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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How is particle creation (or annihilation) in non-relativistic many body physics?

How is that, in many body physics, particle creation and annihilation is possible even though it is a non-relativistic theory?
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41 views

Hydro regime of strongly coupled field theory, low viscosity

I am trying to get an intuition for the following argument: In heavy ion collisions the central collision area can be described by almost ideal hydrodynamics at very early times after the impact. This ...
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306 views

Paths in the path integral

In the path integral approach one defines in some heuristic way the functional path integral \begin{equation} Z=\int{\cal{D}}\phi e^{iS(\phi)} \end{equation} and the one claims that one must ...
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199 views

Relative Minus signs from different Feynman Diagrams

I have a problem understanding the occurrence of a the relative minus signs between contributions, coming from different Feynman diagrams, involving fermions. A simple example is Bhabha scattering ...
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436 views

What prevents photons from getting mass from higher order Feynman diagrams

The Higgs boson and gluons have no electric charge and photons couple to charge, so there is no tree level interaction between them and photons. But what prevents higher order diagrams from ...
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266 views

A step in the derivation of the magnetic moment of the electron in Zee's QFT book

In chapter III.6 of his Quantum Field Theory in a Nutshell, A. Zee sets out to derive the magnetic moment of an electron in quantum electrodynamics. He starts by replacing in the Dirac equation the ...
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53 views

Tetrad choice for Pauli-Lubanski in the massless case

The Pauli-Lubanski pseudovector coincides with intrinsic spin in the rest frame of the particle. In a more general frame, one defines a tetrad and projects the PL vector on it to define intrinsic spin ...
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425 views

Time evolution of a quantum field via classical field theory

How do quantum fields evolve in time? (Heisenberg Picture) How does time evolution relate to the (E-L) equations of motion? I’ve had this understanding that there is a duality between classical and ...
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84 views

Question about the foundation of part I in A. Zee's book

Zee says in Section I.3 of QFT in a nutshell: The functional integral $$Z = \int D \varphi e^{i \int d^4 x [\frac{1}{2} (\partial \varphi)^2 - V(\varphi) + J(x) \varphi (x)]} \tag{11} $$ is ...
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331 views

Wick Contraction

I am reading Quantum Field Theory in a Nutshell by A. Zee. Zee introduces the rationale/machinery behind Feynman diagrams in three steps: Baby -> Child -> "Real". The baby problem generates ...
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680 views

What is the conclusion from Aharonov-Bohm Effect?

What is the conclusion that we can draw from the Aharonov-Bohm effect? Does it simply suggest that the vector potential has measurable effects? Does it mean that it is a real observable in quantum ...
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Evaluate functional integral in partition function of thermal $\phi^4$ theory (Kapusta/Gale p.34-35)

my question is about some steps in the book "Finite Temperature Field Theory" by Kapusta and Gale. To explain the setting, I how to evaluate the functional integrals in the expression $$ \ln ...
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82 views

Significance of total divergence anomaly term

What is the significance of the fact that the anomany term (calculated from the triangle diagram) is a total divergence? Or, in other words, what is the significance of $$\partial_\mu j^\mu_A\sim ...
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200 views

Dilaton field and Scale symmetry breaking

I have read at some places that a dilaton field is associated with the spontaneous breaking of scale symmetry in a theory. (While others would be difficult to trace right now, the most easily ...
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69 views

Hamiltonian split into Mass term and Decay Width

I have encountered the following procedure several times now, and none of the sources ever explain the physical reason behind it: The Hamiltonian $H$ is split into $M$ and $\Gamma$. WHY? Where ...
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122 views

Heisenberg's Unified Field Theory

While searching in the Internet, I came to know about Werner Heisenberg's attempt to obtain an Unified Field Theory (see the book Introduction to Unified Field Theory of Elementary Particles). But ...
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283 views

QFT Hilbert spaces over other rings than the complex numbers $\mathbb{C}$

I would like some help evaluating a physics theory recently proposed by a physics professor at the College of Dupage. I think the theory is utterly wrong, for very simple reasons. If an amateur ...
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298 views

Higgs branch and Coulomb branch

I heard that the distinguish between Higgs branch and Coulomb branch is the limit of some parameters. (If i remember correctly, something like FI parameters. ) Here i want to know what is FI ...
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65 views

What is the difference between $N=(2,2)$ with $N=(2,2)^*$ in 2d?

