Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-09-30
Rept.Math.Phys. 41 (1998) 49-90
Physics
High Energy Physics
High Energy Physics - Theory
45 pages, LaTeX2e, to appear in Reports on Mathematical Physics v. 41 No. 1 (1998)
Scientific paper
10.1016/S0034-4877(98)80182-1
Canonical structure of the space-time symmetric analogue of the Hamiltonian formalism in field theory based on the De Donder-Weyl (DW) theory is studied. In $n$ space-time dimensions the set of $n$ polymomenta is associated to the space-time derivatives of field variables. The polysymplectic $(n+1)$-form generalizes the simplectic form and gives rise to a map between horizontal forms playing the role of dynamical variables and vertical multivectors generalizing Hamiltonian vector fields. Graded Poisson bracket is defined on forms and leads to the structure of a Z-graded Lie algebra on the subspace of the so-called Hamiltonian forms for which the map above exists. A generalized Poisson structure arises in the form of what we call a ``higher-order'' and a right Gerstenhaber algebra. Field euations and the equations of motion of forms are formulated in terms of the graded Poisson bracket with the DW Hamiltonian $n$-form $H\vol$ ($\vol$ is the space-time volume form and $H$ is the DW Hamiltonian function). A few applications to scalar fields, electrodynamics and the Nambu-Goto string, and a relation to the standard Hamiltonian formalism in field theory are briefly discussed. This is a detailed and improved account of our earlier concise communications (hep-th/9312162, hep-th/9410238, and hep-th/9511039).
No associations
LandOfFree
Canonical Structure of Classical Field Theory in the Polymomentum Phase Space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Canonical Structure of Classical Field Theory in the Polymomentum Phase Space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Canonical Structure of Classical Field Theory in the Polymomentum Phase Space will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-92594