Quantum Lattice Gauge Fields and Groupoid $$\hbox {C}^{*}$$ C โ -Algebras
Quantum Lattice Gauge Fields and Groupoid $$\hbox {C}^{*}$$ C โ -Algebras
We present an operator-algebraic approach to the quantization and reduction of lattice field theories. Our approach uses groupoid $$\hbox {C}^{*}$$ -algebras to describe the observables. We introduce direct systems of Hilbert spaces and direct systems of (observable) $$\hbox {C}^{*}$$ -algebras, and, dually, corresponding inverse systems of configuration spaces and (pair) โฆ