Generalized Geometrical Phase in the Case of Continuous Spectra

Details Generalized Geometrical Phase in the Case of Continuous Spectra Generalized Geometrical Phase in the Case of Continuous Spectra

2008-04-25

arxiv.org/abs/0804.4082v1

Physics

Quantum Physics

7 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.101.150407

A quantal system in an eigenstate, of operators with a continuous nondegenerate eigenvalue spectrum, slowly transported round a circuit C by varing parameters in its Hamiltonian, will acquire a generalized geometrical phase factor. An explicit formula for a generalized geometrical phase is derived in terms of the eigenstates of the Hamiltonian. As an illustration the generalized geometrical phase is calculated for relativistic spinning particles in slowly-changing electromagnetic fields. It is shown that the the S-matrix and the usual scattering (with negligible reflexion) phase shift can be interpreted as a generalized geometrical phase.

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