Summary
A quantum theory of the sourceless Maxwell field in vacuum gravitational magnetic monopoles is proposed. The nontrivial (Hopf) bundle structure of these space-times manifests itself (via the Coulombic part of the Maxwell fields) in an algebra of superselected quantum operators and resulting non-Fock representations. The superselected sectors provide new quantum numbers (analogous to spin and mass) which find their origin in the first Chern class of the bundle. The conserved quantity of the greatest interest is the total magnetic mass and the induced-superselection rules can be viewed as a qualitative manifestation, at the quantum level, of the multiple connectedness of the space-times under consideration.
Riassunto
Si propone una teoria quantistica del campo di Maxwell senza sorgente in monopoli magnetici gravitazionali nel vuoto. La struttura a fascio (di Hopf) non banale di questi spazi-tempi si manifesta (via la parte Coulombiana dei campi di Maxwell) in un’algebra di operatori quantistici superselezionati e in rappresentazioni risultanti non di Fock. I settori superselezionati forniscono nuovi numeri quantici (analoghi allo spin e alla massa) che trovano la loro origine nella prima classe di Chern del fascio. La quantità conservata di massimo interesse è la massa magnetica totale e le regole di superselezione indotte si possono considerare una manifestazione qualitativa, al livello quantistico, della connessione multipla degli spazi-tempi considerati.
Реэюме
Предлагается квантовая теория Максвелловского поля беэ источников с вакуумными гравитационными магнитными монополями. Нетривиальная структура для зтих семейств пространств и времен проявляется череэ алгебру квантовых операторов и реэультируюшие нефоковские представления. Суперотобранные секторы дают новые квантовые числа (аналогичные спину и массе), которые воэникают в первом классе Черна для семейства. Сахраняюшаяся величина, которая представляет наибольщий интерес, есть полная магнитная масса. Индуцированные правила суперотбора можно рассматривать как качественное проявление, на квантовом уровне, множественной свяэанности рассматриваемых пространств и времен.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Penrose: inBattelle Rencontres (Benjamin, New York, N.Y., 1967).
A. Magnon:J. Math. Phys. (N.Y.),27, 1059 (1986);
A. Magnon:J. Math. Phys. (N.Y.),27, 1066 (1986).
A. Magnon:Dual mass, H-spaces and non-linear graviton with topological origin, to appear inJ. Math. Phys. (N.Y.), (July 1986).
A. Magnon:Mass, dual mass, and gravitational entropy, to appear inJ. Math. Phys. (N.Y.), (1986).
A. Magnon:Existence and observability of spinor structure, submitted toJ. Math. Phys. (N.Y.), (1986).
A. Magnon:Mass and dual mass, a gravitational analogue of the Dirac quantization rule and its physical implications, submitted toJ. Math. Phys. (N.Y.), (1986).
A. Ashtekar andA. Sen:J. Math. Phys. (N.Y.),21, 526 (1980).
C. Nash andS. Sen:Topology and geometry for physicists (Academic Press, New York, N.Y., 1983).
N. Steenrod:The Topology of Fiber Bundles (Princeton University Press, Princeton, N.J., 1951).
M. Daniel andC. M. Viallet:Rev. Mod. Phys.,52, 176 (1980).
Author information
Authors and Affiliations
Additional information
This research was supported in part by the National Science Foundation under Grant No. PHY82-17853, supplemented by funds from the National Aeronautics and Space Administration.
Rights and permissions
About this article
Cite this article
Magnon, A. Magnetic mass and superselection phenomena. Nuov Cim A 99, 63–73 (1988). https://doi.org/10.1007/BF02735212
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02735212