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The Berry Phase and Topological Sectors

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Bulletin of the Russian Academy of Sciences: Physics Aims and scope

Abstract

A new scheme is devised for studying the topological Berry phase in terms of local observables using bundles over partially ordered sets.

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Notes

  1. In works where the theory of bundles is not used, the Dirac field is usually defined as spinor operator-valued generalized function \(\psi (f) = \left\{ {{{\psi }^{{{\nu }}}}({{f}_{{{\nu }}}})} \right\}_{{{{\nu }} = 1}}^{4}\) over the space of rapidly diminishing (Schwarz) functions.

  2. We approximate M4 with partially ordered set K.

  3. Physically, connections describe interactions between fields of matter (fermions) representing cross sections; in this sense, A is the vector potential.

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ACKNOWLEDGMENTS

A.S. Sitdikov thanks Profs. R.G. Nazmitdinov and I.N. Boboshin for their inspiring discussions of issues considered in this work at the LXIX International Conference “Nucleus 2019.”

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Authors and Affiliations

  1. Kazan State Power Engineering University, 420066, Kazan, Tatarstan, Russia

    A. S. Sitdikov & N. V. Nikolaeva

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  1. A. S. Sitdikov
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  2. N. V. Nikolaeva
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Correspondence to A. S. Sitdikov.

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Translated by N. Semenova

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Sitdikov, A.S., Nikolaeva, N.V. The Berry Phase and Topological Sectors. Bull. Russ. Acad. Sci. Phys. 85, 1451–1456 (2021). https://doi.org/10.3103/S1062873821120340

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