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algebra amplitude analytic asymptotic boundary conditions bounded classical Comm commutation cone consider continuous correlation functions corresponding covariant defined denote derivation diagram differential equations dimensional distribution domain dynamical energy equilibrium ergodic Euclidean exists expansion exponential ferromagnetic Feynman Feynman integrals finite formalism Fourier transform gauge given Green's functions Hamiltonian Hilbert space holonomic system inequalities infinite integral interaction invariant Ising model Japan Kyoto Lagrangian lattice Lebowitz limit linear manifold mass Math mathematical matrix method microfunction momentum nonlinear obtained octonionic operators parameter particles perturbation phase transition Phys physical potential Preprint problem propagation properties quantum field theory relations renormalization representation resp respect S-matrix satisfies scaling scattering theory singularity solution space-time spectral spectrum spin statistical mechanics stochastic string structure symmetry temperature Theorem thermodynamic tion topology unique unitarity Univ variables vector vertex function Wightman Wightman functional zero