Divergence-Free Quantum Field Theory by N.S. Baaklini

Complete and Updated Development

The development of divergence-free quantum field theory seems to be a perfectly consistent effective-action framework for resolving the outstanding problem of divergences in fundamental relativistic theory, most significantly with regard to quantum gravity. Preliminary brief articles pertaining to this development may be found at the author's public collection: http://www.vixra.org/author/n_s_baaklini. However, complete and updated reports concerning the development of the effective action framework for divergence-free quantum field theory can only be found described on this page, and in the following listing. These reports will be continuously refined, improved, and extended, and the listing may grow with the advent of new applications and results. Interested readers and researchers may obtain current versions of these reports (pdf documents) directly from the author: nsbqft@aol.com

The following is a list of titles regarding the available reports, with attendant brief descriptions.

Effective Action Framework for Divergence-Free Quantum Field Theory:
This report presents the basic effective action framework for divergence-free quantum field theory; the loopwise perturbative development of the effective action for a generic field theory, and the manner by which this development is defined in order to evade the conventional divergences of Feynman integrals. It gives a much improved and extended version of the article at: http://www.vixra.org/abs/1312.0056. It gives clear prescriptions for computing contributions in correspondence with ordinary Feynman graphs. It shows the shortest methods of computing divergence-free higher-loop Feynman integrals, and the manner of approximating those that cannot be computed exactly.

The Divergence-Free Effective Action for a Scalar Field Theory:
This report gives detailed computations and results of the application of the divergence-free framework to a scalar field model with quartic coupling. Effective action contributions up to three loops are computed in detail. It is an improved and extended version of the article at: http://www.vixra.org/abs/1312.0065.

Divergence-Free Quantum Gravity in a Scalar Model:
This report gives detailed application of the divergence-free effective action development to a scalar model with gravity-like, non-polynomial interactions characterized by a dimensional coupling constant. Computations are carried to the 3-loop order. It is detailed and improved version of the article at: http://www.vixra.org/abs/1604.0115.

Divergence-Free Non-Linear Scalar Model:
This report gives detailed application of the divergence-free effective action development to a non-linear scalar model with a dimensional coupling constant. Computations are carried to the 3-loop order. It is detailed and improved version of the article at: http://www.vixra.org/abs/1604.0156.

Divergence-Free Scalar Electrodynamics:
This report gives detailed application of the divergence-free effective action development to the theory of scalar electrodynamics, describing the interaction of the electromagnetic photon field with a charged scalar. Computations are carried to the 3-loop order. It is detailed and improved version of the article at: http://www.vixra.org/abs/1604.0341.

The Divergence-Free Effective Action for Quantum Electrodynamics:
This report gives detailed computations, up to 3 loops, for the application of divergence-free effective action techniques to quantum electrodynamics (Maxwell-Dirac theory describing the coupling of a massless spin-1 photon to a massive spin-1/2 Dirac fermion). It demonstrates the manner by which all contributions are gauge invariant and finite. It is a much improved and extended version of the article at: http://www.vixra.org/abs/1401.0013.

Framework for the Effective Action of Quantum Gauge and Gravitational Fields:
This report gives a simplified framework for constructing the manifestly gauge-invariant effective action of non-Abelian quantum gauge, and gravitational fields. It gives an improved and extended version of the article at: http://www.vixra.org/abs/1401.0121.

Divergence-Free Vector Gauge Field Theory:
This report applies our divergence-free and manifestly gauge-invariant effective action framework to a general non-Abelian gauge field theory (massless spin-1 particles). Computations up to 3-loop are described and completed in great detail.

Divergence-Free Quantum Chromodynamics:
This report applies our divergence-free and manifestly gauge-invariant effective action framework to a systems of SU3 colored gluons (non-Abelian vector gauge fields) and quarks (spin-1/2 Dirac fermion fields). Computations up to 3-loop are described and completed in great detail.

Divergence-Free Pure Einstein Gravidynamics:
This report applies our divergence-free and manifestly gauge-invariant effective action framework to Einstein's gravitational field theory (described by a background metric and a virtual spin-2 graviton). Computations up to 2-loop are described and completed in great detail.

Divergence-Free Einstein Gravidynamics Coupled to a Scalar:
This report applies our divergence-free and manifestly gauge-invariant effective action framework to Einstein's gravitational field theory (described by a background metric and a virtual spin-2 graviton) coupled to a scalar field (spinless particle). Computations up to 2-loop are described and completed in great detail.

Divergence-Free Einstein-Maxwell Gravidynamics:
This report applies our divergence-free and manifestly gauge-invariant effective action framework to Einstein's gravitational field theory (described by a background metric and a virtual spin-2 graviton) coupled to a Maxwellian vector field (decribing a spin-1 massless photon). Computations up to 2-loop are described and completed in great detail.

Divergence-Free Einstein-Dirac Gravidynamics:
This report applies our divergence-free and manifestly gauge-invariant effective action framework to Einstein's gravitational field theory (described by a vierbein field and a virtual spin-2 graviton) coupled to a spin-1/2 fermion (Dirac field). Computations up to 2-loop are described and completed in great detail.