Lie-admissible quantization in a self-interacting scalar field theory

Journal Article · Sat Apr 01 04:00:00 EST 1978 · Hadronic J.; (United States)

OSTI ID:6760253

Ktorides, C N

We revisit the problem of canonical quantization of a self-interacting real scalar field. We are able to separate the quantization of a classical field from that of field powers, once we take into account the distinction between the quantum mechanical Lie algebra and its universal enveloping algebra. We first treat the free real scalar field and recover familiar results. Next, we confront the self-interacting case through a deformation of the enveloping algebra of Lie-admissible type. The basic Lie algebra remains untouched, which means that our building blocks are still the free fields -much in the spirit of perturbation theory. The Lie-admissible deformation, effected via two distributions, leads to final expressions reminiscent of those resulting from the perturbation-renormalization programme. Finally, we show our deformation distributions can lead to deformed-enveloping local operators which do not belong to the Borchers class of the free real scalar field.

• Research Organization: Univ. of Athens, Greece
• OSTI ID: 6760253
• Journal Information: Hadronic J.; (United States), Journal Name: Hadronic J.; (United States) Vol. 1:1; ISSN HAJOD
• 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
ALGEBRA
DEFORMATION
FIELD THEORIES
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICS
QUANTUM FIELD THEORY
SCALAR FIELDS
SYMMETRY GROUPS