Grassmann Matrix Quantum Mechanics

Abstract

We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kahler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit. We discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.

25 pages + appendices

References in corpus (5)

• De Sitter Musings
• Micromanaging de Sitter holography
• Towards a quantum theory of de Sitter space
• Bi-local Construction of Sp(2N)/dS Higher Spin Correspondence
• Large N matrices from a nonlocal spin system

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• Solvable Quantum Grassmann Matrices
• Matrix Quantum Mechanics from Qubits
• Polynomial solution of quantum Grassmann matrices
• Fermionic Matrix Models and Bosonization