Histories quantisation of parameterised systems: I. Development of a general algorithm

Details Histories quantisation of parameterised systems: I. Development of a general algorithm Histories quantisation of parameterised systems: I. Development of a general algorithm

1999-12-17

arxiv.org/abs/gr-qc/9912077v1

Class.Quant.Grav. 17 (2000) 2463-2490

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

34 pages, Latex

Scientific paper

10.1088/0264-9381/17/13/301

We develop a new algorithm for the quantisation of systems with first-class constraints. Our approach lies within the (History Projection Operator) continuous-time histories quantisation programme. In particular, the Hamiltonian treatment (either classical or quantum) of parameterised systems is characterised by the loss of the notion of time in the space of true degrees of freedom (i.e. the `problem of time'). The novel temporal structure of the HPO theory (two laws of time transformation that distinguish between the temporal logical structure and the dynamics) persists after the imposition of the constraints, hence the problem of time does not arise. We expound the algorithm for both the classical and quantum cases and apply it to simple models.

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