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A Calculus Based on a q-deformed Heisenberg Algebra

B. L. Cerchiai·R. Hinterding·J. Madore·J. Wess
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Abstract

We show how one can construct a differential calculus over an algebra where position variables x and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra has a subalgebra generated by x and its inverse which we call the coordinate algebra. A physical field is considered to be an element of the completion of this algebra. We can construct a derivative which leaves invariant the coordinate algebra and so takes physical fields into physical fields. A generalized Leibniz rule for this algebra can be found. Based on this derivative differential forms and an exterior differential calculus can be constructed.

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B. L. Cerchiai, R. Hinterding, J. Madore, J. Wess. 1998-09-28. A Calculus Based on a q-deformed Heisenberg Algebra. https://doi.org/10.1007/s100520050490

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