Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Resource Letter GPP-1: Geometric Phases in Physics

J. Anandan, Christian, J, Wanelik, K

Published Jan 1, 1997• 67 citations
OpenAlex

Abstract

This Resource Letter provides a guide to the literature on the geometric angles and phases in classical and quantum physics. Journal articles and books are cited for the following topics: anticipations of the geometric phase, foundational derivations and formulations, books and review articles on the subject, and theoretical and experimental elaborations and applications.

Related papers

Resource Letter GPP-1: Geometric Phases in Physics

Jeeva Anandan, Joy Christian, Kazimir Wanelik

This Resource Letter provides a guide to the literature on the geometric angles and phases in classical and quantum physics. Journal articles and books are cited for the following topics: anticipations of the geometric phase, foundational derivations and formulations, books and review articles on the subject, and theoretical and experimental elaborations and applications.

arXiv:quant-ph/9702011•American Journal of Physics•Mar 1, 1997•91 citations

The Geometric Phase in Quantum Systems

Saverio Pascazio

The discovery of the geometric phase is one of the most interesting and intriguing findings of the last few decades. It led to a deeper understanding of the concept of phase in quantum mechanics and motivated a surge of interest in fundamental quantum mechanical issues, disclosing unexpected applications in very diverse fields of physics. Although the key ideas underlying the existence of a purely geometrical phase had already been proposed in 1956 by Pancharatnam, it was Michael Berry who revived this issue 30 years later. The clarity of Berry's seminal paper, in 1984, was extraordinary. Research on the topic flourished at such a pace that it became difficult for non-experts to follow the many different theoretical ideas and experimental proposals which ensued. Diverse concepts in independent areas of mathematics, physics and chemistry were being applied, for what was (and can still be considered) a nascent arena for theory, experiments and technology. Although collections of papers by different authors appeared in the literature, sometimes with ample introductions, surprisingly, to the best of my knowledge, no specific and exhaustive book has ever been written on this subject. The Geometric Phase in Quantum Systems is the first thorough book on geometric phases and fills an important gap in the physical literature. Other books on the subject will undoubtedly follow. But it will take a fairly long time before other authors can cover that same variety of concepts in such a comprehensive manner. The book is enjoyable. The choice of topics presented is well balanced and appropriate. The appendices are well written, understandable and exhaustive - three rare qualities. I also find it praiseworthy that the authors decided to explicitly carry out most of the calculations, avoiding, as much as possible, the use of the joke `after a straightforward calculation, one finds...' This was one of the sentences I used to dislike most during my undergraduate studies. A student is inexperienced in such matters and needs to look at details. This book is addressed to graduate physics and chemistry students and was written thinking of students. However, I would recommend it also to young and mature physicists, even those who are already `into' the subject. It is a comprehensive work, jointly written by five researchers. After a simple introduction to the subject, the book gradually provides deeper concepts, more advanced theory and finally an interesting introduction and explanation of recent experiments. For its multidisciplinary features, this work could not have been written by one single author. The collaborative effort is undoubtedly one of its most interesting qualities. I would definitely recommend it to anyone who wants to learn more on the geometric phase, a topic that is both beautiful and intruiguing.

Journal of Physics A Mathematical and General•Nov 26, 2003•27 citations

Resource letter CPPPT-1: Critical point phenomena and phase transitions

Jan Tobochnik

This Resource Letter provides a guide to the literature on critical point phenomena and phase transitions. Journal articles and books are cited for the following topics: continuous phase transitions, critical points, model systems with special attention to the Ising model and the Kosterlitz–Thouless transition, mean-field theory, computer simulation methods, scaling, universality, and the renormalization group.

American Journal of Physics•Mar 1, 2001•10 citations

Advanced Concepts in Quantum Mechanics

Giampiero V. M. Esposito, Giuseppe Marmo, Gennaro Miele +1 more

Introducing a geometric view of fundamental physics, starting from quantum mechanics and its experimental foundations, this book is ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics. Focusing on structural issues and geometric ideas, this book guides readers from the concepts of classical mechanics to those of quantum mechanics. The book features an original presentation of classical mechanics, with the choice of topics motivated by the subsequent development of quantum mechanics, especially wave equations, Poisson brackets and harmonic oscillators. It also presents new treatments of waves and particles and the symmetries in quantum mechanics, as well as extensive coverage of the experimental foundations.

Cambridge University Press eBooks•Oct 31, 2014•18 citations

Resource Letter: CQO-1: Coherence in Quantum Optics

John J. Slosser, Pierre Meystre

This Resource Letter provides a brief introduction and an annotated guide to the literature about the roles of quantum coherence in quantum optics. Books, conference proceedings, and selected journal articles are listed for the following topics: Early history, lasers, in particular novel systems such as lasers without inversion, nonclassical states of light including squeezed states, cavity quantum electrodynamics, cooling and trapping of atomic samples, atom optics, and quantum optical tests of the foundations of quantum mechanics.

