Solution of a linearized model of Heisenberg’s fundamental equation II

Abstract

We propose to look at (a simplified version of) Heisenberg’s fundamental field equation [see Heisenberg, W., Introduction to the Unified Field Theory of Elementary Particles (Wiley, New York, 1966)] as a relativistic quantum field theory with a fundamental length, as introduced by Brüning and Nagamachi [J. Math. Phys. 45, 2199 (2004)], and give a solution in terms of Wick power series of free fields which converge in the sense of ultrahyperfunctions but not in the sense of distributions. The solution of this model has been prepared by Nagamachi and Brüning [arXiv:0804.1663] by calculating all n-point functions by using path integral quantization. The functional representation derived in this part is essential for the verification of our condition of extended causality. The verification of the remaining defining conditions of a relativistic quantum field theory is much simpler through the use of Wick power series. Accordingly in this second part, we use Wick power series techniques to define our basic fields and derive their properties.