The quantum theory of a free particle in two dimensions with nonlocal 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.
Nonlocality and ellipticity in a gauge invariant quantization / Esposito, G; Stornaiolo, C. - In: INTERNATIONAL JOURNAL OF MODERN PHYSICS A. - ISSN 0217-751X. - 15:3(2000), pp. 449-460. [10.1142/s0217751x00000215]
Nonlocality and ellipticity in a gauge invariant quantization
ESPOSITO GPrimo
;
2000
Abstract
The quantum theory of a free particle in two dimensions with nonlocal 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.File | Dimensione | Formato | |
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