A Mathematical Base for Fibre Bundle Formulation of Lagrangian Quantum Field Theory

Journal Article · Thu Apr 07 00:00:00 EDT 2011 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3582756· OSTI ID:21513181

Iliev, Bozhidar Z ^[1]

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1. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigradsko chaussee, 1784 Sofia (Bulgaria)

The paper contains a differential-geometric foundations for an attempt to formulate Lagrangian (canonical) quantum field theory on fibre bundles. In it the standard Hilbert space of quantum field theory is replace with a Hilbert bundle; the former playing a role of a (typical) fibre of the letter one. Suitable sections of that bundle replace the ordinary state vectors and the operators on the system's Hilbert space are transformed into morphisms of the same bundle. In particular, the field operators are mapped into corresponding field morphisms.

• OSTI ID: 21513181
• Journal Information: AIP Conference Proceedings, Vol. 1340, Issue 1; Conference: International workshop on complex structures, integrability and vector fields, Sofia (Bulgaria), 13-17 Sep 2010; Other Information: DOI: 10.1063/1.3582756; (c) 2011 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIBERS
FIELD OPERATORS
FUNCTIONAL ANALYSIS
HILBERT SPACE
LAGRANGIAN FIELD THEORY
LAGRANGIAN FUNCTION
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
QUANTUM MECHANICS
BANACH SPACE
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
FUNCTIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
MECHANICS
QUANTUM OPERATORS
SPACE