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

Abstract

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.

Plain Latex, 25 p., references added, abstract and title changed (originally :``Osterwalder Schrader Reconstruction and Diffeomorphism Invariance''), introduction extended, one appendix with illustrative model added, accepted by Class. Quantum Grav

Cited by in corpus (19)

• Nonperturbative Quantum Gravity
• The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
• Cauchy Slice Holography: A New AdS/CFT Dictionary
• Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
• Spacetime foam: a review
• Reduced Loop Quantization with four Klein-Gordon Scalar Fields as Reference Matter
• Positivity of Spin Foam Amplitudes
• On the Relation between Operator Constraint --, Master Constraint --, Reduced Phase Space --, and Path Integral Quantisation
• Loop quantization as a continuum limit
• CDT---an Entropic Theory of Quantum Gravity
• Hamiltonian Renormalization III. Renormalisation Flow of 1+1 dimensional free scalar fields: Properties
• On a spacetime duality in 2+1 gravity
• On the causal Barrett--Crane model: measure, coupling constant, Wick rotation, symmetries and observables
• The Geometry of Quantum Mechanics
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Scalar fields in Causal Dynamical Triangulations
• On the Gribov Problem for Generalized Connections
• On the Support of Physical Measures in Gauge Theories
• Effective theories of connections and curvature: abelian case