Quantization, dequantization, and distinguished states

Abstract

Geometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and—using techniques of geometric quantization—construct the quantum algebra and equip it with a distinguished state. We compare our result with the construction due to Sorkin—which starts from the same input data—and show that our distinguished state coincides with the Sorkin-Johnson state. Sorkin’s construction was originally applied to the free scalar field over a causal set (locally finite, partially ordered set). Our perspective suggests a natural generalization to less linear examples, such as an interacting field.