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A convergent lattice approximation for nonlinear electromagnetic fields in four dimensions (1993)

Albeverio, S. ; Iwata, K. ; Schmidt, M.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 34 (1993), S. 3327-3342

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: A discrete version of the quaternionic Cauchy–Riemann equation ∂A=F, where F is Gauss–Poisson white noise, is discussed. On the lattice δZ4 random variables Fδ(δn) and Aδ(δn) are constructed which approximate the corresponding random fields F and A, respectively, in the limit δ→0. In the Gaussian case the random variables Aδ(δn) can be interpreted as the lattice approximation of the free electromagnetic Euclidean potential field whereas in the non-Gaussian case one obtains an approximation of nonlinear interacting electromagnetic quantum fields. Convergence to the continuum limit is proven.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.530079

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