American Journal of Physics•Apr 1, 1997•7 citations

Geometric Phases and The Sagnac Effect: Foundational Aspects and Sensing Applications

Ismael L. Paiva, Rain Lenny, Eliahu Cohen

Abstract Geometric phase is a key player in many areas of quantum science and technology. In this review article, several foundational aspects of quantum geometric phases and their relations to classical geometric phases are outlined. How the Aharonov–Bohm and Sagnac effects fit into this context is then discussed. Moreover, a concise overview of technological applications of the latter, with special emphasis on gravitational sensing, like in gyroscopes and gravitational wave detectors is presented.

arXiv:2110.05824•Advanced Quantum Technologies•Jan 15, 2022•20 citations
This Resource Letter provides a guide to the literature on the geometric angles and phases in classical and quantum physics. Journal articles and books are cited for the following topics: anticipations of the geometric phase, foundational derivations and formulations, books and review articles on the subject, and theoretical and experimental elaborations and applications.
The discovery of the geometric phase is one of the most interesting and intriguing findings of the last few decades. It led to a deeper understanding of the concept of phase in quantum mechanics and motivated a surge of interest in fundamental quantum mechanical issues, disclosing unexpected applications in very diverse fields of physics. Although the key ideas underlying the existence of a purely geometrical phase had already been proposed in 1956 by Pancharatnam, it was Michael Berry who revived this issue 30 years later. The clarity of Berry's seminal paper, in 1984, was extraordinary. Research on the topic flourished at such a pace that it became difficult for non-experts to follow the many different theoretical ideas and experimental proposals which ensued. Diverse concepts in independent areas of mathematics, physics and chemistry were being applied, for what was (and can still be considered) a nascent arena for theory, experiments and technology. Although collections of papers by different authors appeared in the literature, sometimes with ample introductions, surprisingly, to the best of my knowledge, no specific and exhaustive book has ever been written on this subject. The Geometric Phase in Quantum Systems is the first thorough book on geometric phases and fills an important gap in the physical literature. Other books on the subject will undoubtedly follow. But it will take a fairly long time before other authors can cover that same variety of concepts in such a comprehensive manner. The book is enjoyable. The choice of topics presented is well balanced and appropriate. The appendices are well written, understandable and exhaustive - three rare qualities. I also find it praiseworthy that the authors decided to explicitly carry out most of the calculations, avoiding, as much as possible, the use of the joke `after a straightforward calculation, one finds...' This was one of the sentences I used to dislike most during my undergraduate studies. A student is inexperienced in such matters and needs to look at details. This book is addressed to graduate physics and chemistry students and was written thinking of students. However, I would recommend it also to young and mature physicists, even those who are already `into' the subject. It is a comprehensive work, jointly written by five researchers. After a simple introduction to the subject, the book gradually provides deeper concepts, more advanced theory and finally an interesting introduction and explanation of recent experiments. For its multidisciplinary features, this work could not have been written by one single author. The collaborative effort is undoubtedly one of its most interesting qualities. I would definitely recommend it to anyone who wants to learn more on the geometric phase, a topic that is both beautiful and intruiguing.
Introducing a geometric view of fundamental physics, starting from quantum mechanics and its experimental foundations, this book is ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics. Focusing on structural issues and geometric ideas, this book guides readers from the concepts of classical mechanics to those of quantum mechanics. The book features an original presentation of classical mechanics, with the choice of topics motivated by the subsequent development of quantum mechanics, especially wave equations, Poisson brackets and harmonic oscillators. It also presents new treatments of waves and particles and the symmetries in quantum mechanics, as well as extensive coverage of the experimental foundations.
This Resource Letter provides a brief introduction and an annotated guide to the literature about the roles of quantum coherence in quantum optics. Books, conference proceedings, and selected journal articles are listed for the following topics: Early history, lasers, in particular novel systems such as lasers without inversion, nonclassical states of light including squeezed states, cavity quantum electrodynamics, cooling and trapping of atomic samples, atom optics, and quantum optical tests of the foundations of quantum mechanics.
Abstract Geometric phase is a key player in many areas of quantum science and technology. In this review article, several foundational aspects of quantum geometric phases and their relations to classical geometric phases are outlined. How the Aharonov–Bohm and Sagnac effects fit into this context is then discussed. Moreover, a concise overview of technological applications of the latter, with special emphasis on gravitational sensing, like in gyroscopes and gravitational wave detectors is presented.