Related papers: A critical assessment of the angular momentum sum …
The gauge invariant operator formulation of the angular momentum sum rule ${1\over2} = J_q + J_g$ for the proton is presented and contrasted with the sum rule for the first moment of the polarised structure function $g_1^p$. The decoupling…
We present a study of the tensorial structure of the hadronic matrix elements of the angular momentum operators $\bm{J}$. Well known results in the literature are shown to be incorrect, and we have taken pains to derive the correct…
We explain the origin of the controversy about the existence of a transverse angular momentum sum rule, and show that it stems from utilizing an incorrect result in the literature, concerning the expression for the expectation values of the…
I derive a rigorous relation between the expectation value of the transverse component of the angular momentum <J_T> of a quark in a transversely polarized nucleon in terms of the Generalized Parton Distributions H and E, namely…
Definitions of orbital angular momentum based on Wigner distributions are used as a framework to discuss the connection between the Ji definition of the quark orbital angular momentum and that of Jaffe and Manohar. We find that the…
Four expressions involving sums of position and velocity coordinates bounding the total angular momentum of particle systems, and by extension of any continuous or discontinuous material systems, are derived which are tighter for any…
We present an analytic two-loop calculation within the scalar diquark model of the potential linear and angular momenta, defined as the difference between the Jaffe-Manohar and Ji notions of linear and angular momenta. As expected by parity…
Recently, a longitudinal sum rule for the electric polarizability of nuclei was used to revise a relativistic correction in a dipole sum rule for the polarizability (nucl-th/9802011). This revision is shown to be wrong because of neglecting…
The proton's transverse polarization structure is examined in terms of the Lorentz-covariant Pauli-Lubanski vector in QCD. We find that there are contributions from leading, subleading, and next-to-subleading partonic contributions in the…
Some 67 years ago (1951) Wolfgang Pauli mooted the three sum rules: \[ \sum_n (-1)^{2S_n} g_n = 0; \qquad \sum_n (-1)^{2S_n} g_n \; m_n^2 =0; \qquad \sum_n (-1)^{2S_n} g_n \; m_n^4=0. \] These three sum rules are intimately related to both…
A sum rule is an identity connecting the entropy of a measure with coefficients involved in the construction of its orthogonal polynomials (Jacobi coefficients). Our paper is an extension of Gamboa, Nagel and Rouault (2016), where we have…
We make use of a simple scalar diquark model to study the potential transverse momentum and potential angular momentum, defined as the difference between the Jaffe-Manohar and Ji notions of transverse momentum and orbital angular momentum,…
The construction of unitary operator bases in a finite-dimensional Hilbert space is reviewed through a nonstandard approach combinining angular momentum theory and representation theory of SU(2). A single formula for the bases is obtained…
Momentum sum rules for fragmentation functions are considered. In particular, we give a general proof of the Sch\"afer-Teryaev sum rule for the transverse momentum dependent Collins function. We also argue that corresponding sum rules for…
We derive general expressions for non-energy weighted and energy-weighted cluster sum rules for systems of three charged particles. The interferences between pairs of particles are found to play a substantial role. The energy-weighted sum…
In this work we provide explicit calculations that support the conclusions stated in Phys. Rev. Lett. 111, 039102 (2013) (comment), regarding recent literature on transverse polarization. We also compare and contrast two methods of deriving…
Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the T-odd Sivers effect in semi-inclusive deep-inelastic…
In this paper we follow the Schwinger approach for angular momentum but with the polar basis of harmonic oscillator as a starting point. We derive by a new method two analytic expressions of the elements of passage matrix from the double…
We present the first complete parametrization for the matrix elements of the generic light-front gauge-invariant energy-momentum tensor, derive the expressions giving separately the spin and orbital angular momentum of quarks and gluons as…
The objective of this paper is, in the main, twofold: Firstly, to develop an algebraic setting for dealing with Bell polynomials and related extensions. Secondly, based on the author's previous work on multivariate Stirling polynomials…