Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

The canonical theory of a test particle in a background curved spacetime is a fantastic example of a Hamiltonian constrained system, that is a system whose Hamiltonian is a generator of the gauge transformations. On this example we will explain definitions of the physical observables and the procedure of the canonical quantization. Taking into account that the existence of a (specially) relativistic quantum mechanics is usually questioned, the results I am going to present in this talk may even go beyond the well known quantum physics. In particular, the issue of a quantum position and quantum time operators will be revisited and solved within the geometric framework.