Discrete Subgroups of the Poincaré Group
نویسنده
چکیده
The framework of point form relativistic quantum mechanics is used to construct interacting four-momentum operators in terms of creation and annihilation operators of underlying constituents. It is shown how to write the creation and annihilation operators in terms of discrete momenta, arising from discrete subgroups of the Lorentz group, in such a way that the Poincaré commutation relations are preserved. For discrete momenta the bosonic creation and annihilation operators can be written as multiplication and differentiation operators acting on a holomorphic Fock space. It is shown that with such operators matrix elements of the relativistic Schrödinger equation become an infinite coupled set of first order partial differential equations.
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