U(N|M) quantum mechanics on Kaehler manifolds

Abstract

We study the extended supersymmetric quantum mechanics, with supercharges transforming in the fundamental representation of U(N|M), as realized in certain one-dimensional nonlinear sigma models with Kaehler manifolds as target space. We discuss the symmetry algebra characterizing these models and, using operatorial methods, compute the heat kernel in the limit of short propagation time. These models are relevant for studying the quantum properties of a certain class of higher spin field equations in first quantization.

21 pages, a reference added

References in corpus (5)

• Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields
• Detours and Paths: BRST Complexes and Worldline Formalism
• U(N) spinning particles and higher spin equations on complex manifolds
• Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras
• (p,q)-form Kaehler Electromagnetism

Cited by in corpus (5)

• Quantum mechanical path integrals in the first quantised approach to quantum field theory
• Half-integer Higher Spin Fields in (A)dS from Spinning Particle Models
• Extended SUSY quantum mechanics: transition amplitudes and path integrals
• Quantum theory of massless (p,0)-forms
• $U(N)$ Yang-Mills in non-commutative space time