From symmetry to structure: gauge-invariant operators in multi-matrix quantum mechanics
Abstract
A bstract Recently the algebraic structure of gauge-invariant operators in multi-matrix quantum mechanics has been clarified: this space forms a module over a freely generated ring. The ring is generated by a set of primary invariants, while the module structure is determined by a finite set of secondary invariants. In this work, we show that the number of primary invariants can be computed by performing a complete gauge fixing, which identifies the number of independent physical degrees of freedom. We then compare this result to a complementary counting based on the restricted Schur polynomial basis. This comparison allows us to argue that the number of secondary invariants must exhibit exponential growth of the form $${e}^{c{N}^{2}}$$ at large N , with c a constant.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Quantum Mechanics and Non-Hermitian Physics
Noncommutative and Quantum Gravity Theories
Publication details
- Journal / source
- Journal of High Energy Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 2026
- Issue
- 1
- Publication date
- 5 January 2026
- Language
- EN