Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-06-01
Nucl.Phys.B415:195-242,1994
Physics
High Energy Physics
High Energy Physics - Theory
48 pages, IASSNS-HEP-93/32
Scientific paper
10.1016/0550-3213(94)90072-8
We propose a generalization of Heisenberg picture quantum mechanics in which a Lagrangian and Hamiltonian dynamics is formulated directly for dynamical systems on a manifold with non--commuting coordinates, which act as operators on an underlying Hilbert space. This is accomplished by defining the Lagrangian and Hamiltonian as the real part of a graded total trace over the underlying Hilbert space, permitting a consistent definition of the first variational derivative with respect to a general operator--valued coordinate. The Hamiltonian form of the equations is expressed in terms of a generalized bracket operation, which is conjectured to obey a Jacobi identity. The formalism permits the natural implementation of gauge invariance under operator--valued gauge transformations. When an operator Hamiltonian exists as well as a total trace Hamiltonian, as is generally the case in complex quantum mechanics, one can make an operator gauge transformation from the Heisenberg to the Schr\"odinger picture. When applied to complex quantum mechanical systems with one bosonic or fermionic degree of freedom, the formalism gives the usual operator equations of motion, with the canonical commutation relations emerging as constraints associated with the operator gauge invariance. More generally, our methods permit the formulation of quaternionic quantum field theories with operator--valued gauge invariance, in which we conjecture that the operator constraints act as a generalization of the usual canonical commutators.
No associations
LandOfFree
Generalized quantum dynamics 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 Generalized quantum dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized quantum dynamics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-103197