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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Adiabatic quantum evolution of single photon or biphoton system

The prerequisite for adiabatic quantum evolution of single photon or biphoton system is as follows. We have to prepare a single photon or biphoton quantum system which has a ground and a higher level ...
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3k views

QM and Renormalization (layman)

I was reading Michio Kaku's Beyond Einstein. In it, I think, he explains that when physicsts treat a particle as a geometric point they end up with infinity when calculating the strength of the ...
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979 views

Calculating conductivity from Green's functions

I am trying to calculate the conductivity in the linear response regime of a disordered electron gas. (or eventually of a mean field Heavy fermion system with known one particle green's functions). I ...
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357 views

Field Strength Renormalisation in Peskin and Schroeder

In chapter 7 of Peskin and Schroeder they define the field strength renormalisation $Z$ for a quantum field to be the residue of the Fourier transform of the correlation function $$\langle \Omega | \...
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832 views

What goes wrong when one tries to quantize a scalar field with Fermi statistics?

At the end of section 9 on page 49 of Dirac's 1966 "Lectures on Quantum Field Theory" he says that if we quantize a real scalar field according to Fermi statistics [i.e., if we impose Canonical ...
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476 views

How are low energy effective actions derived in string theory?

For example the eq 2.1 here with regards to Type IIB. Unless I am terribly missing/misreading something Polchinski doesn't ever seem to derive these low energy supergravity actions. I would like to ...
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144 views

Are scalar fields invariant under unitary operators?

Is this correct? Are scalar fields defined as being invariant under $U^{\dagger}U$ transformations? If so, is this transformation also called the trivial transformation? Thanks for any help or ...
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1answer
696 views

What led to the electroweak and strong forces splitting?

Is the reason for the split believed to be spontaneous symmetry breaking? If so, did SSB occur because the Universe was cooling rapidly from extremely high temperatures?
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102 views

3d Ising Fixed point on general space manifold?

The headline question: Is it known how to construct an equivalent of the 3-D Ising Fixed point theory on an arbitrary 3-D manifold? Or any non-trivial d > 2 fixed point? The answer is maybe as simple ...
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278 views

Is color confinement detected?

I'm a graduate student studying QFT. I'm quite interested that is color confinement detected or proved? (both directly and indirectly) Or it is just an assumption?
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161 views

Can an observer be the observed?

As a supplement to this question as to whether particles can be observers, supposing that the answer is yes. One could suppose a setup where particle A is observing particle B, but what to stop us ...
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Do commutation relations exist between superfields?

To quantize a theory, Klein gordon field for example, commutation relations are stablished. Or anticommuting ones in the fermionic case. If I have the Wess.Zumino model or the free model: $$S~=~\int\...
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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 ...
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280 views

Renormalization, symmetries and freedom to choose counterterms

I am considering the perturbative renormalization of a simple non-phenomenological QFT with Lagrangian ${\cal L}$ (for scalar fields with multiple generations). I understand that I can renormalize it, ...
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1answer
448 views

What is on the AdS side in AdS/CFT supergravity or string theory?

What really is on the AdS side in AdS/CFT, does it always have to be string theory or is sometimes supergravity "enough" or better suited to do calculations? From the answers to my earlier question, ...
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3answers
999 views

Connection between $\Delta x \Delta p \geq \frac{\hbar}{2}$ and $\Delta E \Delta t \geq \frac{\hbar}{2}$

Is there a way to derive second equation from the first one? I mean is there a connection between those two uncertainty relations? \begin{align} \Delta x \Delta p &\geq \frac{\hbar}{2}\\ \Delta ...
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2answers
167 views

Lorentz homogeneous group and observables

For generators of the Lorentz group we have the following algebra: $$ [\hat {R}_{i}, \hat {R}_{j} ] = -\varepsilon_{ijk}\hat {R}_{k}, \quad [\hat {R}_{i}, \hat {L}_{j} ] = -\varepsilon_{ijk}\hat {L}_{...
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1k views

