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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Heisenberg uncertainity principle is valid in the case of QFT? [duplicate]

The Heisenberg uncertainty principle is valid (or taken into account) in the case of QFT?
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Can charged scalar have non zero vev?

In Higgs-Kibble mechanism, if we consider a SU[2]_L doublet of complex scalar fields, then one of them is charged and the other neutral. Why does the neutral field acquire vev and not the charged one?
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Is there one wavefunction per field? [closed]

Is the big picture of quantum field theory that: There are fields (EM, electron, Higgs, gravity, etc.) A field can be described by a wavefunction indicating the probability density of 1 or more '...
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What is the most essential theoritical constrains should be imposed on arbitrary potential's parameters?

I'm little confused about the unitarity and perturbativity constrains which imposed on a potential's parameters, like 2HD potential. Look for example: [arXiv:1507.03618v3 [hep-ph]] First, I'd like to ...
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bare Phonon and Symmetry Breaking

In condensed matter physics, the phonon is considered as a quasiparticle which is a result of the quantization of lattice vibrations. In many textbooks on solid state physics, it can be done if we ...
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Higgs mechanism in quantum GLSM

My question is regarding the following Gauged Linear Sigma Model (GLSM) in two dimensions. $$\tag{1} S=\int d^2x\Big(-D_{\mu}\overline{\phi} D^{\mu}\phi +\frac{D^2}{2e'^2} +D(|\phi|^2-r)\Big).$$ ...
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Sudakov double logarithm

I have calculated a few NLO corrections in QED and in the final result the Sudakov double logarithms have always canceled. So I thought that they have no physical meaning. On the other hand I have ...
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71 views

Non-abelian current commutators

There many articles, in which non-abelian current commutators are computed. The general result is that quantum corrections lead to additional term in commutator $$[J^a_\mu (x), J^b_\nu (y)] \delta (x^...
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96 views

Photons are self-conjugate but neutrinos may or may not: why is that?

Caution: This may be a very naive question but I find it confusing. Moreover, I believe this question is based on potential misconception. I would like it to be clarified. Although the neutrinos are ...
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64 views

Vacuum expectation value in presence of a source

If a vacuum is translationally invariant i.e., $P^\mu|0\rangle=0$ or $e^{(\pm ip\cdot x)}|0\rangle=0$, we can express the the vacuum expectation value of a field as $\langle 0|\phi(x)|0\rangle$ as $$\...
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28 views

About series expansion of effective potential and its justification

The books on quantum field theory often uses an expansion of the effective action $\Gamma[\phi_c]$ in terms of $\phi_{cl}$ and its derivatives given by $$ \Gamma[\phi_c]=\int d^4x[-V_{eff}(\phi_c)+Z(\...
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58 views

Physical interpretations of the generating functions $Z[J]$ and $W[J]$ (or $E[J]$)

In quantum field theory, the generator of all Green's functions $Z[J]$ and that of the connected Green's functions $E[J]$ are related as $$Z[J]=\exp[-iE[J]]=\int D\phi\exp[i\int d^4x(\mathcal{L}(\phi)+...
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60 views

Propagator from Path integral

In class we have proved something like: $$ \frac{\partial^2 Z(J,\bar{J})}{\partial J(x) \partial \bar{J}(x')}\frac{1}{Z}|_{J=\bar{J}=0}=\Delta(x-x').$$ That by introducing source terms to path ...
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45 views

Yukawa Potential in non-relativistic limit

In Peskin's book "An Introduction to Quantum Field Theory", on page 121 (section 4.7) , it tries to recover the Yukawa Potential in the nonrelativistic limit, but there's a simplification that I don't ...
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Determinants in path integrals in gauge theories and geometry

I know that in the formalism of path integral it is easy to show how determinants, corresponding to gauge fixing condition and FP ghosts, appear. But there is strict explanation of these determinants ...
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1answer
79 views

Anomaly, Ward identity [closed]

While studying notes on anomaly by Adel Bilal (http://arxiv.org/abs/0802.0634), I stuck in a calculation. Here it goes as follows: The three-current correlator in perturbation theory as a one-loop ...
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1answer
110 views

Confusion in understanding of quantum fluctuations and vacuum energy

I'm having a bit of trouble understanding what exactly is meant by a quantum fluctuation of a quantum field and its relation to the vacuum energy attributed to such a field. Is the point, that due ...
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297 views

What is meant by the term “value” of a scalar quantum field?

