Invariance

My book was conceived as a musical companion for FOUR-DIMENSIONAL MAN: The Philosophical Methodology of the Ṛg Veda by Antonio T. de Nicolás. In his first edition of that work de Nicolás showed how a profoundly mathematical logic pervades the sacred hymns of our ancient Hindu "mother" culture, a culture in which sound has remained the primary vehicle of truth.

In 1915 and 1916 Emmy Noether was asked by Felix Klein and David Hilbert to assist them in understanding issues involved in any attempt to formulate a general theory of relativity, in particular the new ideas of Einstein. She was consulted particularly over the difficult issue of the form a law of conservation of energy could take in the new theory, and she succeeded brilliantly, finding two deep theorems.

The book gives an introduction to Weyl non-regular quantization suitable for the description of physically interesting quantum systems, where the traditional Dirac-Heisenberg quantization is not applicable. The latter implicitly assumes that the canonical variables describe observables, entailing necessarily the regularity of their exponentials (Weyl operators). However, in physically interesting cases – typically in the presence of a gauge symmetry – non-observable canonical variables are introduced for the description of the states, namely of the relevant representations of the observable algebra.