Abstract
Wigner distribution functions are the quantum analogue of the classical phase space distribution and being quantum implies that they are not genuine phase space distribution and thus lack any probabilistic interpretation. Nevertheless, Wigner distributions are still interesting since they can be related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) under some limit. We study the Wigner distribution of quarks and also the orbital angular momentum (OAM) of quarks in the dressed quark model.
Highlights
Wigner functions were first introduced by E.P
Wigner distributions are related to the generalized transverse momentum dependent parton distributions (GTMDs) which are off-diagonal quark-quark correlators obtained by integrating out the lightcone energy (k−) from the fully unintegrated correlators
Eq(2) defining the Wigner distributions can be parametrized in terms of generalized transverse momentum dependent parton distributions (GTMDs)[7] and for the twist two case we have four GTMDs (F1,i) corresponding to the Dirac operator γ+ and four more for γ+γ5 (G1,i)
Summary
Wigner functions were first introduced by E.P. Wigner[1] in an attempt to provide quantum corrections to classical statistical mechanics thereby providing a probability distribution for a quantum state. Wigner distribution for the quarks and gluons in the rest frame of the nucleon were introduced in Refs. Wigner distributions in infinite momentum frame obtained by integrating the GTMDs over the momentum transfer in the transverse direction ∆⊥ were introduced in Ref. 4. These Wigner distributions are functions of the two position and three momentum variables. We present a calculation of the quark Wigner distributions in light-front Hamiltonian formulation using overlaps of light-front wave functions (LFWFs) which is based on the approach shown in Ref. 6. We calculate the Wigner distributions and the OAM for a quark dressed with a gluon in light-front Hamiltonian approach
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