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- Title
Quantum Mechanics with Real Numbers: Entanglement, Superselection Rules and Gauges.
- Authors
Vedral, Vlatko
- Abstract
We show how imaginary numbers in quantum physics can be eliminated by enlarging the Hilbert space followed by an imposition of--what effectively amounts to--a superselection rule. We illustrate this procedure with a qubit and apply it to the Mach-Zehnder interferometer. The procedure is somewhat reminiscent of the constrained quantization of the electromagnetic field, where, in order to manifestly comply with relativity, one enlarges the Hilbert space by quantizing the longitudinal and scalar modes, only to subsequently introduce a constraint to make sure that they are actually not directly observable.
- Subjects
QUANTUM mechanics; REAL numbers; QUANTUM theory; QUANTUM numbers; ELECTROMAGNETIC fields; HILBERT space; GEOMETRIC quantization
- Publication
Quanta, 2023, Vol 12, Issue 1, p164
- ISSN
1314-7374
- Publication type
Article
- DOI
10.12743/quanta.v12i1.241