Topological Considerations in the Construction of Quantum Theories

Benjamin Feintzeig (University of California, Irvine)

Topological Considerations in the Construction of Quantum Theories

Abstract  

It is well known that the process of quantization, constructing a quantum theory out of a classical theory, is not always a well-defined procedure in physics. There are many inequivalent methods that lead to different choices for what to use as our quantum theory. In this paper, I show that paying close attention to topological information in classical physics, which encodes manifestly physically significant notions of approximation, can help us choose between competing quantization procedures. I show that by requiring the topological information about approximation to line up between classical and quantum physics, we constrain and inform the quantum theories that we end up with.