Construction of spaces of kinematic quantum states for field theories via projective techniques

Abstract

We present a method of constructing a space of quantum states for a field theory: given phase space of a theory, we define a family of physical systems each possessing a finite number of degrees of freedom, next we define a space of quantum states for each finite system, finally using projective techniques we organize all these spaces into a space of quantum states which corresponds to the original phase space. This construction is kinematic in this sense that it bases merely on the structure of the phase space and does not take into account possible constraints on the space. The construction is a generalization of a construction by Kijowski - the latter one is limited to theories of linear phase spaces, while the former one is free of this limitation.

44 pages, no figures, Latex2e

References in corpus (5)

• Loop Quantum Cosmology: A Status Report
• The teleparallel equivalent of general relativity
• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry
• Kinematic quantum states for the Teleparallel Equivalent of General Relativity
• Variables suitable for constructing quantum states for the Teleparallel Equivalent of General Relativity II

Cited by in corpus (19)

• Teleparallel Gravity: From Theory to Cosmology
• Flux formulation of loop quantum gravity: Classical framework
• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry
• Kinematic quantum states for the Teleparallel Equivalent of General Relativity
• Projective Limits of State Spaces I. Classical Formalism
• Projective Limits of State Spaces II. Quantum Formalism
• Projective Loop Quantum Gravity I. State Space
• On Teleparallel Quantum Gravity in Schwarzschild Space-Time
• Variables suitable for constructing quantum states for the Teleparallel Equivalent of General Relativity II
• Hamiltonian Renormalisation V: Free Vector Bosons
• A modification of the projective construction of quantum states for field theories
• Projective Limits of State Spaces: Quantum Field Theory without a Vacuum
• Projective Loop Quantum Gravity II. Searching for Semi-Classical States
• Quantum lattice gauge fields and groupoid C*-algebras
• Kinematic projective quantum states for Loop Quantum Gravity coupled to tensor fields
• Polarization-free Quantization of Linear Field Theories
• Constrained projective quantum states for the degenerate Plebanski gravity
• Space of quantum states built over metrics of fixed signature
• Hilbert spaces built over metrics of fixed signature