When quantum fields are studied on manifolds with boundary, the corresponding one-loop quantum theory for bosonic gauge fields with linear covariant gauges needs the assignment of suitable boundary conditions for elliptic differential operators of Laplace type. There are however deep reasons to modify such a scheme and allow for pseudo-differential boundary-value problems. When the boundary operator is allowed to be pseudo-differential while remaining a projector, the conditions on its kernel leading to strong ellipticity of the boundary-value problem are studied in detail. This makes it possible to develop a theory of one-loop quantum gravity from first principles only, i.e. thephysical principle of invariance under infinitesimal diffeomorphisms and the mathematical requirement of a strongly elliptic theory. It therefore seems that a non-local formulation of quantum field theory has some attractive features which deserve further investigation.
Quantum field theory from first principles / Esposito, G. - (2001), pp. 80-92. (Intervento presentato al convegno Geometrical Aspects of Quantum Fields tenutosi a Londrina nel April 2000).
Quantum field theory from first principles
ESPOSITO GPrimo
2001
Abstract
When quantum fields are studied on manifolds with boundary, the corresponding one-loop quantum theory for bosonic gauge fields with linear covariant gauges needs the assignment of suitable boundary conditions for elliptic differential operators of Laplace type. There are however deep reasons to modify such a scheme and allow for pseudo-differential boundary-value problems. When the boundary operator is allowed to be pseudo-differential while remaining a projector, the conditions on its kernel leading to strong ellipticity of the boundary-value problem are studied in detail. This makes it possible to develop a theory of one-loop quantum gravity from first principles only, i.e. thephysical principle of invariance under infinitesimal diffeomorphisms and the mathematical requirement of a strongly elliptic theory. It therefore seems that a non-local formulation of quantum field theory has some attractive features which deserve further investigation.File | Dimensione | Formato | |
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