Discrete analytic function theory of n variables

Discrete Analytic Function

Circle Packing: Experiments In Discrete Analytic Function Theory

D-Theory: Field Theory via Dimensional Reduction of Discrete Variables

A new non-perturbative approach to quantum field theory — D-theory — is proposed, in which continuous classical fields are replaced by discrete quantized variables which undergo dimensional reduction. The 2-d classical O(3) model emerges from the (2 + 1)-d quantum Heisenberg model formulated in terms of quantum spins. Dimensional reduction is demonstrated explicitly by simulating correlation le...

A Function-Analytic Development of Field Theory

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A New Approach to the Theory of Discrete Analytic Functions

Lf(m,n)=f(m,n)+if(m+1,n)+i~f(m+1,n+1)+i3f(m,n+ 1) =o. (1.1) The concept of a discrete analytic function was introduced by Ferrand [l] and many properties of discrete analytic functions were obtained by D&in [2]. A convolution product for discrete analytic functions was defined by DufEn and Duris [3] and an operational calculus was developed by Hayabara [4] and further extended by Deeter and Lor...