Quantum Invariants

TL;DR

This paper demonstrates that a specific partition function in super-symmetric quantum and string theories remains invariant under parameter variations, highlighting a fundamental symmetry property.

Contribution

It provides an elementary proof that the partition function Z(Q,A,g) is independent of the parameter lambda in super-symmetric quantum theories.

Findings

Partition function Z(Q,A,g) is invariant under lambda variations.

The invariance holds in super-symmetric quantum and string theories.

The proof is elementary and straightforward.

Abstract

In super-symmetric quantum theory, or in string theory, (including generalizations of these theories to underlying quantum spaces) we study a certain partition function Z(Q,A,g). Here Q denotes a supercharge, A denotes an observable with the property A^2 = I, and g denotes an element of a symmetry group of Q. The supercharge may depend on a parameter lambda, namely Q = Q(lambda). We give an elementary argument to show that Z, as defined, does not actually depend on lambda.