In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G invariance is central to the emergence of the H connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-Abelian generalization of Berry’s phase, can also be found in systems that have slow variables taking values in such a coset space.In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G invariance is central to the emergence of the H connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-Abelian generalization of Berry’s phase, can also be found in systems that have slow variables taking values in such a coset space.

arXiv:hep-th/9504116Journal of Mathematical PhysicsFeb 1, 199615 citations

Berry phases, geometric actions and applications

Luiz Agostinho Ferreira, Abraham Hirsz Zimerman, J. F. Gomes

Nov 30, 19900 citations

On geometric interpretation of the berry phase

Mikhail Orionovich Katanaev

arXiv:1212.1782Russian Physics JournalMar 1, 20124 citations

Nonadiabatic Berry’s phase for a quantum system with a dynamical semisimple Lie group

Shun-Jin Wang

The nonadiabatic Berry's phase is investigated for a quantum system with a dynamical semisimple Lie group within the framework of the generalized cranking approach. An expression for nonadiabatic Berry's phase is given, which indicates that the nonadiabatic Berry's phase is related to the expectation value of Cartan operators along the cranking direction in group space, and that it depends on (i) the geometry of the group space, (ii) the time evolution ray generated by the Hamiltonian (i.e., by the dynamics) in some irreducible representation Hilbert space, and (iii) the cranking rate. The expression also provides a simple algorithm for calculating the nonadiabatic Berry's phase. The general formalism is illustrated by examples of SU(2) dynamic group.The nonadiabatic Berry's phase is investigated for a quantum system with a dynamical semisimple Lie group within the framework of the generalized cranking approach. An expression for nonadiabatic Berry's phase is given, which indicates that the nonadiabatic Berry's phase is related to the expectation value of Cartan operators along the cranking direction in group space, and that it depends on (i) the geometry of the group space, (ii) the time evolution ray generated by the Hamiltonian (i.e., by the dynamics) in some irreducible representation Hilbert space, and (iii) the cranking rate. The expression also provides a simple algorithm for calculating the nonadiabatic Berry's phase. The general formalism is illustrated by examples of SU(2) dynamic group.

Physical Review ANov 1, 199022 citations

Berry phase from symmetry groups

Robert Olkiewicz

Reports on Mathematical PhysicsDec 1, 19934 citations

Schwinger-Keldysh effective field theory of type-B Goldstone: near-diagonal geometry and Berry term

Pei Zheng, Mei Huang

In this work, we formulate a finite temperature Schwinger-Keldysh effective field theory for type-B Goldstone modes based on geometric objects globally defined on the coset manifold. In particular, after taking the classical limit, we organize the required two time contour structure by a near-diagonal geometry in which the $r$ -type field is interpreted as the physical Goldstone configuration and the $a$ -type field is identified as corresponding tangent displacement. Within this geometric viewpoint, the Berry term essential for type-B Goldstones is obtained directly through the transgression of the Berry curvature. Moreover, we show that this exact Berry transgression is compatible with dynamical KMS condition. In order to construct the conservative, dissipative and noise sectors, we classify possible tensors globally defined on the coset manifold. Based on this framework, we discuss in detail two concrete model examples. The dispersion relations of the Goldstone modes and the associated two-point correlation functions are calculated in the presence of dissipation.In this work, we formulate a finite temperature Schwinger-Keldysh effective field theory for type-B Goldstone modes based on geometric objects globally defined on the coset manifold. In particular, after taking the classical limit, we organize the required two time contour structure by a near-diagonal geometry in which the $r$-type field is interpreted as the physical Goldstone configuration and the $a$-type field is identified as corresponding tangent displacement. Within this geometric viewpoint, the Berry term essential for type-B Goldstones is obtained directly through the transgression of the Berry curvature. Moreover, we show that this exact Berry transgression is compatible with dynamical KMS condition. In order to construct the conservative, dissipative and noise sectors, we classify possible tensors globally defined on the coset manifold. Based on this framework, we discuss in detail two concrete model examples. The dispersion relations of the Goldstone modes and the associated two-point correlation functions are calculated in the presence of dissipation.

arXiv:2608.09776Aug 10, 20260 citations

r

-type field is interpreted as the physical Goldstone configuration and the

a

-type field is identified as corresponding tangent displacement. Within this geometric viewpoint, the Berry term essential for type-B Goldstones is obtained directly through the transgression of the Berry curvature. Moreover, we show that this exact Berry transgression is compatible with dynamical KMS condition. In order to construct the conservative, dissipative and noise sectors, we classify possible tensors globally defined on the coset manifold. Based on this framework, we discuss in detail two concrete model examples. The dispersion relations of the Goldstone modes and the associated two-point correlation functions are calculated in the presence of dissipation.