NILPOTENT QUANTUM MECHANICS

作者：Frydryszak Andrzej M^*

来源：International Journal of Modern Physics A, 2010, 25(5): 951-983.

DOI：10.1142/S0217751X10047786

• Nilpotent commuting variables
• nilpotent mechanics
• supersymmetric quantum mechanics

We develop a generalized quantum mechanical formalism based on the nilpotent commuting variables (eta-variables). In the nonrelativistic case such formalism provides natural realization of a two-level system (qubit). Using the space of eta-wavefunctions, eta-Hilbert space and generalized Schrodinger equation we study properties of pure multi-qubit systems and also properties of some composed, hybrid models: fermion-qubit, boson-qubit. The fermion-qubit system can be truly supersymmetric, with both SUSY partners having identical spectra. It is a novel feature that SUSY transformations relate here only nilpotent object. The eta-eigenfunctions of the Hamiltonian for the qubit-qubit system give the set of Bloch vectors as a natural basis.

• 出版日期2010-2-20