Covariant description of Hamiltonian form for field dynamics

Journal Article · Sat Oct 01 04:00:00 EDT 2005 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2005.04.009· OSTI ID:20690196

Ozaki, Hiroshi ^[1]

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1. Department of Physics, Tokai University, 1117 Kitakaname, Hiratsuka 259-1292 (Japan)

Hamiltonian form of field dynamics is developed on a space-like hypersurface in space-time. A covariant Poisson bracket on the space-like hypersurface is defined and it plays a key role to describe every algebraic relation into a covariant form. It is shown that the Poisson bracket has the same symplectic structure that was brought in the covariant symplectic approach. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in which the interaction Hamiltonian density generates a deformation of the space-like hypersurface. The equation just corresponds to the Yang-Feldman equation in the Heisenberg pictures in quantum field theory. By converting the covariant Poisson bracket on the space-like hypersurface to four-dimensional commutator, we can pass over to quantum field theory in the Heisenberg picture without spoiling the explicit relativistic covariance. As an example the canonical QCD is displayed in a covariant way on a space-like hypersurface.

• OSTI ID: 20690196
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 319; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CANONICAL TRANSFORMATIONS
COMMUTATORS
DIFFERENTIAL EQUATIONS
FOUR-DIMENSIONAL CALCULATIONS
HAMILTONIANS
HEISENBERG PICTURE
QUANTUM CHROMODYNAMICS
RELATIVISTIC RANGE
SPACE-TIME