Self-consistent quantum-field theory

Eduard Prugovečki

R. Haussmann

José A. R. Cembranos, Marcos Skowronek

The formulation of Quantum Field Theory (QFT) in phase space offers a unique alternative to operator and path-integral paradigms, providing distinct conceptual advantages for semiclassical expansions. In this work, we present a systematic and self-consistent functional framework that maps stationary Schrodinger functional equations directly onto phase-space star-eigenvalue equations across different spin statistics. Operating within a non-manifestly covariant equal-time formalism, we derive explicit vacuum Wigner functionals for scalar, gauge, and fermionic fields, establishing the rigorous theoretical consistency of the formalism from first principles prior to phenomenological applications. We analyze how ordering prescriptions and continuous symmetries manifest under the functional star-product, including an explicit phase-space formulation of Noether’s theorem and field regularization. Finally, the framework is extended to interacting systems via a functional Rayleigh–Schrodinger perturbative scheme, illustrated explicitly through the non-trivial first-order Wigner functional correction W(1) and the vacuum energy correction for a ϕ4 self-interacting theory, establishing a solid foundation for evaluating real-time quantum field dynamics.

CHRISTOF WETTERICH

H.-J. Unger

Victor Vaguine

The quantum field theory (QFT) is one of branches of the Standard Model. According to QFT, quantum fields are the primary entities and particles are the excitations of these fields, coming in discrete lumps with no inner structures and with properties assigned by declaration. Such view is in conflict with the observed vacuum energy density, 140 orders of magnitudes less than required by the QFT. In addition, such view is challenged by Aphysical Quantum Mechanics (AQM), a deeper quantum theory. According to AQM, the fundamental understanding of quantum reality is expanded by the addition of two fundamental categories, aphysical and elementary consciousness of elementary particles. Based on AQM and as an example, the total ontology of the intrinsic (fundamental) electron is presented with its inner structure of perfect geometry consisting of the physical charged c-ring and aphysical cylinder, and with its properties such as self-mass, spin, magneto-electrostatic field configuration and magnetic moment. The position parameter in the inner structure demonstrates that there are no two identical intrinsic electrons in the Universe thus placing a question mark over the QFT principle of indistinguishability.