Hamiltonian symplectomorphisms and the Berry phase

0 Hamiltonian Symplectomorphisms and the Berry Phase

On the space L, of loops in the group of Hamiltonian symplecto-morphisms of a symplectic manifold, we define a closed Z-valued 1-form Ω. If Ω vanishes, the prequantization map can be extended to a group representation. On L one can define an action integral as an R/Z-valued function, and the cohomology class [Ω] is the obstruction to the lifting of that action integral to an R-valued function. ...

1 Hamiltonian Symplectomorphisms and the Berry Phase

On the space L, of loops in the group of Hamiltonian symplecto-morphisms of a symplectic quantizable manifold, we define a closed Z-valued 1-form Ω. If Ω vanishes, the prequantization map can be extended to a group representation. On L one can define an action integral as an R/Z-valued function, and the cohomology class [Ω] is the obstruction to the lifting of that action integral to an R-value...

Berry Phase and Supersymmetry

We study the constraints of supersymmetry on the non-Abelian holonomy given by U = P exp(i ∫ A), the path-ordered exponential of a connection A. For theories with four supercharges, we show that A satisfies the tt* equations if it is a function of chiral multiplets. In contrast, when A is a function of vector multiplets, it satisfies the Bogomolnyi monopole equations. We describe applications o...

Quantum Hamiltonian diagonalization and Equations of Motion with Berry Phase Corrections

Semiclassical Diagonalization of Quantum Hamiltonian and Equations of Motion with Berry Phase Corrections

It has been recently found that the equations of motion of several semiclassical systems must take into account terms arising from Berry phases contributions. Those terms are responsible for the spin Hall effect in semiconductor as well as the Magnus effect of light propagating in inhomogeneous media. Intensive ongoing research on this subject seems to indicate that a broad class of quantum sys...