Abstract
In the preceding chapter, we have developed the parts of the theory of fiber bundles which are relevant to our study of geometric phases and briefly described gauge theories. We introduced abstract gauge theories as generalizations of the Abelian gauge theory of electromagnetism. There is also another Abelian gauge theory which we encountered in Chap. 4. We call the latter the Abelian gauge theory of quantum mechanics. The parameter space of this gauge theory is the projective Hilbert space P(H) associated with a Hilbert space H, the matter fields are the pure state vectors which belong to H, the gauge or symmetry group is the group U(1) of the phases of the state vectors, and the gauge potential is the Aharonov-Anandan (A-A) connection.
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© 2003 Springer-Verlag Berlin Heidelberg
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Bohm, A., Mostafazadeh, A., Koizumi, H., Niu, Q., Zwanziger, J. (2003). Mathematical Structure of the Geometric Phase I: The Abelian Phase. In: The Geometric Phase in Quantum Systems. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10333-3_6
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DOI: https://doi.org/10.1007/978-3-662-10333-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05504-1
Online ISBN: 978-3-662-10333-3
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