Gauge fixing and degrees of freedom

Today, my friend (@Will) posed a very intriguing question - Consider a complex scalar field theory with a $U(1)$ gauge field $(A_\mu, \phi, \phi^*)$. The idea of gauge freedom is that two solutions ...
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1answer
517 views

Solving Klein-Gordon equation in the Rindler coordinates - the Unruh effect

I am reading 't Hooft's notes on Black Holes. I want to find the solutions of the Klein-Gordon equation $(\tilde{x},\tilde{y}, \rho, \tau)$ in the Rindler coordinates which are $$x=\tilde{x}\,\,\,\,\ ...
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82 views

chirality oscillations in weak interaction

As far as I have understood, the mass $m$ of a fermion causes a coupling of the both chiralities $\psi_L$ and $\psi_R$. This coupling would induce an oscillation of the chirality within a time scale ...
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304 views

Why do we only have complete particle generations?

There are 3 generations of fermions in the standard model. I know that there is a theorem that states, that only complete generations are allowed. This means that there have to be quarks with three ...
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92 views

Baryogenesis - P and CP Violation

There are 4 requirements for baryogenesis to happen: 1. A process that violates baryonnumber conservation 2. The universe has to be out of equilibrium 3. P has to be violated 4. CP has to be violated ...
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1answer
169 views

Mathematical explanation of why Higgs has a vev

If Higgs ($\phi$) is a complex doublet: $ \phi_{1}+i\phi_{2}$ $\phi_{3}+i\phi_{4}$ how do I show that $\phi_3$ has a vev but the others do not? $V(\phi)=\mu^{2}(\phi^{\dagger}\phi)+\lambda(\phi^{\...
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Descent equation and anomaly polynomial

I am just reading Ryu, Moore and Ludwig's paper on classifications of topological insulators and quantum anomaly. They are trying to relate the quantum anomaly as a signal of the presence of a ...
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2answers
395 views

Etymology of “Renormalisation”

Just out of curiosity, does anyone know why "renormalisation" is so named? Who first came up with the term, and why was it used? I did a mathematics undergraduate so to me "normalisation" means ...
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1k views

What is a general definition of the spin of a particle?

In quantum field theory, one defines a particle as a unitary irreducible representations of the Poincaré group. The study of these representations allows to define the mass and the spin of the ...
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355 views

How does spin appear in QFT?

In QFT, as I read, it appears naturally. It is connected with Poincare algebra, doesn't it? __ As explanation of the main part of the question. Operator of relativistic orbital angular momentum 4-...
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1answer
991 views

What is the formal definition of spin-independent vs. spin-dependent scattering?

In the search for WIMPs as the dark matter particle, there is an important distinction between spin-independent and spin-dependent scattering. Roughly, WIMPs scattering from nucleons through a spin-...
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1answer
1k views

Contact Term and Schwinger Term

In field theory, when 4-divergences of time-ordered Green's functions are computed, there are extra terms known as 'Schwinger terms'. When deriving the quantum equations of motion for time-ordered ...
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1answer
156 views

Poles bit in a propagator

Hi I am trying to derive the K-G propagator and am stuck on the bit where Cauchy's Integral formula is needed i.e evaluating from $$\int \frac{d^{3}p}{(2\pi)^3}\left\lbrace\frac{1}{2E_{p}}e^{-ip.(x-y)}...
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1answer
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707 views

Renormalization Group for non-equilibrium

For equilibrium/ground state systems, a (Wilson) renormalization group transformation produces a series of systems (flow of Hamiltonians/couplings $H_{\Lambda}$ where $\Lambda$ is the cut-off) such ...
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205 views

Path integral measure and symmetry

For a generic field theory the path integral measure is defined as, \begin{equation} \mathcal{D}\Phi = \prod_i d\Phi(x_i), \end{equation} where $\Phi$ is a generic field (i.e. it may be scalar, ...
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477 views

What determines the spin of fields in gauge field theories?

