Twisted Conormal Bundles and Canonical Relations

TL;DR

This paper investigates twisted conormal bundles as canonical relations, constructs a subcategory within the symplectic category, and develops their quantization into semi-classical Fourier integral operators, including symbol calculus.

Contribution

It introduces a new subcategory of canonical relations based on twisted conormal bundles and details their quantization and symbol composition.

Findings

Defined a subcategory of canonical relations from twisted conormal bundles

Quantized these relations into semi-classical Fourier integral operators

Described the intrinsic symbol line bundle and composition rules

Abstract

I study a special type of canonical relations given by twisted conormal bundles, construct a "subcategory" of the symplectic "category" out of these canonical relations and quantize them into semi-classical Fourier integral operators. Furthermore, I give a description of the intrinsic line bundle of symbols of these operators and describe how the symbols compose when the operators compose.