View source for Interaction Theory for Infinite Arrays

=Introduction =

We want to use the [[Kagemoto and Yue Interaction Theory]] to derive a system of equations for the infinite array.

= System of equations =

We start with the final system of equations of the [[Kagemoto and Yue Interaction Theory]], namely
<center><math>
A_{m\mu}^l = \sum_{n=0}^{\infty}
\sum_{\nu = -\infty}^{\infty} B_{mn\mu\nu}^l
\Big[ \tilde{D}_{n\nu}^{l} +
\sum_{j=1,j \neq  l}^{N} \sum_{\tau =
-\infty}^{\infty} A_{n\tau}^j (-1)^\nu K_{\tau - \nu}  (k_n
R_{jl}) \mathrm{e}^{\mathrm{i}(\tau -\nu) \varphi_{jl}} \Big], 
</math></center>
<math>m \in \mathbb{N}</math>, <math>\mu \in \mathbb{Z}</math>, <math>l=1,\dots,N</math>.

[[Category:Infinite Array]]