Quantum Mechanics in Chemistry (Simons, Jack; Nichols, Jeff)

Super Chern-Simons Quantum Mechanics

The Super Chern-Simons mechanics, and quantum mechanics of a particle, on the coset super-manifolds SU(2|1)/U(2) and SU(2|1)/[U(1)× U(1)], is considered. Within a convenient quantization procedure the well known Chern-Simons mechanics on SU(2)/U(1) is reviewed, and then it is shown how the fuzzy supergeometries arise. A brief discussion of the supersphere is also included. ⋆ To appear in Procee...

Theoretical Chemistry I Quantum Mechanics

Infinite Dimensional Algebras in Chern-simons Quantum Mechanics

We study a charged particle in an electromagnetic field without kinetic or potential term. Although dynamically trivial, this system is interesting because it has an infinite dimensional symmetry group. We discuss the way in which this group behaves under quantization. Ref. SISSA XX/91/EP (February 1991)

The path integral for Chern-Simons quantum mechanics

The path integral representation for a system of N non-relativistic particles on the plane, interacting through a Chern-Simons gauge field, is obtained from the operator formalism. An effective interaction between the particles appears, generating the usual Aharonov-Bohm phases. The spin-statistics relation is also considered. PACS numbers: 03.65.Bz, 31.15Kb, 74.20Kk Typeset using REVTEX e-mail...

Classical and Quantum Mechanics of Non-Abelian Chern-Simons Particles

We investigate the classical and quantum properties of a system of SU(N) non-Abelian Chern-Simons (NACS) particles. After a brief introduction to the subject of NACS particles, we first discuss about the symplectic structure of various SU(N) coadjoint orbits which are the reduced phase space of SU(N) internal degrees of freedom or isospins. A complete Dirac’s constraint analysis is carried out ...