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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…

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…

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…

There are different operators of quark and gluon momenta, orbital angular momenta, and gluon spin in the nucleon structure study. The precise meaning of these operators are studied based on gauge invariance, Lorentz covariance and canonical…

It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However, we never have the quark and gluon momentum, orbital angular…

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…

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…

A major controversy has arisen in QCD as to how to split the total angular momentum into separate quark and gluon contributions, and as to whether the gluon angular momentum can itself be split, in a gauge invariant way, into a spin and…

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…

This two-paper series addresses and fixes the long-standing gauge invariance problem of angular momentum in gauge theories. This QED part reveals: 1) The spin and orbital angular momenta of electrons and photons can all be consistently…

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…

We discuss in detail and from the geometrical point of view the issues of gauge invariance and Lorentz covariance raised by the approach proposed recently by Chen et al. to the proton spin decomposition. We show that the gauge invariance of…

Since the announcement of the proton spin crisis by the European Muon Collaboration there has been considerable progress in unravelling the distribution of spin and orbital angular momentum within the proton. We review the current status of…

One of the challenges of hadronic physics is to fully understand the structure of the proton. In particular, there is nowadays a great interest in the decomposition of its total angular momentum into orbital angular momentum and intrinsic…

Starting from covariant expressions, a gauge independent separation of orbital and spin angular momentum for electrodynamics is presented. This results from the non-symmetric canonical energy momentum tensor of the electromagnetic field.…

The claim some years ago, contrary to all textbooks, that the angular momentum of a photon (and gluon) can be split in a gauge-invariant way into an orbital and spin term, sparked a major controversy in the Particle Physics community. A…

Understanding the spin structure of the proton is one of the main challenges in hadronic physics. While the concepts of spin and orbital angular momentum are pretty clear in the context of non-relativistic quantum mechanics, the…

The exact decomposition of the proton spin has been a much debated topic, on the experimental as well as the theoretical side. In this talk we would like to report on recent non-perturbative results and ongoing efforts to explore the proton…

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 address and solve the long-standing gauge-invariance problem of the nucleon spin structure. Explicitly gauge-invariant spin and orbital angular momentum operators of quarks and gluons are obtained. This was previously thought to be an…