During the slow roll of a scalar field, the scalar field is changing its value over time. But what is meant by the term "value" of a scalar field? Since the scalar field is quantized, I don't ...
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Simple, physical explanations for Hadamard behaviour of two-point functions

The two-point function of local quantum fields on a curved spacetime exhibits a singularity of a very particular form, known as Hadamard form, for null separated points $(x,y)$ (including the ...
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Quartic interactions of a complex scalar field

For a quartic self-interaction of a complex scalar field (matrix), one can write the terms: $aTr((\phi^*\phi)^2)$ and $bTr(\phi^*\phi)^2$ ; the trace and the "double" trace term, with two different ...
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Reaching equilibrium in a blackbody and light-matter interaction

Suppose we have a metallic cavity maintained at a fixed temperature. Suppose we start with any distribution of radiation that is not in equilibrium with the container. Gradually, when the equilibrium ...
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Rest mass of phonon: is this concept definable?

Phonons are obtaied by non-relativistic quantization of the lattice vibration. The dispersion relation is given by $\omega=c_s k$ where $c_s$ is the velocity of sound. What can we say about the mass ...
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35 views

Inner product of standard-momentum one-particle states in Weinberg

My question has essentially already been addressed in Questions concerning some parts of the section on one-particle states in Weinberg's first volume on QFT (third question), but unfortunately ...
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243 views

From Quantum Mechanics to Quantum field theory to String theory?

Today during a very "unique" study session, I might have internalized why Quantum mechanics was not enough, and Quantum field theory makes sense. It seems the reasons are that When a potential is ...
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With the descent of Newtonian mechanics is Newton's third law still valid?

Or more specifically, with the standard model, quantum theory and other advances in physics, all those experiments in CERN and other accelerators, was there any occurrence where this law was violated? ...
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LSZ formula in spontaneously broken gauge symmetry

The LSZ formula connects scattering amplitudes with the pole structure of correlation functions. I've only seen the derivation for $\phi^4$, and the poles where then simply the dressed propagators of ...
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126 views

Physical interpretation of the retarded vs. Feynman propagators?

We calculate the real-space propagator $\Delta(x)$ for a free real scalar field $\varphi(x)$ with mass $m$ by performing the Fourier transform (using sign convention +---) $$\Delta(x) = \int \frac{d^...
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“Constant Fermion”

I was talking to a professor in my institution which works in Lorentz Violation of various QF theories. While we talk about a SUSY lagrangian, I asked him if we could have a fermion acquiring VEV and ...
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80 views

Schwartz QFT solution

Is there a way I Can find a solutions manual for Matthew Schwartz's "Quantum Field Theory and the Standard Model" book?
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48 views

How does a $\Theta$ function arise in this correlator?

I am currently reading the paper by Coleman on Symmetry breaking in 2d, which can be found here. On page 262 (4th page in the document), he is evaluating the following distribution: $$ F_{\mu}(k)=\...
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35 views

Thermal mass and Thermal Width

I have a question about understanding the physical interpretation of the thermal mass and width of a particle. If we consider a particle in a plasma (which lets say is in the early universe and so ...
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56 views

How to calculate the contour integration with branch point? [closed]

The question come from a Mutusbara Sum like this $${ \sum _{ { z=i\omega }_{ n } } { \frac { -\alpha E\pi }{ 4{ z }^{ 3 }\sqrt { -\alpha -z } } } }$$ it equal a contour integral around Imaginary ...
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1answer
87 views

Perturbativity of SM Higgs quartic coupling [closed]

I'm little confused about the maximal appropriate value for the SM Higgs quartic coupling. I know that the Higgs mass, $m_h= 125 \,\text{GeV}$ and that $ \lambda = m_h^2 / 2 v^2 \simeq 0.1 $ for $v = ...
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Elementary particles interaction time (in LHC, for example)

Feynman description of an interaction contains diagrams with different total time steps (that contribute only a little to the amplitude, I guess). Is there a calculation, for a given interaction, what ...
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3answers
310 views

Is Bohmian Mechanics incompatible with loop corrections?

For those who continue to be unsatisfied with Quantum Mechanics (QM), Bohmian Mechanics (BM) is an alternative worth considering. It is sometimes claimed that BM is equivalent to QM, but Lubos Motl ...
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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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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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1answer
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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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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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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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 ...
3
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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, ...
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1answer
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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1answer
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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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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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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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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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). ...
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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 ...
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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 ...