Quantization, dequantization, and distinguished states

TY - JOUR

T1 - Quantization, dequantization, and distinguished states

AU - Hawkins, Eli

AU - Rejzner, Kasia

AU - Minz, Christoph

PY - 2024/9/13

Y1 - 2024/9/13

N2 - 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.

AB - 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.

U2 - 10.1088/1751-8121/ad7427

DO - 10.1088/1751-8121/ad7427

M3 - Article

SN - 1751-8113

VL - 57

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 39

M1 - 395205

ER -