Classical tensors from quantum states

TL;DR

This paper presents a method to derive classical tensor fields on manifolds from quantum states by embedding them into Hilbert spaces, especially focusing on manifolds with Lie-group structures.

Contribution

It introduces a general procedure to compute classical tensors from quantum states via manifold embeddings into Hilbert spaces, emphasizing Lie-group structures.

Findings

Tensor fields derived from quantum states can be computed using manifold embeddings.

The procedure applies particularly to manifolds with Lie-group structures.

This approach bridges quantum states and classical geometric structures.

Abstract

The embedding of a manifold M into a Hilbert-space H induces, via the pull-back, a tensor field on M out of the Hermitian tensor on H. We propose a general procedure to compute these tensors in particular for manifolds admitting a Lie-group structure.