to a nearly ...
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2answers
681 views

What's the deepest reason why QCD bound states have integer charge?

What's the deepest reason why QCD bound states have integer electric charge, i.e. equal to an integer times the electron charge? Given that the quarks have the fractional electric charges they do, ...
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1answer
406 views

Killing vectors for SO(3) (rotational) symmetry

I am reading a paper$^1$ by Manton and Gibbons on the dynamics of BPS monopoles. In this, they write the Atiyah-Hitchin metric for a two-monopole system. The first part is for the one monopole moduli ...
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1answer
2k views

Conservation Laws and Symmetries

Usually, in Quantum Mechanics, an observable is an operator on the space of the possible quantum states (labelled as $|\psi\rangle$). If this quantity is conserved, in the meaning that the associated ...
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1answer
874 views

simple explanation of chiral anomaly?

Can somebody provide a fairly brief explanation of what the chiral anomaly is? I have been unable to find a concise reference for this. I know QFT at the P&S level so don't be afraid to use math.
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1answer
1k views

What is the essence of BCFW recursion techniques?

I have recently briefly read about new methods as the Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion method. Can anybody please tell me about the essence of it? What does it mean for the ...
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1answer
200 views

Why are topological solitons present in some phases for lattice models?

Over a spatial continuum, it is easy to see why some topological solitons like vortices and monopoles have to be stable. For similar reasons, Skyrmions also have to be stable, with a conserved ...
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gravitational convergence of light

light has a non-zero energy-stress tensor, so a flux of radiation will slightly affect curvature of spacetime Question: assume a flux of radiation in the $z$ direction, in flat Minkowski space it ...
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440 views

Longitudinal and transverse part of vector field components

I was reviewing a paper of coupling to vector field and tensor field. I have got stuck with the term $$A_k \varepsilon^{kmn}\partial_mV_n=V^{T}.(\nabla\times A^{T})-\nabla.(A^{T}\times ...