Higher prequantum geometry

TL;DR

This paper surveys higher prequantum geometry, discussing its motivations, constructions, and applications, with a focus on prequantizing local field theories in a gauge-invariant manner using higher differential geometry.

Contribution

It provides an overview of higher prequantum geometry, highlighting how higher differential geometry addresses the open problem of local, gauge-invariant prequantization of field theories.

Findings

Higher differential geometry offers solutions to prequantization challenges.

Cohesive homotopy theory formalizes higher prequantum concepts.

Examples illustrate applications in field theory prequantization.

Abstract

This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution to this problem exists in higher differential geometry. In section 2 we survey examples and problems of interest. In section 3 we survey the abstract cohesive homotopy theory that serves to make all this precise and tractable.