Extended phase space. II. Unified meson fields
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), Vol. 21:6
- Country of Publication:
- United States
- Language:
- English
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FIELD THEORIES
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MESONS
SCALAR FIELDS
FOURIER TRANSFORMATION
DISTRIBUTION FUNCTIONS
LAGRANGIAN FUNCTION
POINCARE GROUPS
QUANTUM NUMBERS
SPACE-TIME
BOSONS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
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FUNCTIONS
HADRONS
INTEGRAL TRANSFORMATIONS
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645400* - High Energy Physics- Field Theory