What is the difference between $N=(2,2)$ with $N=(2,2)^*$ in 2 dimensional theory? In some sense, i heard, they are totally different theory. I heard from breaking of $N=(4,4)$ supersymmetry it ...
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102 views

Semiclassical approximation in Quantum Field Theory

I've recently stumbled upon a semiclassical approximation to quantum field theory that I've never heard of and have a hard time understanding. Consider the Hamiltonian, \begin{equation} H = \frac{c}{ ...
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92 views

Annihilation Operator on the Fock space

I agree that $$\hat a|0\rangle=0$$ But then, based on the above, the following should hold $$\hat a_k |N_1,...,N_{k-1},0,N_{k+1},...\rangle=|N_1\rangle\oplus\cdots\oplus |N_{k-1}\rangle\oplus \hat ...
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403 views

Complex integration by shifting the contour

In section 12.11 of Jackson's Classical Electrodynamics, he evaluates an integral involved in the Green function solution to the 4-potential wave equation. Here it is: $$\int_{-\infty}^\infty dk_0 ...
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Physical meaning behind causal massless scalar propogator

I know that for a scalar massless field in $(3+1)$ spacetime that: $$ \langle 0 | \phi(x) \phi(y) | 0 \rangle \propto |x-y|^{-2} = (-(t_x-t_y)^2 + (\vec{x}-\vec{y})^2)^{-1}. $$ I also know that $$ ...
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286 views

Why is fundamental physics taught in terms of particles?

According to this paper, there can be no relativistic quantum theory of localizeable particles ("relativity plus quantum mechanics exclusively requires a field ontology"). Sean Caroll has also argued ...
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Electric charges on compact four-manifolds

Textbook wisdom in electromagnetism tells you that there is no total electric charge on a compact manifold. For example, consider space-time of the form $\mathbb{R} \times M_3$ where the first factor ...
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119 views

What is IR CFT and UV CFT?

What is IR CFT and UV CFT? In many physics related materials, they often mention IR, and UV. I think it is related with regularization (I remember in QFT, there is UV cutoff in some regularization ...
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166 views

Why doesn't Graphene have a band gap?

Is there any simple justification about graphene having no band gap? How bout its linear E-K? Why bilayer graphene has a quadratic E-K and electric field can open a band gap there? I do not ...
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607 views

QFT Dyson series: why are we solving the Schrodinger equation?

In quantum field theory, the solution of the time evolution operator of the Schrodinger equation (in the interaction picture) is given by Dyson's series, which is used to calculate the S-matrix. Why ...
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235 views

Deriving photon propagator

In Peskin & Schroeder's book on page 297 in deriving the photon propagator the authors say that $$\left(-k^2g_{\mu\nu}+(1-\frac{1}{\xi})k_\mu k_\nu\right)D^{\nu\rho}_F(k)=i\delta^\rho_\mu ...
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83 views

Symmetry transformation on Quantum Field

I stumbled upon this point several times, the latest beeing this question: Connection between conserved charge and the generator of a symmetry I want to understand, why Quantum fields transform under ...
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67 views

The interpretation of charge-conjugated wave-equation solutions

I would like to clarify a confusion which is related with the charge conjugation operator which is haunting me for quite a time.I already asked similar questions here and I admit I haven't got a real ...
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386 views

Connection between conserved charge and the generator of a symmetry

I'm trying to understand the connection between Noether charges and symmetry generators a little better. In Schwartz QFT book, chapter 28.2, he states that the Noether charge $Q$ generates the ...
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150 views

Self-adjointness

I know I have posted this question before some time ago. But no one could help so I decided to put my problem in another background. The Schrödinger equation of a free scalar field is given by ...
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138 views

Regarding Non-renormalizatibility of GR

I've been doing some reading trying to get to a better understanding of some renormalization issues with the Einstein-Hilbert action. But, something odd came into mind that I'm hoping some users may ...
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131 views

Derivation of Baryon Number conservation?

