Quantizing Braids and Other Mathematical Objects: The General Quantization Procedure

TL;DR

This paper introduces a universal quantization procedure applicable to various mathematical structures, enabling the physical realization of mathematical invariants, demonstrated through the quantization of braids.

Contribution

It presents a novel, general quantization method for diverse mathematical objects, expanding the scope of quantum topology and related fields.

Findings

Successfully quantized braids using the new method

Mathematical invariants become physically observable

Provides a blueprint for physically implementable quantum systems

Abstract

Extending the methods from our previous work on quantum knots and quantum graphs, we describe a general procedure for quantizing a large class of mathematical structures which includes, for example, knots, graphs, groups, algebraic varieties, categories, topological spaces, geometric spaces, and more. This procedure is different from that normally found in quantum topology. We then demonstrate the power of this method by using it to quantize braids. This general method produces a blueprint of a quantum system which is physically implementable in the same sense that Shor's quantum factoring algorithm is physically implementable. Mathematical invariants become objects that are physically observable.