Period Integrals, Quantization and Gauge
In the early seventies it became apparent to me that certain topological features of physical theories were being ignored. A basic feature of topology is related to "counting". That is, you never have 1.23 holes, you have an integer number of holes. The same is true for the topological property of self intersection. The number of self intersections is an integer.

The Quantum theory also places emphasis on the rational numbers. There are states with rational values of "angular momentum". Quanta come in integer numbers. Charge, after Millikan's experiments is recognized as a rational entity.

How do you put these physical ideas together.

The first job is to formulate what is a topological property. The simplest (but not complete) definition is that a topological property is a deformation invariant. Using the Lie derivative with respect to a vector field V as the description of an evolutionary process permits the closed integrals of closed forms to be defined as deformation invariants. These closed integrals of closed forms are called deRham period integrals. Their values have rational ratios.

The article below was an attempt to utilze this idea as a marriage between topology and quantum mechanics. In the article, the two 3 forms of A^H and A^F were utilized, as well as the 2-form H and the 1-form A. Properties of these species of period integrals were examined as applied to various physical theories.

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Last update 07/02/2001
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