Hamiltonian formulation for the gauge theory of the gravitational coupling

Journal Article · Sat Aug 01 04:00:00 EDT 1981 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.525115· OSTI ID:6245604

Giachetti, R; Ricci, R; Sorace, E

This paper studies the Hamiltonian mechanics of a relativistic particle interacting with a gravitational field considered as a gauge field of the Poincare group. We follow a general method developed by Sternberg for the case of internal symmetries, that describes the interaction by a suitable modification of the symplectic form. This approach is reviewed and the explicit examples of the electromagnetic and Yang--Mills gauge interactions are widely explained in local coordinates. The peculiar features of a gauge theory of the Poincare group are then discussed and the geometrical picture that emerges suggests the way of modifying the symplectic form for a correct description of the gravitational coupling.

• Research Organization: Osservatorio Astrofisico di Arcetri, I.N.F.N.-Sezione di Firenze, Firenze, Italy
• OSTI ID: 6245604
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 22:8; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645400 -- High Energy Physics-- Field Theory
657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BASIC INTERACTIONS
COUPLING
GAUGE INVARIANCE
GRAVITATIONAL FIELDS
GRAVITATIONAL INTERACTIONS
HAMILTONIANS
INTERACTIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MANIFOLDS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MINKOWSKI SPACE
POINCARE GROUPS
QUANTUM OPERATORS
SPACE
SYMMETRY GROUPS
YANG-MILLS THEORY