Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and General

A note on the recent Foldy-Wouthuysen transformations for particles of arbitrary spin

J. Jayaraman

Published Jan 1, 1975• 20 citations
Publisher

Abstract

The authors present a discussion on the recently constructed unitary operator for arbitrary spin, which transforms the Foldy-Wouthuysen Hamiltonian into that of the Weaver, Hammer and Good (WHG) description and demonstrate its incompatibility with preserving the local transformation property of the WHG wavefunction.
DOI
10.1088/0305-4470/8/1/001

Related papers

Generalization of exact operators of the Foldy-Wouthuysen transformation to arbitrary-spin particles in nonstationary fields

Alexander J. Silenko

Exact nonexponential and exponential operators of the Foldy-Wouthuysen transformation for arbitrary-spin particles are determined in the nonstationary case. Some fundamental properties of these operators and the Foldy-Wouthuysen Hamiltonian are also identified.

arXiv:2411.07251•Physical Review A•May 29, 2025•0 citations

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

Alexander J. Silenko

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 obtained exponential operator can be also used for a derivation of the Foldy-Wouthuysen Hamiltonian and its comparison with Hamiltonians found by other methods. This procedure makes it possible to check the validity of any other method of the Foldy-Wouthuysen transformation.

arXiv:1605.09755•Physical Review A•Sep 6, 2016•34 citations

Invariant Scalar Product and Observables in a Relativistic Theory of Particles of Arbitrary Spin

P. M. Mathews

In a recent paper a relativistically covariant Schr\"odinger equation was derived for particles of arbitrary spin $s$, locally covariant wave functions without redundant components being used to describe states of a particle. Here we determine the invariant scalar product with respect to which the representation of Poincar\'e transformations on these wave functions is unitary. It is shown that the conventional position and spin operators, not being Hermitian with respect to this scalar product, cannot be observables. New operators which can represent these observables are constructed with the aid of a generalized Foldy-Wouthuysen transformation which is determined explicitly for arbitrary spin.

Physical Review•Mar 25, 1966•27 citations

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

Alexander J. Silenko

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.

•May 31, 2016•0 citations

Gauge invariance, time-dependent Foldy-Wouthuysen transformations, and the Pauli Hamiltonian

Terry Goldman

The Foldy-Wouthuysen derivation of the generalized Pauli Hamiltonian is reexamined, and described as an operator gauge transformation. The unitary inequivalence of the Pauli and Dirac Hamiltonians is shown to occur, because in general it is only the entire coupled field Hamiltonian which is gauge invariant, not the particle Hamiltonian alone.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Feb 15, 1977•38 citations

Generalization of exact operators of the Foldy-Wouthuysen transformation to arbitrary-spin particles in nonstationary fields

Anonymous

Physical Review A•May 19, 2025•0 citations
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 obtained exponential operator can be also used for a derivation of the Foldy-Wouthuysen Hamiltonian and its comparison with Hamiltonians found by other methods. This procedure makes it possible to check the validity of any other method of the Foldy-Wouthuysen transformation.
In a recent paper a relativistically covariant Schr\"odinger equation was derived for particles of arbitrary spin sss, locally covariant wave functions without redundant components being used to describe states of a particle. Here we determine the invariant scalar product with respect to which the representation of Poincar\'e transformations on these wave functions is unitary. It is shown that the conventional position and spin operators, not being Hermitian with respect to this scalar product, cannot be observables. New operators which can represent these observables are constructed with the aid of a generalized Foldy-Wouthuysen transformation which is determined explicitly for arbitrary spin.
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.