Extended phase space. II. Unified meson fields

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

DOI:https://doi.org/10.1063/1.524590· OSTI ID:5410787

Das, A

The classical scalar equation in the extended phase space V/sub 8/ is studied. It is the generalization of the usual Klein--Gordon equation and is covariant under the extended Poincare group P/sub 8/. In this equation there is obvious symmetry of the variables q and p and thus the principle of reciprocity is automatically incorporated. The scalar field is expressed as a Fourier integral phi(q,p)approx...integral.. dk dx ..cap alpha..(k,x)e/sup i/(kq+px) to compute the integral constants like the total energy, total momentum, etc. Then the integral constants turn out to be meaningful quantities by interpreting f(k,x)approx.vertical-bar..cap alpha..vertical-bar/sup 2/ as the statistical distribution function for the scalar field particles. Next the scalar field is expressed as the Fourier--Bessel integral phi x ( rho,theta)approx. summation/sub t/=-infinity/sup infinity/ ..integral../sub 0//sup infinity/ dk k..cap alpha..(k, t)J/sub t/(krho)e/sup i/ttheta=summation/sub t/=-infinity/sup infinity/phi/sup( t/) rho=(q-italic/sup 2/+p/sup 2/)/sup 1/2/, theta=arctan( p/q). The integral constants are computed from a single (t)-mode phi/sup( t/). These are accessible to physical interpretations. Especially, the total charge can be linked up with the Gell-Man--Nishijima's formula, provided one of the quantum numbers (t), say t/sub 3/, is identified with the isotopic quantum number and 2t/sub 4/ is identified with strangeness. With each of the (t)-mode phi/sup( t/) a meson field is associated so that the phi-field itself is the unified meson field.

• Research Organization: Department of Mathematics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
• OSTI ID: 5410787
• 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
BOSONS
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
ELEMENTARY PARTICLES
EQUATIONS
FIELD THEORIES
FOURIER TRANSFORMATION
FUNCTIONS
HADRONS
INTEGRAL TRANSFORMATIONS
KLEIN-GORDON EQUATION
LAGRANGIAN FUNCTION
LIE GROUPS
MATHEMATICAL SPACE
MESONS
PHASE SPACE
POINCARE GROUPS
QUANTUM NUMBERS
SCALAR FIELDS
SPACE
SPACE-TIME
SYMMETRY GROUPS
TRANSFORMATIONS
WAVE EQUATIONS