Moduli Space Quantum Mechanics

TL;DR

This paper explores quantum mechanics within moduli spaces, analyzing operator relations, wave functions, and the impact of geometry and potentials on state localization and energy levels.

Contribution

It introduces a mini-superspace approach to moduli space quantum mechanics, linking geometry and operator non-commutativity to wave function localization and energy spectra.

Findings

Moduli-dependent functions act as operators constrained by the Emergent String Conjecture.

Wave functions are localized in the bulk of moduli spaces with positive energies.

Potentials cause states to localize away from classical minima, often leading to excited states.

Abstract

In this paper, continuing the discussion about Species Quantum Mechanics, we investigate quantum mechanics in moduli spaces using a mini-superspace approach. From this perspective, moduli-dependent functions can be viewed as operators, and we explore how the taxonomic relations from the Emergent String Conjecture can constrain the non-commutativity between these operators. Next, we study wave functions on moduli spaces, and we find that the geometry of moduli space plays an important role and leads to excited wave functions localised in the bulks of moduli spaces, and with positive energy eigenvalues. For cases when potentials are present, these effects result in moduli localised away from classical minima, and often result in excited, positive energy states.