Quantum lattice gauge fields and groupoid C*-algebras
arXiv:1705.03815 · doi:10.1007/s00023-018-0717-z
Abstract
We present an operator-algebraic approach to the quantization and reduction of lattice field theories. Our approach uses groupoid C*-algebras to describe the observables and exploits Rieffel induction to implement the quantum gauge symmetries. We introduce direct systems of Hilbert spaces and direct systems of (observable) C*-algebras, and, dually, corresponding inverse systems of configuration spaces and (pair) groupoids. The continuum and thermodynamic limit of the theory can then be described by taking the corresponding limits, thereby keeping the duality between the Hilbert space and observable C*-algebra on the one hand, and the configuration space and the pair groupoid on the other. Since all constructions are equivariant with respect to the gauge group, the reduction procedure applies in the limit as well.
arXiv comment23 pages, 6 figures
References in corpus (13)
- Spin Network States in Gauge Theory
- Generalized Measures in Gauge Theory
- On the support of the Ashtekar-Lewandowski measure
- The Role of Type III Factors in Quantum Field Theory
- On the Gauss Law and Global Charge for QCD
- Charge Superselection Sectors for QCD on the Lattice
- Construction of spaces of kinematic quantum states for field theories via projective techniques
- A gauge model for quantum mechanics on a stratified space
- Projective Limits of State Spaces II. Quantum Formalism
- Projective Limits of State Spaces I. Classical Formalism
- Dynamics for QCD on an infinite lattice
- A Lattice Gauge Model of Singular Marsden-Weinstein Reduction. Part I. Kinematics
- A modification of the projective construction of quantum states for field theories