Structural Algebraic Quantum Field Theory
arXiv:2206.00146 · doi:10.1134/S154747712306002X
Abstract
Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or particles that are made up of elementary constituents like the hadrons, which contain quarks and gluons. We introduce a structure-inclusive algebraic formulation of quantum field theory that could handle such particles and in which orthogonal polynomials play a central role. For simplicity, we consider non-elementary scalar particles in 3+1 Minkowski space-time and, in three appendices, we treat spinors with structure, massless vector fields, and the massive vector bosons. We show how to do scattering calculation in a nonlinear scalar-spinor coupling model where we find that loop integrals in the Feynman diagrams are remarkably finite. The aim of this short exposé is to motivate further studies and research using this approach.
arXiv commentIn this revised version, the four postulates of free quantum fields in SAQFT has been augmented by an essential fifth one concerning interaction (see the first bulleted comment in section 5)
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