Spin operator and spin states in Galilean covariant Fermi field theories

Abstract

Spin degrees of freedom of the Galilean covariant Dirac field in (4+1) dimensions and its nonrelativistic counterpart in (3+1) dimensions are examined. Two standard choices of spin operator, the Galilean covariant and Dirac spin operators, are considered. It is shown that the Dirac spin of the Galilean covariant Dirac field in (4+1) dimensions is not conserved, and the role of non-Galilean boosts in its nonconservation is stressed out. After reduction to (3+1) dimensions the Dirac field turns into a nonrelativistic Fermi field with a conserved Dirac spin. A generalized form of the Levy-Leblond equations for the Fermi field is given. One-particle spin states are constructed. A particle-antiparticle system is discussed.

Minor corrections in the text; journal version

References in corpus (7)

• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Effective Lagrangian and Topological Interactions in Supersolids
• Nonuniversal prefactors in correlation functions of 1D quantum liquids
• Spin-charge separation in one-dimensional fermion systems beyond the Luttinger liquid theory
• Theory of spin current in chiral helimagnet
• Classical and relativistic dynamics of supersolids: variational principle