Theory of involutional transformations applied to the Dirac theory of the electron. I. Remarks on the Dirac plane waves

Journal Article · Fri Aug 01 04:00:00 EDT 1980 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.524667· OSTI ID:5207650

Kim, S K

The involutional transformations are shown to play a fundamental role in the Dirac relativistic theory of electron. The symmetric plane waves in the momentum representation, which are the simultaneous eigenfunctions of the energy and helicity operator, are given by the columns of a unitary matrix defined by U=Y/sub E/Y/sub s/, where Y/sub E/ and Y/sub s/ are IUH (involutional, unitary, and Hermitian) matrices which diagonalize the Dirac Hamiltonian and the helicity of a free particle respectively. It is shown that all the known properties of the Dirac plane waves stem from the properties of the involutional transformations Y/sub E/ and Y/sub s/.

• Research Organization: Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122
• OSTI ID: 5207650
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 21:8; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
658000 -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
DIRAC OPERATORS
ELECTRONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
HAMILTONIANS
LEPTONS
MATHEMATICAL OPERATORS
MATRICES
QUANTUM OPERATORS
SYMMETRY
TRANSFORMATIONS
UNITARY SYMMETRY
WAVE EQUATIONS