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arXiv · hep-th/9410220

Finite-Difference Equations in Relativistic Quantum Mechanics

V. Aldaya·J. Guerrero
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Abstract

Relativistic Quantum Mechanics suffers from structural problems which are traced back to the lack of a position operator $\hat{x}$, satisfying $[\hat{x},\hat{p}]=i\hbar\hat{1}$ with the ordinary momentum operator $\hat{p}$, in the basic symmetry group -- the Poincaré group. In this paper we provide a finite-dimensional extension of the Poincaré group containing only one more (in 1+1D) generator $\hatπ$, satisfying the commutation relation $[\hat{k},\hatπ]=i\hbar\hat{1}$ with the ordinary boost generator $\hat{k}$. The unitary irreducible representations are calculated and the carrier space proves to be the set of Shapiro's wave functions. The generalized equations of motion constitute a simple example of exactly solvable finite-difference set of equations associated with infinite-order polarization equations.

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V. Aldaya, J. Guerrero. 1995-05-17. Finite-Difference Equations in Relativistic Quantum Mechanics. https://doi.org/10.1088/0305-4470%2F28%2F4%2F005

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