Aspects of non-associative structures in physics

TL;DR

This paper reviews how non-associative and non-commutative mathematical structures appear in advanced physics theories, especially in string theory and generalized Maxwell theory, highlighting their cohomological and quantization aspects.

Contribution

It provides a summary of the emergence and interpretation of non-associative structures in physics, emphasizing cohomology and star product approaches.

Findings

Non-associative structures arise in string theory models.

Cohomological interpretation explains obstructions to associativity.

Star product offers an alternative quantization method.

Abstract

We summarize the emergence of non-commutative/non-associative structures in Dirac's generalization of Maxwell theory, focusing mostly on the magnetic field analogue of the non-geometric R-flux string model. The cohomological interpretation of the obstructions to associativity in terms of 3-cocycles and the use of the star product as alternative to ordinary quantization are also discussed in this context.