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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QED proper vertex Ward identity derived from global symmetry and Schwinger-Dyson Equations?

In QED, according to Schwinger-Dyson equation, $$\left(\eta^{\mu\nu}(\partial ^2)-(1-\frac{1}{\xi})\partial^{\mu}\partial^{\nu}\right)\langle 0|\mathcal{T}A_{\nu}(x)...|0\rangle = e\,\langle ...
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What is the difference between $N=(2,2)$ with $N=(2,2)^*$?

What is the difference between $N=(2,2)$ with $N=(2,2)^*$? In some sense, i heard, they are totally different theory. I heard from breaking of $N=(4,4)$ supersymmetry it comes $N=(2,2)^*$. What is ...
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The problem in Sredniki's textbook: How do I calculate loop corrections for $\phi\phi\to\phi\phi$ with this Lagrangian?

The problem in Sredniki's textbook 10.5 : For a free scalar field $\psi$, the Lagrangian is $$\cal{L}= -\frac{1}{2}\partial^\mu\psi\partial_\mu\psi-\frac{1}{2}m^2\psi^2$$ Here we use the metric ...
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66 views

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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78 views

Deriving Feynman rules from a Lagrangian for vertex factors for “more complicated” interactions

I am trying to derive Feynman rules from a given Lagrangian and I got stuck on some vertex factors. What for example is the vertex factor that corresponds to the four-scalar interaction that is ...
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67 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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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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Does tunneling transmission probability depend on the density of states or velocity?

In some quantum text books [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. ($T(E) = C \times DOS_1(E) \times DOS_2(E)$, where C ...
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Computing box diagrams with non-vanishing external momenta

I'm trying to explicitly compute the following box diagram in the Feynman-t'Hooft gauge: If I neglect the impulsion of the $s$ quark, then the final amplitude is given by $$\mathcal{A} \propto ...
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1answer
88 views

Fierz identity for Weyl spinors in tensor currents

Using Fierz identity I found that certain four-fermion operator with left $l_i$ and right-chiral $r_i$ Weyl spinors vanish $\bar{l}_1\sigma_{\mu\nu} r_2 \bar{r}_3 \sigma^{\mu\nu} l_4 =$ $ ...
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161 views

Is electric charge truly conserved for bosonic matter?

Even before quantization, charged bosonic fields exhibit a certain "self-interaction". The body of this post demonstrates this fact, and the last paragraph asks the question. Notation/ Lagrangians ...
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408 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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1answer
363 views

Time-ordering in QFT

In Srednicki QFT page 37. In the derivation of LSZ reduction formula, he introduces the time-order operator $T$, so no time-dependent creation/annihilation operators are left in the transition ...
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1answer
77 views

What is the meaning of a state in QFT?

I guess this may be more of a mathematical than a physics question, but it comes down to physical interpretations, so I'm posting it here. In classical Quantum Mechanics, we can define a state ...
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1answer
53 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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2answers
121 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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1answer
35 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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48 views

Fermions in Schwarzschild spacetime

To my understanding Geroch proved that on 4-dimensional non-compact manifold a necessary and sufficient condition for a manifold to have a notion of spinors is to be parallelizabe .1 (General ...
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1answer
61 views

In QFT, do the fields evolve with determinism, in principle?

In quantum mechanics, the outcomes of a certain measurement might not be deterministic. However, the wavefunction evolves with determinism according to Schrodinger's equation. Is QFT analogous in ...
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15 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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1answer
55 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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35 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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1answer
141 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 ...
6
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1answer
120 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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43 views

Hoft algebra and quantum double [on hold]

the quantum double of SL(2,R) the transition from a Minkowski to SL(2;R) momentum space translates for the structure of relativistic symmetries in a deformation of the Poincare group to the quantum ...
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1answer
56 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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129 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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LSZ reduction vs adiabatic hypothesis in perburbative calculation of interacting fields

As far as I know, there are two ways of constructing the computational rules in perturbative field theory. The first one (in Mandl and Shaw's QFT book) is to pretend in and out states as free ...
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27 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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152 views

Proof of Loss of Lorentz Invariance in Finite Temperature Quantum Field Theory

In the standard quantum field theory we always take the vacuum to be a invariant under Lorentz transformation. For simple cases, at least for free fields, is very simple to actually prove this. Now ...
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1answer
138 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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249 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
46 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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109 views

Fermi Energy Variation

What would be a good Internet link that would properly explain Fermi Energy? How does the Fermi Energy of a material vary with external influence, such as doping of the material, and applied ...
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1answer
52 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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52 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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3answers
131 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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2answers
121 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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1answer
221 views

Determinant for a coupled fluctuation Lagrangian

Lets consider a bosonic physical system in variables $t, x$ and $y(x)$ ($x$ dependent) with a classical Lagrangian $L$. To first order in fluctuations $x \to x+\xi_1$ and $y \to y+\xi_2$ the ...
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1answer
89 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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45 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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Is a “third quantization” possible?

Classical mechanics: $t\mapsto \vec x(t)$, the world is described by particle trajectories $\vec x(t)$ or $x^\mu(\lambda)$, i.e. the Hilbert vector is the particle coordinate function $\vec x$ (or ...
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87 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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1answer
94 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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1answer
85 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 ...
5
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1answer
188 views

Secondary constraints leads to the value of lagrange multiplier

From Lagrangian I got two primary constraint $\phi_i$ and $\phi$. And my Hamiltonian in presence of the constraints becomes- $$H_p=p\dot q-L+\lambda_i\phi_i+\lambda\phi$$ here the $\lambda_i$ and ...
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118 views

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 ...
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101 views

Unitarity and renormalizability

What is the difference between the unitarity of the theory and its renormalizability? Can we say that renormalizable theory is unitary after renormalization? The questions have arisen after I have ...
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1answer
62 views

Scattering theory textbooks

I am looking for a possibly extensive list of great textbooks on elastic and inelastic scattering of particles within quantum field theory. So far I am familiar with: Peskin and Schroeder: An ...
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861 views

Is the Standard Model consistent (UV complete)?

This is a question about the self-consistency of the Standard Model - which I believe is the same as asking whether it is UV complete - in other words, can it be used to predict experimental results ...