16,422 research outputs found
Quantization as a dimensional reduction phenomenon
Classical mechanics, in the operatorial formulation of Koopman and von
Neumann, can be written also in a functional form. In this form two Grassmann
partners of time make their natural appearance extending in this manner time to
a three dimensional supermanifold. Quantization is then achieved by a process
of dimensional reduction of this supermanifold. We prove that this procedure is
equivalent to the well-known method of geometric quantization.Comment: 19 pages, Talk given by EG at the conference "On the Present Status
of Quantum Mechanics", Mali Losinj, Croatia, September 2005. New results are
contained in the last part of the pape
Ultraviolet cutoffs for quantum fields in cosmological spacetimes
We analyze critically the renormalization of quantum fields in cosmological
spacetimes, using non covariant ultraviolet cutoffs. We compute explicitly the
counterterms necessary to renormalize the semiclassical Einstein equations,
using comoving and physical ultraviolet cutoffs. In the first case, the
divergences renormalize bare conserved fluids, while in the second case it is
necessary to break the covariance of the bare theory. We point out that, in
general, the renormalized equations differ from those obtained with covariant
methods, even after absorbing the infinities and choosing the renormalized
parameters to force the consistency of the renormalized theory. We repeat the
analysis for the evolution equation for the mean value of an interacting scalar
fieldComment: 19 pages. Minor changes. References adde
Functional Approach to Classical Yang-Mills Theories
Sometime ago it was shown that the operatorial approach to classical
mechanics, pioneered in the 30's by Koopman and von Neumann, can have a
functional version. In this talk we will extend this functional approach to the
case of classical field theories and in particular to the Yang-Mills ones. We
shall show that the issues of gauge-fixing and Faddeev-Popov determinant arise
also in this classical formalism.Comment: 4 pages, Contribution to the Proceedings of the International Meeting
"Quantum Gravity and Spectral Geometry" (Naples, July 2-7, 2001
A New Look at the Schouten-Nijenhuis, Fr\"olicher-Nijenhuis and Nijenhuis-Richardson Brackets for Symplectic Spaces
In this paper we re-express the Schouten-Nijenhuis, the Fr\"olicher-Nijenhuis
and the Nijenhuis-Richardson brackets on a symplectic space using the extended
Poisson brackets structure present in the path-integral formulation of
classical mechanics.Comment: 27+1 pages, Latex, no figure
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