Weierstrassian Functions in R^{n}, the Yang-Mills Monopole Condensate and Spacetime Foam

Authors: Serdar NERGİZ, Cihan SAÇLIOĞLU

Abstract: The Weierstrassion \wp,\zeta and \sigma functions are generalized to {\bf R}^{n}. The n=3 and n=4 cases are used in instanton solutions which may be interpreted as explicit realizations of spacetime foam and the monopole condensate, respectively. The new functions satisfy higher dimensional versions of the periodicity properties and Legendre's relations obeyed by their familiar complex counterparts. For n=4, the construction reproduces functions found earlier by Fueter using quaternionic methods. Integrating over lattice points along all directions but two, one recovers the original Weierstrassian elliptic functions.