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according anticommuting antisymmetric antisymmetric coefficients arbitrary functional calculations causality condition causality equations Chapter commutation complex conjugate contain corresponding definition denotes depend derivatives with respect differential equations differential operator Dirac equation dj(x dq(x easily example expansion coefficients exponential fact factor finite formula Fourier transform Fresnel Fresnel integrals func function q(x functional derivatives functional differential functional integrals functional matrices functional power series functional transformation functional vector Green's functions Hermite functional hermitean conjugate infinite interaction functional Introducing invariant inverse kernel Klein-Gordon equation left-hand side light cone linear mass shell matrix elements matrix multiplication law means notation obtain orthonormal set particles perm Phys polynomial power series expansion quadratically integrable quantities regularized functions representation result rewrite right-hand side S-matrix satisfies scalar seen solution space-like space-time spinor symmetric tions unitarity and causality unitarity condition vanish variables write