Constructing Hamiltonian quantum theories from path integrals in a diffeomorphism invariant context

Details Constructing Hamiltonian quantum theories from path integrals in a diffeomorphism invariant context Constructing Hamiltonian quantum theories from path integrals in a diffeomorphism invariant context

1999-04-28

arxiv.org/abs/quant-ph/9904094v2

Class.Quant.Grav. 17 (2000) 4919-4940

Physics

Quantum Physics

Plain Latex, 25 p., references added, abstract and title changed (originally :``Osterwalder Schrader Reconstruction and Diffeo

Scientific paper

10.1088/0264-9381/17/23/310

Osterwalder and Schrader introduced a procedure to obtain a (Lorentzian) Hamiltonian quantum theory starting from a measure on the space of (Euclidean) histories of a scalar quantum field. In this paper, we extend that construction to more general theories which do not refer to any background, space-time metric (and in which the space of histories does not admit a natural linear structure). Examples include certain gauge theories, topological field theories and relativistic gravitational theories. The treatment is self-contained in the sense that an a priori knowledge of the Osterwalder-Schrader theorem is not assumed.

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