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We argue against the rapidly spreading idea of gauge-invariant-extension (GIE) approach in the nucleon spin decomposition problem, which implies the existence of infinitely many gauge-invariant decomposition of the nucleon spin.

The question whether the total gluon angular momentum in the nucleon can be decomposed into its spin and orbital parts without conflict with the gauge-invariance principle has been an object of long-lasting debate. Despite a remarkable…

A non-uniqueness problem of gauge invariant separation of quark and gluon contributions to nucleon spin is considered. We show that there is a wide number of gauge invariant spin decompositions each of them reduces to the canonical one in a…

We discuss the uniqueness or non-uniqueness problem of the decomposition of the gluon field into the physical and pure-gauge components, which is the basis of the recently proposed two physically inequivalent gauge-invariant decompositions…

In a series of papers, we have established the existence of two gauge-invariant decompositions of the nucleon spin, which are physically nonequivalent. The orbital angular momenta of quarks and gluons appearing in these two decompositions…

Is gauge-invariant complete decomposition of the nucleon spin possible? Although it is a difficult theoretical question which has not reached a complete consensus yet, a general agreement now is that there are at least two physically…

We investigate the relation between the known decompositions of the nucleon spin into its constituents, thereby clarifying in what respect they are common and in what respect they are different essentially. The decomposition recently…

We discuss the shortfalls of existing resolutions of the long-standing gauge invariance problem of the canonical decomposition of the nucleon spin to the spin and angular momentum of quarks and gluons. We provide two logically flawless…

Recently, many nucleon spin decompositions have been proposed in the literature, creating a lot of confusion. This revived in particular old controversies regarding the measurability of theoretically defined quantities. We propose a brief…

We propose a short summary of the present situation concerning the proton spin decomposition. We briefly discuss some of the main controversies about the issues of gauge invariance, uniqueness and measurability. As a conclusion, we argue…

Based on gauge-invariant decomposition of covariant angular momentum tensor of QCD in an arbitrary Lorentz frame, we investigate the relation between the known decompositions of the nucleon spin into its constituents, thereby clarifying in…

In this brief note insightful remarks are made on the controversy on the decomposition of the proton spin into the spin and orbital angular momenta of quarks and gluons. It is argued that the difference in the perception on the nature of…

In a recent paper, we have shown that the way of gauge-invariant decomposition of the nucleon spin is not necessarily unique, but there still exists a preferable decomposition from the observational viewpoint. What was not complete in this…

We consider a non-uniqueness problem of gauge invariant nucleon spin decomposition. A gauge invariant decomposition with a generalized Coulomb constraint for the physical gluon has been constructed. The decomposition scheme is consistent…

This article reviews our present understanding of QCD spin physics: the proton spin puzzle and new developments aimed at understanding the transverse structure of the nucleon. We discuss present experimental investigations of the nucleon's…

Our knowledge of the nucleon spin structure has greatly improved over the last twenty years or so, but still many fundamental questions remain unsolved. I will try to review some of the puzzling aspects of the structure of the nucleon spin,…

I review the recent progress in understanding the complete gauge invariant decomposition of the nucleon spin with particular emphasis on its twist structure.

The general question, crucial to an understanding of the internal structure of the nucleon, of how to split the total angular momentum of a photon or gluon into spin and orbital contributions is one of the most important and interesting…

~Based on the gauge invariant quark canonical momentum we construct two theoretically possible decompositions of nucleon momentum to those of quarks and gluons. We predict that either 6% or 21% of nucleon momentum is carried by gluons,…

How do the quark and gluon share the nucleon momentum? How does the nucleon spin distribute among its constituents? What means the quark and gluon momentum, spin and orbital angular momentum? These problems are analyzed and a solution is…