Mathematical Physics

    

Model P(φ)_4 Quantum Field Theory a Nonstandard Approach Based on Nonstandard Pointwise-Defined Quantum Fields Part II: the Field Operators and the Approximate Vacuum

Authors: Jaykov Foukzon

A new non-Archimedean approach to interacted quantum fields is presented. In proposed approach, a field operator φ(x,t) no longer a standard tempered operator-valued distribution, but a non-classical operator-valued function. We prove using this novel approach that the quantum field theory with Hamiltonian P(φ)_4 exists and that the corresponding C^*­ algebra of bounded observables satisfies all the Haag-Kastler axioms except Lorentz covariance. We prove that the λ(φ^4 )_4 quantum field theory model is Lorentz covariant. In this paper we consider a some-what different hyperfinite cut-off theory, namely the λφ_4^4 theory in a periodic box. This gives a cut-off interaction which is translation invariant, and therefore it is useful for the study of the vacuum state. In a finite interval we prove that the total Hamiltonian is self #­adjoint and has a complete set of normalizable eigenstates. https://physicsessays.org/browse-journal-2/product/2172-7-jaykov-foukzon-model.html

Comments: Physics Essays Volume 39,Issue1, Pages 53-87, 2026 https://physicsessays.org/browse-journal-2/product/2172-7-jaykov-foukzon-model.html

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[v1] 2024-10-21 20:58:20

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