Representations of relativistic particles of arbitrary spin in Poincaré, Lorentz, and Euclidean covariant formulations of relativistic quantum mechanics
arXiv:1809.09717 · doi:10.1103/PhysRevC.99.025202
Abstract
Relativistic treatments of quantum mechanical systems are important for understanding hadronic structure and dynamics at sub-nucleon distance scales. Hadronic states in different inertial reference frames are needed to compute current matrix elements that probe hadronic structure and dynamics. Relativistic invariance is an important consideration as the resolution of the probe is increased. Many different treatments of relativistic dynamics are used in practice, including Poincaré covariant methods, Lorentz covariant methods, Euclidean covariant methods and methods based on quantum fields. Wave functions are typically matrix elements of interacting relativistic states in a basis of non-interacting relativistic states. The purpose of this work is to develop the relation between these different representations of relativistic states that are used in different applications from a unified point of view, starting with positive mass irreducible representations of the Poincaré group.
arXiv comment44 pages - revision includes new section on dynamics
References in corpus (40)
- An accurate nucleon-nucleon potential with charge-independence breaking
- Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
- Baryons as relativistic three-quark bound states
- Nucleon and pion electromagnetic form factors in a light-front constituent quark model
- Covariant nucleon electromagnetic form factors from the Goldstone-boson-exchange quark model
- Pion Generalized Parton Distributions with covariant and Light-front constituent quark models
- Strange and nonstrange baryon spectra in the relativistic interacting quark-diquark model with a Gürsey and Radicati-inspired exchange interaction
- Strange baryon spectroscopy in the relativistic quark model
- Three-nucleon force in relativistic three-nucleon Faddeev calculations
- Baryon Form Factors of Relativistic Constituent-Quark Models
- Time- and Spacelike Nucleon Electromagnetic Form Factors beyond Relativistic Constituent Quark Models
- Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space
- Hamiltonian Relativistic Two-Body Problem: Center of Mass and Orbit Reconstruction
- Poincaré Invariant Three-Body Scattering at Intermediate Energies
- Solving Bethe-Salpeter scattering state equation in Minkowski space
- Relativistic Effects in Exclusive pd Breakup Scattering at Intermediate Energies
- Spin in relativistic quantum theory
- Charge Form Factors of Quark-Model Pions II
- Electromagnetic Currents and the Blankenbecler-Sugar Equation
- Two-Body Dirac Equations for Nucleon-Nucleon Scattering
- Comparison of Relativistic Nucleon-Nucleon Interactions
- Covariant spectator theory of quark-antiquark bound states: Mass spectra and vertex functions of heavy and heavy-light mesons
- Electromagnetic interactions of three-body systems in the covariant spectator theory
- Electromagnetic meson form factor from a relativistic coupled-channel approach
- Light-Front spin-dependent Spectral Function and Nucleon Momentum Distributions for a Three-Body System
- The Relativistic Three-Body Bound State in a 3D Formulation
- Poincare Covariant Quark Models of Baryon Form Factors
- Charge-conjugation symmetric complete impulse approximation for the pion electromagnetic form factor in the Covariant Spectator Theory
- Cluster properties in relativistic quantum mechanics of N-particle systems
- A Euclidean formulation of relativistic quantum mechanics
- Exchange current contributions in null-plane quantum models of elastic electron deuteron scattering
- Relativistic Quantum Mechanics - Particle Production and Cluster Properties
- RQM description of the charge form factor of the pion and its asymptotic behavior
- Covariant Spectator Theory of np scattering: Isoscalar interaction currents
- Baryon Spectrum Analysis using Dirac's Covariant Constraint Dynamics
- Scattering and reflection positivity in relativistic Euclidean quantum mechanics
- Exploring the Pion phenomenology within a fully covariant constituent quark model
- Scattering asymptotic conditions in Euclidean relativistic quantum theory
- Review of the N-quantum Approach to Bound States
- Scattering solutions of Bethe-Salpeter equation in Minkowski and Euclidean spaces