Role of space--time topology in quantum phenomena: Superselection of charge and emergence of nontrivial vacua
Schwarzschild--Kruskal space--time admits a two-parameter family of everywhere regular, static, source-free Maxwell fields. It is shown that there exists a corresponding two-parameter family of unitarily inequivalent representations of the canonical commutation relations. Elements of the underlying Hilbert space may be interpreted as ''quantum fluctuations of the Maxwell field off nontrivial classical vacua.'' The representation corresponding to the ''trivial'' sector: i.e., the zero classical solution: is the usual Fock representation. All others are ''non-Fock.'' In particular, in all other sectors, the Maxwell field develops a nonzero vacuum expectation value. The parameters labelling the family can be interpreted as electric and magnetic charges. Therefore, unitary inequivalence naturally leads to superselection rules for these charges. These features arise in spite of the linearity of field equations only because the space--time topology is ''nontrivial.'' Also, because of linearity, an exact analysis is possible at the quantum level; recourse to perturbation theory is unnecessary.
- Research Organization:
- Departement de Physique, Universite de Clermont-Fd, 63170 Aubiere, France
- OSTI ID:
- 5541870
- Journal Information:
- J. Math. Phys. (N.Y.); (United States), Vol. 21:3
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GRAVITATIONAL INTERACTIONS
MINKOWSKI SPACE
QUANTUM FIELD THEORY
CANONICAL DIMENSION
FOCK REPRESENTATION
SUPERSELECTION RULES
ALGEBRA
COMMUTATION RELATIONS
COUPLING CONSTANTS
EXPECTATION VALUE
HILBERT SPACE
MAXWELL EQUATIONS
NONLINEAR PROBLEMS
SPACE-TIME
TOPOLOGY
VACUUM STATES
BANACH SPACE
BASIC INTERACTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
INTERACTIONS
MATHEMATICAL SPACE
MATHEMATICS
SCALE DIMENSION
SELECTION RULES
SPACE
645400* - High Energy Physics- Field Theory