Cohomology in algebra, geometry, physicsand statistics

Symmetry and Separation of variables

We present a condition under which a differential operator on a two dimensional manifold admits a so-called separated solution and the separation is non-trivial in a sense, that we explain. Along the way we "develop" definitions in order to make these propositions precise, such as of a symmetry generating an operator and of a function that does not depend on a set of variables with respect to a coordinate chart.

We are motivated by problems in Physics, where the separation of variables is often used, e.g., in specific problems of electromagnetic waves, quantum mechanics (hydrogen atom), or in general relativity.  In mathematical Physics the notion of separation was studied in many works, including the works of Kalnins, Winternitz, Miller and Koornwinder. In a part of the Physics literature, the notion of the separation is studied without giving a definition of a separated solution.

In mathematics, more abstract versions of the separation occurred in the works of Stackel, Kostant, and M. Eastwood. However, as far as we know, no sufficient condition on the non-triviality of a separated solution occurs in any of these works.

The talk is based on a bachelor thesis of the speaker. Joint work with S. Krysl (Math. Inst., Charles University)

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We  open the  blue  lecture  room at 13.15  and close  at 15.00.
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