Complex Rational Numbers in Quantum Mechanics

Details Complex Rational Numbers in Quantum Mechanics Complex Rational Numbers in Quantum Mechanics

2005-08-03

arxiv.org/abs/quant-ph/0508038v1

International Journal of Modern Physics B Vol 20, 1730-1741 (2006)

Physics

Quantum Physics

12 pages Contribution for Proceedings, ISSUR-05, in Int. Jour. Mod. Physics, B

Scientific paper

10.1142/S021797920603425X

A binary representation of complex rational numbers and their arithmetic is described that is not based on qubits. It takes account of the fact that $0s$ in a qubit string do not contribute to the value of a number. They serve only as place holders. The representation is based on the distribution of four types of systems, corresponding to $+1,-1,+i,-i,$ along an integer lattice. Complex rational numbers correspond to arbitrary products of four types of creation operators acting on the vacuum state. An occupation number representation is given for both bosons and fermions.

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