Abstract
A quantum system with positions and momenta in GF(pℓ) is considered. Such a system can be constructed from ℓ smaller systems, in which the positions and momenta take values in Zp, if the Hamiltonian of this ℓ-partite system is compatible with GF(pℓ). The concept of compatibility of a Hamiltonian with GF(pℓ) allows the quantum formalism in the ℓ-partite system to be expressed in terms of Galois arithmetic. Transformations of the basis in GF(pℓ) produce unitary transformations of the quantum states, which form a representation of GL(ℓ,Zp). They are used to define which subset of the general set of Hamiltonians in the ℓ-partite system is compatible with GF(pℓ).
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