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arXiv · hep-th/9907212

Non-Locality and Ellipticity in a Gauge-Invariant Quantization

Giampiero Esposito·Cosimo Stornaiolo
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Abstract

The quantum theory of a free particle in two dimensions with non-local boundary conditions on a circle is known to lead to surface and bulk states. Such a scheme is here generalized to the quantized Maxwell field, subject to mixed boundary conditions. If the Robin sector is modified by the addition of a pseudo-differential boundary operator, gauge-invariant boundary conditions are obtained at the price of dealing with gauge-field and ghost operators which become pseudo-differential. A good elliptic theory is then obtained if the kernel occurring in the boundary operator obeys certain summability conditions, and it leads to a peculiar form of the asymptotic expansion of the symbol. The cases of ghost operator of negative and positive order are studied within this framework.

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Giampiero Esposito, Cosimo Stornaiolo. 1999-07-29. Non-Locality and Ellipticity in a Gauge-Invariant Quantization. https://doi.org/10.1142/s0217751x00000215

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