New explicit expressions for Dirac bilinears

Abstract

We derive new explicit expressions for the Dirac bilinears based on a generic representation of the massive Dirac spinors with canonical polarization. These bilinears depend on a direction $n$ in Minkowski space which specifies the form of dynamics. We argue that such a dependence is unavoidable in a relativistic theory with spin, since it originates from Wigner rotation effects. Contrary to most of the expressions found in the literature, our ones are valid for all momenta and canonical polarizations of the spinors. As a by-product, we also obtain a generic explicit expression for the covariant spin vector.

9 pages, version accepted in PRD

References in corpus (24)

• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Generalized Parton Distributions
• Impact Parameter Dependent Parton Distributions and Off-Forward Parton Distributions for $\zeta \to 0$
• Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry
• Generalized parton distributions and strong forces inside nucleons and nuclei
• The angular momentum controversy: What's it all about and does it matter?
• Generalized parton correlation functions for a spin-1/2 hadron
• Quark Wigner Distributions and Orbital Angular Momentum
• Spin densities in the transverse plane and generalized transversity distributions
• Impact Parameter Dependent Parton Distributions and Transverse Single Spin Asymmetries
• Transverse Charge Densities
• Spatial distribution of angular momentum inside the nucleon
• A New Method for Helicity Calculations
• Geometrical approach to the proton spin decomposition
• On the Origin of Model Relations among Transverse-Momentum Dependent Parton Distributions
• Front Form Spinors in Weinberg-Soper Formalism and Melosh Transformations for any Spin
• Multipole decomposition of the nucleon transverse phase space
• Spin in relativistic quantum theory
• A Covariant Method for Calculating Helicity Amplitudes
• Interpolating Helicity Spinors Between the Instant Form and the Light-front Form
• Feynman versus Bakamjian-Thomas in Light Front Dynamics
• The diagonal spin basis and calculation of processes involving polarized particles
• Connecting the Breit Frame to the Infinite Momentum Light Front Frame: How G_E turns into F_1
• Spinor techniques for massive fermions with arbitrary polarization

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