arXiv subjects

Israel Weimin Sun

Publications and source records attributed to Israel Weimin Sun.

4 recordsLinked to original sources

arXiv2019

An Empty Chiral Rotation for the Adler-Bell-Jackiw Anomaly

This is an article which intends to shake down the traditional belief that the celebrated Adler-Bell-Jackiw anomaly stems from the chiral rotation non-invariance of the fermionic measure. The fermionic functional integration measure in quantum field theory should be defined so as to reproduce the standard Feynman diagrammatic expansion. This implies that a plain definition of the fermionic measure automatically serves such a purpose. A dilemma then arises: how could one identify the ABJ anomaly as a nontrivial Jacobian factor for a chiral transformation ? The true answer is indeed surprising and unexpected, that is, the Jacobian factor is actually a random and indeterminate object, hence it carries no physical information. A true explanation for the ABJ anomaly is suggested.

physics.gen-ph↗

arXiv2019

Mathematical Melody in Quantum Anomaly via the Path Integral Approach: A Lesson from the Transverse Current Anomalies in QED

I address and solve the natural problem of calculating the transverse current anomalies in quantum electrodynamics by means of the path-integral method. An explicitly divergent and regulator-dependent anomaly term is produced for the vector current, in apparent contradiction with the null-result prediction of the one-loop perturbative evaluation. This paradox is carefully explained using the concept of infinite-dimensional Grassmann functional integration, signifying a modification to the conventional wisdom of understanding anomalies in field theory.

physics.gen-ph↗

arXiv2018

Some remarks on the current issues in nucleon spin structure study

I give some personal remarks on some current issues in the nucleon spin structure study. At an elementary level I propose a new angular momentum separation for the massless Dirac field in a free theory which mimics the usual free photon angular momentum separation pattern in Coulomb gauge. In connection with this construction I introduce a somewhat idiosyncratic formalism in a free massless Dirac theory which I call "dressed axial $U(1)_A$ symmetry". I show that this new "fermion spin operator", which is more correctly called "helicity vector operator", can be incorporated into this new symmetry pattern in a natural way. This set of "dressed axial vector current" and its corresponding charges show an interesting internal structure and may be useful in a broader physical context. I then discuss the case of the QED model with a massless Dirac fermion. In the case of covariant quantization, I give a new and correct proof that the additional term in the total angular momentum operator stemming from the gauge-fixing term does not contribute at the level of physical matrix elements, which is discussed in the relevant literature. At the level of asymptotic fields I construct the helicity vector operator of the QED theory which actually coincides with the usual projection of the total angular momentum operator when acting on a beam of collinearly moving free particles. I then consider the QCD model with only two massless light quarks. In this context I discuss the approximate concept of "asymptotic quark and gluon fields" which is relevant to the usual parton model picture and propose to use the asymptotic "quark helicity vector" operator to describe the quark helicity contribution to an IMF proton. Finally, I give some remarks on the concept of IMF itself, which show that this very concept should be understood with some reservation from a rigorous mathematical consideration.

physics.gen-ph↗

arXiv2018

Quantum Gauge Transformation, Gauge-Invariant Extension and Angular Momentum Decomposition in Abelian Higgs Model

I discuss the momentum and angular momentum decomposition problem in the Abelian Higgs model. The usual gauge-invariant extension (GIE) construction is incorporated naturally into the framework of quantum gauge transformation $\grave{a}$ ${\it la}$ Strocchi and Wightman and with this I investigate the momentum and angular momentum separation in a class of GIE conditions which correspond to the so-called "static gauges". Using this language I find that the so-called "generator criterion" does not generally hold even for the dressed physical field. In the case of $U(1)$ symmetry breaking, I generalize the standard GIE construction to include the matter field degrees of freedom so that the usual separation pattern of momentum and angular momentum in the unitarity gauge can be incorporated into the same universal framework. When the static gauge condition could not uniquely fix the gauge, I show that this GIE construction should be expanded to take into account the residual gauge symmetry. In some cases I reveal that the usual momentum or angular momentum separation pattern in terms of the physical dressed field variables needs some type of modification due to the nontrivial commutator structure of the underlying quantum gauge choice. Finally, I give some remarks on the general GIE constructions in connection with the possible commutator issues and modification of momentum and angular momentum separation patterns.

hep-th↗