Vladimir V. Kisil, Enrique Ram\'{\i}rez de Arellano The Riesz-Clifford Functional Calculus for Non-Commuting Operators and Quantum Field Theory (46K, LaTeX2e) ABSTRACT. We present a Riesz-like hyperholomorphic functional calculus for a set of non-commuting operators based on the Clifford analysis. Applications to the quantum field theory are described. Keywords. Functional calculus, Weyl calculus, Riesz calculus, Clifford analysis, quantization, quantum field theory. AMSMSC Primary:47A60, Secondary: 81T10