aqora

Topological Berry phase terms for spin systems in arbitrary dimensions(Fundamental Problems and Applications of Quantum Field Theory-Topological Aspects of Quantum Field Theory-)

Akihiro Tanaka

素粒子論研究Apr 20, 20070 citations

CONFORMAL FIELD THEORY, QUANTUM GROUP AND BERRY PHASE

P. Bandyopadhyay

From an analysis of the relationship between the conformal field theory in 1+1 dimension, the Chern–Simons theory in 2+1 dimension and chiral anomaly in 3+1 dimension, we study here the relationship between the central charge c, Chern–Simons coupling k and the Berry phase factor μ where the phase is given by e i2πμ which is associated with the chiral anomaly and their association with the quantum symmetry in the framework of the Landau problem of 2D electron gas in a magnetic field. A possible link between the deformation parameter q of the deformed algebra U q ( SL (2)) with these parameters is suggested. It is also shown how a Z p spin system is realized for a quantum space and the parameter p is linked up with the deformation parameter q and; in turn with the central charge c and the Berry phase factor μ. Finally some implications of this result in a statistical system are discussed.From an analysis of the relationship between the conformal field theory in 1+1 dimension, the Chern–Simons theory in 2+1 dimension and chiral anomaly in 3+1 dimension, we study here the relationship between the central charge c, Chern–Simons coupling k and the Berry phase factor μ where the phase is given by e i2πμ which is associated with the chiral anomaly and their association with the quantum symmetry in the framework of the Landau problem of 2D electron gas in a magnetic field. A possible link between the deformation parameter q of the deformed algebra U q ( SL (2)) with these parameters is suggested. It is also shown how a Z p spin system is realized for a quantum space and the parameter p is linked up with the deformation parameter q and; in turn with the central charge c and the Berry phase factor μ. Finally some implications of this result in a statistical system are discussed.

International Journal of Modern Physics AApr 20, 200022 citations

Topological aspects of a quantum particle and berry phase

Dipti Chattopadhyay

Jan 1, 19940 citations

Berry's phase for compact Lie groups

Strahov, E

The Lie group adiabatic evolution determined by a Lie algebra parameter dependent Hamiltonian is considered. It is demonstrated that in the case when the parameter space of the Hamiltonian is a homogeneous K\\"ahler manifold its fundamental K\\"ahler potentials completely determine Berry geometrical phase factor. Explicit expressions for Berry vector potentials (Berry connections) and Berry curvatures are obtained using the complex parametrization of the Hamiltonian parameter space. A general approach is exemplified by the Lie algebra Hamiltonians corresponding to SU(2) and SU(3) evolution groups.The Lie group adiabatic evolution determined by a Lie algebra parameter dependent Hamiltonian is considered. It is demonstrated that in the case when the parameter space of the Hamiltonian is a homogeneous K\\"ahler manifold its fundamental K\\"ahler potentials completely determine Berry geometrical phase factor. Explicit expressions for Berry vector potentials (Berry connections) and Berry curvatures are obtained using the complex parametrization of the Hamiltonian parameter space. A general approach is exemplified by the Lie algebra Hamiltonians corresponding to SU(2) and SU(3) evolution groups.

Nov 30, 200016 citations

THREE ELABORATIONS ON BERRY’S CONNECTION, CURVATURE AND PHASE

R. Jackiw

We discuss how symmetries and conservation laws are affected when Berry’s phase occurs in a quantum system: symmetry transformations of coordinates have to be supplemented by gauge transformations of Berry’s connection, and consequently constants of motion acquire terms beyond the familiar kinematical ones. We show how symmetries of a problem determine Berry’s connection, curvature and, once a specific path is chosen, the phase as well. Moreover, higher order corrections are also fixed. We demonstrate that in some instances Berry’s curvature and phase can be removed by a globally well-defined, time-dependent canonical transformation. Finally, we describe how field theoretic anomalies may be viewed as manifestations of Berry’s phase.We discuss how symmetries and conservation laws are affected when Berry’s phase occurs in a quantum system: symmetry transformations of coordinates have to be supplemented by gauge transformations of Berry’s connection, and consequently constants of motion acquire terms beyond the familiar kinematical ones. We show how symmetries of a problem determine Berry’s connection, curvature and, once a specific path is chosen, the phase as well. Moreover, higher order corrections are also fixed. We demonstrate that in some instances Berry’s curvature and phase can be removed by a globally well-defined, time-dependent canonical transformation. Finally, we describe how field theoretic anomalies may be viewed as manifestations of Berry’s phase.

International Journal of Modern Physics AFeb 1, 1988136 citations

BERRY PHASE IN YANG–BAXTER SYSTEMS AND BOGOLIUBOV HAMILTONIAN AS A DERIVATIVE OF DIRAC HAMILTONIAN VIA BRAID RELATION

Mo‐Lin Ge, Kang Xue, Jing‐Ling Chen

Conference in Honor of C N Yang's 85th BirthdayDec 1, 20080 citations

DYNAMIC LIE ALGEBRA STRUCTURE OF QUANTAL SYSTEM AND BERRY’S PHASE FACTOR

Abstract

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DYNAMIC LIE ALGEBRA STRUCTURE OF QUANTAL SYSTEM AND BERRY’S PHASE FACTOR

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