Exact form of the exponential Foldy-Wouthuysen transformation operator for an arbitrary-spin particle

Abstract

The exact exponential Foldy-Wouthuysen transformation operator applicable for a particle with an arbitrary spin is derived. It can be successfully utilized for verifying any Foldy-Wouthuysen transformation method based on the exponential operator. When a verified method is relativistic, the relativistic exponential operator should be expanded in the semirelativistic power series. The use of the obtained exponential operator for a derivation of the Foldy-Wouthuysen Hamiltonian makes it possible to check the validity of any other method of the Foldy-Wouthuysen transformation, while this possibility may need a greater computational effort.

14 pages, final version

References in corpus (15)

• Local Relativistic Exact Decoupling
• Topological spin transport of relativistic electron
• Spin-torsion coupling and gravitational moments of Dirac fermions: theory and experimental bounds
• Semiclassical Diagonalization of Quantum Hamiltonian and Equations of Motion with Berry Phase Corrections
• General method of the relativistic Foldy-Wouthuysen transformation and proof of validity of the Foldy-Wouthuysen Hamiltonian
• General properties of the Foldy-Wouthuysen transformation and applicability of the corrected original Foldy-Wouthuysen method
• Semiclassical Dynamics of Dirac particles interacting with a Static Gravitational Field
• Classical Limit of Relativistic Quantum Mechanical Equations in the Foldy-Wouthuysen Representation
• Berry Curvature in Graphene: A New Approach
• Quantum-mechanical description of spin-1 particles with electric dipole moments
• Energy expectation values of a particle in nonstationary fields
• High-precision description and new properties of a spin-1 particle in a magnetic field
• Hamilton Operator and the Semiclassical Limit for Scalar Particles in an Electromagnetic Field
• New symmetry properties of pointlike scalar and Dirac particles
• Validation of the Eriksen Method of the Exact Foldy-Wouthuysen Representation

Cited by in corpus (16)

• General treatment of quantum and classical spinning particles in external fields
• Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms
• Position and spin in relativistic quantum mechanics
• Relativistic quantum-mechanical description of twisted paraxial electron and photon beams
• Relativistic quantum mechanics of a Proca particle in Riemannian spacetimes
• The Exact Foldy-Wouthuysen Transformation for a Dirac Theory Revisited
• Non-relativistic expansion of single-nucleon Dirac equation: Comparison between Foldy-Wouthuysen transformation and similarity renormalization group
• Paraxial wave function and Gouy phase for a relativistic electron in a uniform magnetic field
• Analysis of half-spin particle motion in Kerr-Newman field by means of effective potentials in second-order equations
• Dynamics of the relativistic electron spin in an electromagnetic field
• Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian
• Antimatter Gravity: Second Quantization and Lagrangian Formalism
• Supersymmetric quantum mechanics requires $g=2$ for vector bosons
• Exact Foldy-Wouthuysen transformation for a Dirac equation describing the interaction of spin-1/2 relativistic particles with an external electromagnetic field
• Scalar Product for a Version of Minisuperspace Model with Grassmann Variables
• On the 256-dimensional gamma matrix representation of the Clifford algebra Cl(1,7) and its relation to the Lie algebra SO(1,9)