Foldy-Wouthyusen wave functions and conditions of transformation between Dirac and Foldy-Wouthuysen representations

Abstract

The block-diagonalization of the Hamiltonian is not sufficient for the transformation to the Foldy-Wouthuysen (FW) representation. The conditions enabling the transition from the Dirac representation to the FW one are formulated and proved. The connection between wave functions in the two representations is derived. The results obtained allows calculating expectation values of operators corresponding to main classical quantities.

21 pages

References in corpus (2)

• Exact Foldy-Wouthuysen transformation for gravitational waves and magnetic field background
• Connection Between Wave Functions in the Dirac and Foldy-Wouthuysen Representations

Cited by in corpus (29)

• General treatment of quantum and classical spinning particles in external fields
• General method of the relativistic Foldy-Wouthuysen transformation and proof of validity of the Foldy-Wouthuysen Hamiltonian
• Position and spin in relativistic quantum mechanics
• General properties of the Foldy-Wouthuysen transformation and applicability of the corrected original Foldy-Wouthuysen method
• Comparative analysis of direct and "step-by-step" Foldy-Wouthuysen transformation methods
• Exact form of the exponential Foldy-Wouthuysen transformation operator for an arbitrary-spin particle
• Energy expectation values of a particle in nonstationary fields
• Foldy-Wouthuysen Transformation, Scalar Potentials and Gravity
• Relativistic quantum-mechanical description of twisted paraxial electron and photon beams
• Spin gravitational resonance and graviton detection
• The Exact Foldy-Wouthuysen Transformation for a Dirac Theory with the complete set of CPT-Lorentz violating terms
• Analysis of half-spin particle motion in Kerr-Newman field by means of effective potentials in second-order equations
• Validation of the Eriksen Method of the Exact Foldy-Wouthuysen Representation
• I. The Isotopic Foldy-Wouthuysen Representation and Chiral Symmetry
• Quantum mechanics of fermion confined to a curved surface in Foldy-Wouthuysen representation
• Second-order stationary solutions for fermions in an external Coulomb field
• Stationary solutions of the second-order equation for fermions in Kerr-Newman space-time
• Effective Low-Energy Potential for Slow Dirac Fermions in Einstein-Cartan Gravity with Torsion and Chameleon
• Effective electric and magnetic polarizabilities of pointlike spin-1/2 particles
• Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian
• General form of the covariant field equations of arbitrary spin and the relativistic canonical quantum mechanics
• The Foldy-Wouthuysen transformation with Dirac matrices in the chiral representation: closed expressions for energy operators of fermions moving in electrostatic fields
• The possibility to experimentally determine the structure of a fermionic vacuum in quantum electrodynamics
• Closed Foldy-Wouthuysen transformations for fermions moving in gauge-invariant time-dependent electromagnetic fields
• Something new about radial wave functions of fermions in the repulsive Coulomb field
• 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
• The Dirac impenetrable barrier in the limit point of the Klein energy zone
• Transformation of bound states of relativistic hydrogen-l ike atom into two-component form