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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 122
On the Asymptotic Analysis of the Discrete Dirac Equation M. Holschneider, Ch. Gunn
We describe a discrete version of the one-dimensional Dirac equation. Images from computer simulations of this system led to our attempt to understand the asymptotic behavior. Using techniques of Fourier analysis and asymptotic analysis, we obtain results generally valid for operators on the space of square-summable sequences which commute with translation by two, which allow us to prove in the Dirac case that the critical angle of propagation beta satisfies beta <= tan(delta), where delta is the discrete analog of mass, with strong evidence of equality.
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