Abstract
We discuss the Wigner functions of the nucleon which provide multi-dimensional images of the quark distributions in phase space. They combine in a single picture all the information contained in the generalized parton distributions (GPDs) and the transverse-momentum dependent parton distributions (TMDs). In particular, we present results fo r the distribution of unpolarized quarks in a longitudinally polarized nucleon obtained in a light-c one constituent quark model. We show how quark orbital angular momentum can be extracted from these distributions and compare it with alternative definitions given in terms of the GPDs and th e TMDs.
Highlights
The concept of Wigner functions met a renewed interest in the context of QCD to describe the phase-space distributions of partons in the nucleon [1,2,3,4]
We review the concept of Wigner distributions to describe the phase-space distributions of quarks in the nucleon, emphasizing the information encoded in these functions about the quark orbital angular momentum
The quark Wigner distributions are defined in terms of the matrix elements of the Wigner operators W [ ]q sandwiched between nucleon states with polarization S as follows
Summary
The concept of Wigner functions met a renewed interest in the context of QCD to describe the phase-space distributions of partons in the nucleon [1,2,3,4]. These functions represent the quantum mechanical analogues of the classical phase-space density, but do not share with them a probabilistic interpretation. This intrinsic limitation is due to the Heisenberg uncertainty principle which prevents knowing simultaneously the position and momentum of a quantum-mechanical system.
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