Topological approach to proton spin problem: decomposition controversy and beyond

Abstract

Lorentz covariant and gauge invariant definitions of quark and gluon spin and orbital angular momenta continue to pose a great theoretical challenge. A major controversy on the fundamental concepts followed Chen et al proposal: the basic idea is to split the gauge potential into pure gauge and physical components motivated by the gauge symmetry. We term it gauge symmetry paradigm (GSP) to distinguish it from the well-known inertial frame dependent transverse-longitudinal decomposition (TLP). A thorough study adhering to the traditional meaning of Lorentz covariance and gauge invariance is reported; it leads to a new result: logically consistent development of GSP does not exist and Chen et al proposal turns out to be either trivial or metamorphosed into TLP. Going beyond the controversy and the spin sum rules the necessity for a nonperurbative QCD approach to address the proton spin problem is underlined. We suggest topological approach: generalized de Rham theorems for QCD, and spin as a topological invariant for baryons are discussed. Nonabelian Stokes theorem is applied to derive color flux for the closed loop in a variant of Burkardt's U-shaped path. Similarity between Chen et al decomposition and Kondo decomposition of the gauge potential is suggestive of a topological perspective on the Chen et al proposal with interesting physics.

Unraveling the physical meaning of the Jaffe-Manohar decomposition of the nucleon spin

“…the canonical and mechanical OAMs. Next, in sect.III, we demonstrate an important role of the non-abelian Stokes the-orem in the nucleon spin decomposition problem following the recent suggestion by Tiwari [23]. We explicitly show that the relation between the canonical and mechanical OAMs derived by Burkardt can more quickly be obtained by making use of this general theorem [24].…”

“…As first recognized by Burkardt [24], the existence of the two types of quark OAMs in the nucleon is deeply connected with the existence of strong color-electromagnetic field inside the nucleon, which is generated by the QCD dynamics of bound quarks and gluons. As we shall see below, the essence of Burkartdt's observation can more transparently be understood on the basis of the nonabelian Stokes theorem as pointed out in a recent paper by Tiwari [23].…”

Proton spin: A topological invariant

“…The utility of the language of differential forms is recognized in the modern texts on QFT; the term 'de Rham period' is however, not very familiar, and sometimes doubts are expressed as to whether de Rham theorems are applicable for a Lorentzian spacetime manifold and nonabelian gauge theories. A lucid treatment is given by Nash [17]; see also [4]. For the sake of clarity and completeness a brief account is presented here so that the significance of the two kinds of de Rham theorems in nonabelian case becomes clear.…”

“…The extensive reviews dedicated to proton spin problem [2,3] show that in spite of many experiments since then, and also the advances made in the perturbative QCD and lattice QCD calculations the proton spin problem has not been solved satisfactorily. Leaving aside the so called proton spin decomposition controversy [4] nicely reviewed by Wakamatsu [5] and Leader and Lorce [6] it may be asked if a new line of thinking would be fruitful. Scattering experiments have firmly established that proton is not a point particle, and it has a 3-dimensional spatial internal structure.…”

A Study of Outdoor and Indoor Exposure to Particulate Matters on Students of Banaras Hindu University and city side over Varanasi, India

“…The debate on the proton spin decomposition controversy brought into sharp focus the issue of gauge symmetry: choice of a gauge, gauge-fixing, gauge-invariance, and meaning of gauge-covariant operators in quantum field theory [1][2][3][4][5][6]. It seems the importance of the Landau problem in connection with the proton spin was first pointed out by Wakamatsu, see for example, [7].…”