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- W2051240316 abstract "In a previous paper (~) we have studied the possibilities of extending a ~ germ }~, that is, a given invariance algebra of a quantum-mechanical system, and we have proposed a method using the notion of derivation algebra. In particular we have treated, as an example, a system of particles possessing Galilean invariance. In this case the Hamiltonian appears as a derivation which acts on the remainder of the algebra, i.e. the extended derived Galilean algebra ~'. Hence by taking ~' as germ, our approach has permitted us to realize the whole Schr~dinger algebra ~ch = ~'[B su~a, in which the Hamiltonian belongs to the s%,~ subalgebra. This approach has led us to ask the following question. Is it possible to extract from the SU~.~ algebra other types of Hamiltonians which, by construction, act as a derivation on ~' and describe systems which always possess ~' as invariance subalgebra? By answering to the question we will show that it appears an interesting algebraic characterization of the notion of interaction (external fields or internal interactions among constituents of a system). A system of N nonrelativistie particles without spin is characterized in part by the centre-of-mass observables: the position X = K / M and the canonically conjugate variable P. In the Heisenberg picture these observables can be expressed in terms of canonical co-ordinates q(/~) and p(#) corresponding to each mass-point m(/x) (# = 1, ..., ~V) following" @default.
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- W2051240316 date "1973-08-01" @default.
- W2051240316 modified "2023-09-26" @default.
- W2051240316 title "Invariance algebras and interactions in nonrelativistic quantum mechanics" @default.
- W2051240316 cites W1987855271 @default.
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- W2051240316 doi "https://doi.org/10.1007/bf02725403" @default.
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