# Defining relations for the orbit type strata of SU(2)-lattice gauge models

## TL;DR

This paper characterizes the classical phase space structure of an SU(2)-lattice gauge model in the tree gauge, deriving relations for orbit type strata that facilitate quantum state classification.

## Contribution

It provides explicit defining relations for orbit type strata in the reduced classical phase space of SU(2)-lattice gauge models, aiding quantum state analysis.

## Key findings

- Derived relations for orbit type strata in classical phase space.
- Realized phase space as a quotient of complexified group products.
- Facilitates construction of quantum orbit type costratification.

## Abstract

We consider an SU(2)-lattice gauge model in the tree gauge. Classically, this is a system with symmetries whose configuration space is a direct product of copies of SU(2), acted upon by diagonal inner automorphisms. We derive defining relations for the orbit type strata in the reduced classical phase space. The latter is realized as a certain quotient of a direct product of copies of the complexified group SL(2,\CC) (sometimes named the GIT-quotient because it provides a categorical quotient in the sense of geometric invariant theory). The relations derived can be used for the construction of the orbit type costratification of the Hilbert space of the quantum system in the sense of Huebschmann.