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Schlagwörter:
High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP,Quantum Physics, quant-ph
Zusammenfassung:
We formulate quantum mechanics on SO(3) using a non-commutative dual space
representation for the quantum states, inspired by recent work in quantum
gravity. The new non-commutative variables have a clear connection to the
corresponding classical variables, and our analysis confirms them as the
natural phase space variables, both mathematically and physically. In
particular, we derive the first order (Hamiltonian) path integral in terms of
the non-commutative variables, as a formulation of the transition amplitudes
alternative to that based on harmonic analysis. We find that the non-trivial
phase space structure gives naturally rise to quantum corrections to the action
for which we find a closed expression. We then study both the semi-classical
approximation of the first order path integral and the example of a free
particle on SO(3). On the basis of these results, we comment on the relevance
of similar structures and methods for more complicated theories with
group-based configuration spaces, such as Loop Quantum Gravity and Spin Foam
models.
