The Maslov dequantization, idempotent and tropical mathematics: A brief introduction

TL;DR

This paper introduces idempotent and tropical mathematics, explaining their origins from Maslov dequantization as a limiting case of traditional mathematics when the Planck constant approaches zero.

Contribution

It provides a concise overview of the foundational concepts and the connection between Maslov dequantization and tropical mathematics.

Findings

Tropical mathematics arises from Maslov dequantization.

Idempotent mathematics simplifies many algebraic structures.

The approach links quantum and classical mathematical frameworks.

Abstract

This paper is a brief introduction to idempotent and tropical mathematics. Tropical mathematics can be treated as a result of the so-called Maslov dequantization of the traditional mathematics over numerical fields as the Planck constant $\hbar$ tends to zero taking imaginary values.