Geometric Phases in Physics

Wilczek, Frank; Shapere, Alfred D.

doi:10.1142/0613

Cited by 554 publications

(407 citation statements)

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“…Connection A In this subsection we shall present the connection components related to the parametric space G(4, 2) by employing definition (2). In particular, they are 2 × 2 matrices paired in the following with respect to the S + and S − degenerate eigenspaces they act on.…”

Section: Connection and Field Strength Componentsmentioning

confidence: 99%

Geometrical phases for the G(4,2) Grassmannian manifold

Karle

Pachos

2003

Journal of Mathematical Physics

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We generalize the usual abelian Berry phase generated for example in a system with two nondegenerate states to the case of a system with two doubly degenerate energy eigenspaces. The parametric manifold describing the space of states of the first case is formally given by the G(2, 1) Grassmannian manifold, while for the generalized system it is given by the G(4, 2) one. For the latter manifold which exhibits a much richer structure than its abelian counterpart we calculate the connection components, the field strength and the associated geometrical phases that evolve nontrivially both of the degenerate eigenspaces. A simple atomic model is proposed for their physical implementation.

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Section: Connection and Field Strength Componentsmentioning

confidence: 99%

Geometrical phases for the G(4,2) Grassmannian manifold

Karle

Pachos

2003

Journal of Mathematical Physics

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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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“…His analysis was in the * arvind@iisermohali.ac.in † subhash@iiserbhopal.ac.in ‡ nmukunda@gmail.com framework of adiabatic cyclic unitary evolution of pure quantum states obeying the time-dependent Schrödinger equation -at the end of such evolution the state vector (or wave function) in Hilbert space acquires a new previously unrecognized phase. Later rapid developments greatly clarified the situation -the geometric phase is (in the language of quantum mechanics) a ray space quantity; it can be defined even in nonadiabatic and noncyclic evolutions [3][4][5]; and it is meaningful in purely classical wave optical situations, so it is not specifically quantum mechanical in origin. Indeed it was soon realised that a phase found by Pancharatnam in 1956 in classical polarization optics was an early precursor of the geometric phase in a nonadiabatic cyclic situation, with the Poincaré sphere of polarization optics playing the role of ray space in quantum mechanics [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

A classical optical approach to the ‘non-local Pancharatnam-like phases’ in Hanbury-Brown–Twiss correlations

2017

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We examine a recent proposal to show the presence of nonlocal Pancharatnam type geometric phases in a quantum mechanical treatment of intensity interferometry measurements upon inclusion of polarizing elements in the setup. It is shown that a completely classical statistical treatment of such effects is adequate for practical purposes. Further we show that the phase angles that appear in the correlations, while at first sight appearing to resemble Pancharatnam phases in their mathematical structure, cannot actually be interpreted in that manner. We also describe a simpler Mach-Zehnder type setup where similar effects can be observed without use of the paraxial approximation.

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Geometric Phases in Physics

Cited by 554 publications

References 0 publications

Geometrical phases for the G(4,2) Grassmannian manifold

Geometrical phases for the G(4,2) Grassmannian manifold

Aspects of Berry phase in QFT

A classical optical approach to the ‘non-local Pancharatnam-like phases’ in Hanbury-Brown–Twiss correlations

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