Derivation of the geometrical phase

Böhm, Arno; Boya, Luis J.; Kendrick, Brian K.

doi:10.1103/physreva.43.1206

Cited by 91 publications

(50 citation statements)

References 11 publications

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“…we have subtracted from the derivative of the wavefunction its movement along the 'fibre' [25], since it does not change the basis of the wavefunction i.e., its ray. The norm of the above vector is given after a straightforward algebra as:…”

Section: Hilbert Space Metric and Geodesicsmentioning

confidence: 99%

The Pancharatnam and the Berry phases in three-level photonic systems

Ben-Aryeh¹

2003

Journal of Modern Optics

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Section: Hilbert Space Metric and Geodesicsmentioning

confidence: 99%

The Pancharatnam and the Berry phases in three-level photonic systems

Ben-Aryeh¹

2003

Journal of Modern Optics

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“…В связи с этим орбиту вектора f(z) называют горизонтальным лифтом замкнутой кривой С на базе, а его приращение при замыкании С -голономией; см. [24,42].…”

Section: сфера пуанкаре как база расслоенияunclassified

Berry geometric phase in oscillatory processes

Klyshko¹

1993

Usp. Fiz. Nauk

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“…It will be sufficient to sketch the derivation here, the reader is referred to Böhm et al (1991) and (2003) for details. A bundle connection serves to define the notion of parallel transport in a bundle and thus serves to identify neighboring fibers.…”

Section: Projective Spacesmentioning

confidence: 99%

Berry phase and quantum structure

Lyre

2014

Studies in History and Philosophy of Science Part B: Studies in

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Abstract. The paper aims to spell out the relevance of the Berry phase in view of the question what the minimal mathematical structure is that accounts for all observable quantum phenomena. The question is both of conceptual and of ontological interest. While common wisdom tells us that the quantum structure is represented by the structure of the projective Hilbert space, the appropriate structure rich enough to account for the Berry phase is the U(1) bundle over that projective space. The Berry phase is ultimately rooted in the curvature of this quantum bundle, it cannot be traced back to the Hamiltonian dynamics alone. This motivates the ontological claim in the final part of the paper that, if one strives for a realistic understanding of quantum theory including the Berry phase, one should adopt a form of ontic structural realism.

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Derivation of the geometrical phase

Cited by 91 publications

References 11 publications

The Pancharatnam and the Berry phases in three-level photonic systems

The Pancharatnam and the Berry phases in three-level photonic systems

Berry geometric phase in oscillatory processes

Berry phase and quantum structure

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