1,721,739 research outputs found
Quantum deformed geometry on phase-space
No full textIn this paper we extend the standard Moyal formalism to the tangent and cotangent bundle of the phase-space of any Hamiltonian mechanical system. In this manner we build the quantum analog of the classical Hamiltonian vector-field of time evolution and its associated Lie-derivative. We also use this extended Moyal formalism to develop a quantum analog of the Cartan calculus on symplectic manifolds
Metaplectic spinor fields on phase-space: a path-integral approach.
No full textWe study spinor fields on the phase space of a generic Hamiltonian system. Under linearized canonical transformations these spinors transform according to the metaplectic representation of Sp(2N). We derive a path integral for their time evolution and discuss their dynamical and geometrical properties. In particular we show that they can be interpreted as semiclassical wavefunctions for the associated Hamiltonian
A proposal for a differential calculus in quantum mechanics
No full textIn this paper, using the Weyl-Wigner-Moyal formalism for quantum mechanics, we develop a {\it quantum-deformed} exterior calculus on the phase-space of an arbitrary hamiltonian system. Introducing additional bosonic and fermionic coordinates we construct a super-manifold which is closely related to the tangent and cotangent bundle over phase-space. Scalar functions on the super-manifold become equivalent to differential forms on the standard phase-space. The algebra of these functions is equipped with a Moyal super-star product which deforms the pointwise product of the classical tensor calculus. We use the Moyal bracket algebra in order to derive a set of quantum-deformed rules for the exterior derivative, Lie derivative, contraction, and similar operations of the Cartan calculus
Quantum-deformed canonical transformations, W_infinity-algebras and unitary transformation
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