Lie-admissible structure of classical field theory

Conference · Sat Dec 01 04:00:00 EST 1979 · Hadronic J.; (United States)

OSTI ID:6446549

Kobussen, J A

In this paper we summarize Santilli's Lie-admissible approach to Newtonian mechanics with particular reference to: (a) its direct universality; (b) its geometrical structure; and (c) its form-invariance under arbitrary transformations of the local variables. We then initiate the extension of this approach to field theory. The main result consists of a theorem of direct universality of the Lie-admissible equations in classical field theory. The main result consists of a theorem of direct universality of the Lie-admissible equations in classical field theory. This theorem states that in some arbitrary function space the most general possible quasi-linear system of differential equations of second order in time can always be reduced to an equivalent first-order form for which the brackets of the time-evolution law characterize a Lie-admissible algebra. The geometrical character of this algebraic setting is shown to be a field theoretical extension of Santilli's symplectic-admissible two-forms. Furthermore we prove that, as for the Newtonian case, this Lie-admissible and symplectic-admissible approach to field theory is form-invariant under arbitrary transformations. We than enter into a number of illustrative examples, with particular reference to the non-conservative extension of conventional equations.

• Research Organization: Zurich Univ., Switzerland
• OSTI ID: 6446549
• Report Number(s): CONF-7908175-
• Conference Information: Journal Name: Hadronic J.; (United States) Journal Volume: 3:1
• Country of Publication: United States
• Language: English

Related Subjects

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658000 -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
ALGEBRAIC FIELD THEORY
AXIOMATIC FIELD THEORY
CLASSICAL MECHANICS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
GEOMETRY
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICS
MECHANICS
QUANTUM FIELD THEORY
SYMMETRY GROUPS
TRANSFORMATIONS