# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1901.00382