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Asian Journal of Physics Vol 31, Nos 9 – 10 (2022) 979-984

Evaluating solid angles via geometric phase

Riccardo Borghi and Turi Maria Spinozzi
Dipartimento di Ingegneria, Università degli Studi “Roma Tre”, Rome, Italy

The concept of geometric phase is employed to express the solid angle subtended by a closed curve in the three-dimensional space at a given point. To this aim, the general formalism developed for the geometric phase during the eighties is applied to the 2×2 matrix representing the Hamiltonian associated to the unit vector evolving along the projection of the closed path on the unit sphere. The solid angle can be expressed by means of a simple contour integral, which provides a direct implementation of the general expression of the anholonomy associated to the parallel transport of a vector along a closed path on a sphere. A nontrivial example of application of this formula is shown. © Anita Publications. All rights reserved.
Keywords: Quantum Mechnaics, Geometric Phase, Mathematical Methods in Physics.

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References

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