The symmetry connected to Baryon/Lepton Number conservation is, as far as I understand, global U(1) symmetry (which is called here global gauge invariance). Does anyone know of an explicit ...
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215 views

Time evolution in QFT

Standard quantum mechanics postulates that, for an isolated system, time evolution is ruled by unitary operators, then one can prove Schrodinger equation (SE), which is not Lorentz invariant. If we ...
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107 views

Beta function of the non-linear sigma model

In chapter 7.1.1. inTong's notes about String Theory could someone sketch how can I show the statements that he nmakes around eq. 7.5 That the addition of the counterterm can be absorbed by ...
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254 views

Why Lorentz group for fields and Poincaré group for particles?

Wigner treatment associates to particles the irreps of the universal covering of the Poincaré group $$\mathbb{R}(1,3)\rtimes SL(2,\mathbb{C}).$$ Why don't we consider finite dimensional ...
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324 views

What are renormalons from a physics point of view?

This is again a question in the context of this paper about the Exact Renormalization Group. On p 23 and the following few pages, it is explained that for a $\lambda \phi^4$ bare action at the bare ...
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1answer
50 views

Mapping Issues with Unbounded Operators

Consider the operator-valued generalized function $\phi^{(k)}_{l}:=\phi^{(k)}_{l}$ on space-time $\mathcal{M}$. Now, smooth the operator-valued generalized function with test function $f(x)$ ...
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63 views

Why can't muons be the carriers of the strong interaction?

The strong forces operate up to range of $10^{-15}$ meters. The calculations for Muon reveal that they can be propagator for distances up to $10^{-14}$ meters. Why can't I ignore the factor of 10 and ...
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133 views

Relationship between plasma physics and quark gluon plasma

To what extent do the ideas common in modern plasma physics, such as magnetohydrodynamics, cold plasma models, common types of plasma waves, Maxwell's Equations, etc, relate to the study of quark ...
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288 views

How do charged particles interact?

You'll have to forgive me if this question is too wrapped up in "classical" thinking. I've read that electrons and protons interact by trading photons, but this only raises more questions. What ...
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231 views

Transition amplitudes by functional methods in QFT

I am following section 9.2 in Peskin and Schroeder in which the Feynman rules are derived for scalar fields. They define (in eqn (9.14), page 282) the transition amplitude from $\vert\phi_a\rangle$ ...
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161 views

Symmetry factor and coupling constant in scalar field theory

I am just now starting my particles "education" so forgive me if this is elementary... Looking at interaction terms in a scalar field Lagrangian, I get: $$ ...
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64 views

Textbooks on algorithms for the perturbative calculation of High energy physics

For the perturbative calculation of High energy physics, I have known some packages such as FeynArts, FeynCalc, MadGraph, CompHEP, GiNaC, and so on. But I am wondering whether there exists a textbook ...
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376 views

Chiral anomalies

Recently I have read that there is contraction of chiral anomalies in SM. But people are working on chiral anomalies theory. So I have the question: what is the importance of development of the theory ...
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170 views

Is the ground state of a QFT always a pure state? And excited states are mixed?

I am studying entanglement entropy. It's fullfilled for any local quantum system that the entanglement entropy of a region $A$ in a highly mixed state is extensvie, $$ S_A \sim ...
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215 views

what physical quantity do real scalar field operators create/destroy?

Let $\phi(\textbf{x}) \neq \phi^\dagger(\textbf{x})$ be a complex scalar field, and let $\varphi(\textbf{x}) = \varphi^\dagger(\textbf{x})$ be a real scalar field. $\phi(\textbf{x})$ destroys a ...
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Massless integrals in dim-reg

Consider the massless divergent integral $$ \int dk^4 \frac{1}{k^2}, $$ which occurs in QFT. We can't regularize this integral with dim-reg; the continuation from the massive to the massless case is ...