### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 526-533 |

Number of pages | 8 |

Journal | Journal of Mathematical Physics |

Volume | 21 |

Issue number | 3 |

State | Published - Dec 1 1979 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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*Journal of Mathematical Physics*, vol. 21, no. 3, pp. 526-533.

**On the role of space-time topology in quantum phenomena : Superselection of charge and emergence of nontrivial vacua.** / Ashtekar, Abhay; Sen, Amitabha.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the role of space-time topology in quantum phenomena

T2 - Superselection of charge and emergence of nontrivial vacua

AU - Ashtekar, Abhay

AU - Sen, Amitabha

PY - 1979/12/1

Y1 - 1979/12/1

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:36749117587

VL - 21

SP - 526

EP - 533

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 3

ER -