I understand that gauge bosons transform as the adjoint of their respective symmetry groups, but what determines the spin of the field? Can you have some gauge group where the adjoint is spin zero?
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Imposing anti-commutation relations on fermionic quasi-particles

In many theories of CMT, we assume the nature of quasi-particles (without giving proper justifications). For example, we assume nature of quasi-particles to be fermionic in case of a interacting ...
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182 views

Higgs boson sources

Every fundamental interaction in Physics comes from "some bosonic field" or "force carrier", according to QFT. We have 4 fundamental interactions(force carriers): Gravity (Gravitons) ...
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227 views

Proof of rotational and translational invariance?

If $ϕ^† ϕ$ is invariant under $SU(2) \times U(1)$, a Phys.SE question I recently posted, then does that mean $ϕ^† ϕ$ is invariant under rotations and translations?
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1answer
134 views

Can we obtain non-Lorentzian metric from Lorentzian metric, through renormalization methods?

Since low-energy, non-relativistic thermal field theories are defined in Euclidean spacetime, while high-energy relativistic theories are define in Minkowski spacetime, I was wondering if there are ...
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1answer
265 views

Zeta regularization gone bad

This may sound as a mathematical question, but it should be very familiar to physicists. I am trying to perform an expansion of the function $$f(x) = \sum_{n=1}^{\infty} \frac{K_2(nx)}{n^2 x^2},$$ for ...
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0answers
94 views

Exact summation of a sub-class of diagram: do we know the exact solved problem?

In quantum field theories (to be relativistic, (non-)relativistic statistical or whatever), we have the powerful diagrammatic approach at our disposal. Most of the time we can not sum up all the ...
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1answer
1k views

Cross-section in relativistic limit: Fermi's golden rule still valid?

In order to calculate the cross-section of an interaction process the following formula is often used for first approximations: $$ \sigma = \frac {2\pi} {\hbar\,v_i} \left| M_{fi}\right|^2\varrho\...
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2answers
178 views

BRST transformation of adjoint spinor

in Yang-Mills-Theory with matter fields a dirac spinor $\psi$ transforms under BRST as $$\psi \to \delta_\Omega\psi=i\eta\psi $$ with $\eta$ being a ghost field. If I want to get the transformation of ...
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3answers
586 views

Problems with putting mass on Yang-Mills theory by hand

When Yang-Mills field theory was introduced, a problem is that the gauge invariance can not allow mass for the gauge field. Later people invented spontaneous symmetry breaking and Higgs mechanism to ...
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2answers
597 views

Correlation functions in thermal field theory etc

Suppose I am studying a field theory at finite temperature or some black hole formation scenario from boundary theory perspective in the sense of AdS/CFT. How is it possible to gain information about ...
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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 ...
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1answer
335 views

Difference between vector and pseudo-scalar

In physics, a pseudo-scalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion such as improper rotations while a true scalar does not. Can someone show me ...
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1answer
403 views

How does the dressed Klein-Gordon propagator look in position space?

The free Klein-Gordon propagator in momentum space $\sim (p^2-m^2+i\epsilon)^{-1}$ has just a single pole at $p^2=m^2$. The passage to Fourier space is difficult but possible. The result is very ...
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183 views

Poincaré group on quantum Klein-Gordon field (C*-algebraic scenario)

on the same topic as this question, I have been trying to fool around with the free real K-G field in flat spacetime on the C*-algebraic scenario (Haag-Kastler axioms, Weyl quantization, etc). Since ...
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158 views

QFT basics for Klein-Gordon fields

I am teaching myself QFT from Peskin for next years maths course and I have two questions: What is a c-number? Is it a complex number, and if so why does it mean, $[\hat{\phi}(x),\hat{\phi}(y)]~=~&...
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1answer
921 views

Lorentz transformation of classical Klein–Gordon field

I'm trying to see that the invariance of the Klein–Gordon field implies that the Fourier coefficients $a(\mathbf{k})$ transform like scalars: $a'(\Lambda\mathbf{k})=a(\mathbf{k}).$ Starting from the ...