Extended Phase Space. III. Unified spin-1/2 fields

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

DOI:https://doi.org/10.1063/1.524591· OSTI ID:5480630

Das, A

In extended phase space V/sub 8/, the classical field equation for spin-1/2 elementary particles is written as (v/sup k/partial/partialq/sup k/+a/sup k/partial/partialp/sup k/-imI) x psi(q,p)=0. The 16 x 16 matrices v/sup k/,a/sup k/ stand for the instantaneous 4-velocity and 4-acceleration. The equation is called the Boltzmann--Dirac--Yukawa (in short BDY) equation. This equation treats q,p variables on equal footings and is covariant under the extended Poincare group P/sub 8/. The spin-1/2 field psi is decomposed into plane wave solutions, and integral constants such as the total energy, the total momentum, the average position, etc., are computed. These integral constants become meaningful provided the modulus squared of each amplitude is interpreted as the statistical distribution function. Next the psi field is subject to the Hankel transform psi( rho,theta)approx.summation/sup infinity//sub t/=-infinitysummation/sup 8/ /sub R/=1summation/sup 2//sub alpha1..integral../sup infinity//sub 0/dkappa kappa x (..beta../sub( R/..cap alpha..)u/sup( R/..cap alpha..) +gamma-bar/sub( R/..cap alpha..)v/sup( R/..cap alpha..))J/sub t/(kapparho)e/sup i/ttheta =summation/sup infinity//sub t/=-infinitypsi/sup( t/); rho=(q-italic/sup 2/+p/sup 2/)/sup 1/2/, theta=arc The integral constants are constructed from a single (t)-mode psi/sup( t/). These turn out to be physically meaningful for eight spin-1/2 particles. Specially the total charge can be identified with Gell-Man--Nishijima's expression for the baryon provided the quantum number t/sub 3/ corresponds to the isotopic spin, 2t/sub 4/ is identified with the strangeness, and the baryon number b is allowed to take 0,1,2. With each of the (t)-mode psi/sup( t/), eight baryon fields can be associated so that psi stands for the unified baryon fields. Finally some brief comments are made on the possibility of treating lepton fields within the framework of the BDY equation.

• Research Organization: Department of Mathematics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
• OSTI ID: 5480630
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 21:6; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BARYONS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
DISTRIBUTION FUNCTIONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
FIELD THEORIES
HADRONS
HANKEL TRANSFORM
INTEGRAL TRANSFORMATIONS
LEPTONS
LIE GROUPS
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL SPACE
PHASE SPACE
POINCARE GROUPS
QUANTUM NUMBERS
SPACE
SPACE-TIME
SYMMETRY GROUPS
TRANSFORMATIONS
WAVE EQUATIONS