Geometric Phases in Classical and Quantum Mechanics

Chruściński, Dariusz; Jamiołkowski, Andrzej

doi:10.1007/978-0-8176-8176-0

Cited by 288 publications

(359 citation statements)

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“…The ansatz of Born and Oppenheimer 12 is usually derived in the context of molecular Hamiltonians with external magnetic field 27,34 , 4) and project to the component equations of the eigenvalue equation, 5) w.r.t. this basis ( = 1):…”

Section: A the Born-oppenheimer Ansatzmentioning

confidence: 99%

Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

Stottmeister

Thiemann

2016

Journal of Mathematical Physics

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This article, as the first of three, aims at establishing the (time-dependent) BornOppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework, and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g. spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article, and its companion, affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).

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Section: A the Born-oppenheimer Ansatzmentioning

confidence: 99%

Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

Stottmeister

Thiemann

2016

Journal of Mathematical Physics

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“…Since the perturbers surrounding the radiating atom do not move along closed paths, the contributions to the Berry phase coming from the time dependence of the perturber coordinates R(t) were assumed to be negligible in these analyses. It was shown, however, by several researches that the geometric phase makes sense also for non-cyclic adiabatic evolution, corresponding to open paths in parameter space [4][5][6][7]. Therefore, in the present work we address ourselves to the following problem:…”

Section: Introductionmentioning

confidence: 99%

Does non-cyclic Berry phase play any role in the formation of pressure-broadened spectral line shapes?

Ciuryło

Szudy

Baylis

2017

J. Phys.: Conf. Ser.

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“…This is called Pancharatnam-Berry connection [1,2] and it encodes the geometric phase that quantum states pick up under adiabatic variations of the parameters. It has played an important role in several physical systems in condensed matter and atomic physics, see [3,4] for a review.…”

Section: Jhep04(2017)062 1 Introductionmentioning

confidence: 99%

Aspects of Berry phase in QFT

Baggio

Niarchos

Papadodimas

2017

J. High Energ. Phys.

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When continuous parameters in a QFT are varied adiabatically, quantum states typically undergo mixing -a phenomenon characterized by the Berry phase. We initiate a systematic analysis of the Berry phase in QFT using standard quantum mechanics methods. We show that a non-trivial Berry phase appears in many familiar QFTs. We study a variety of examples including free electromagnetism with a theta angle, and certain supersymmetric QFTs in two and four spacetime dimensions. We also argue that a large class of QFTs with rich Berry properties is provided by CFTs with non-trivial conformal manifolds. Using the operator-state correspondence we demonstrate in this case that the Berry connection is equivalent to the connection on the conformal manifold derived previously in conformal perturbation theory. In the special case of chiral primary states in 2d N = (2, 2) and 4d N = 2 SCFTs the Berry phase is governed by the tt * equations. We present a technically useful rederivation of these equations using quantum mechanics methods.

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Geometric Phases in Classical and Quantum Mechanics

Cited by 288 publications

References 0 publications

Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

Does non-cyclic Berry phase play any role in the formation of pressure-broadened spectral line shapes?

Aspects of Berry phase in QFT

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