arXiv subjects

C. N. Ragiadakos

Publications and source records attributed to C. N. Ragiadakos.

11 recordsLinked to original sources

arXiv2024

Pseudo-Conformal Field Theory

The fundamental structure of the 4-dimensional spacetime is assumed to be the lorentzian CR-structure (LCR-structure), which contains two correlated 3-dimensional CR-structures. It is defined by explicit Frobenius integrable relations characterized by "left" and "right" CP(3) points. This LCR-structure is invariant under a very restrictive tetrad-Weyl symmetry, which permits a unique special second order partial differential equation applied to a Yang-Mills field, identified with the gluon field. A class of metrics with the corresponding self-dual forms are defined. After partially fixing the tetrad-Weyl symmetry, the electroweak connection is also defined, which is directly related with the class of LCR-tetrads of the structure. The "free electron" LCR-structure is identified, which has gravitational and electroweak potentials (dressings) with fermionic gyromagnetic ratio g=2. The corresponding massless "neutrino" LCR-structure is also found. These two solitonic configurations constitute the first leptonic generation identified with the Petrov type D LCR-structure. The muon and tau leptonic generations are identified with the Petrov type II and I respectively. Using the electron LCR-structure, I compute the corresponding quark having an additional gluonic potential and providing the explication of the lepton-quark correspondence. The standard model is implied via the causal Bogoliubov, Epstein-Glaser and Scharf procedure viewed as a targeted harmonic analysis in the rigged Hilbert-Fock space of precise Poincare representations of the computed geometric structures.

hep-th↗

arXiv2023

Standard Model Derivation from a 4-d Pseudo-Conformal Field Theory

Pseudo-conformal field theory (PCFT) is a 4-d action, which depends on the lorentzian Cauchy-Riemann (LCR) structure, determined by a tetrad satisfying precise integrability conditions. This LCR-tetrad defines a class of Einstein metrics and an electroweak U(2) connection. A static massive and a massless LCR-manifolds are found. The massive soliton is compatible with the Kerr-Newman manifold. Its two conjugate LCR-structures have g=2 gyromagnetic ratio and opposite charges, suggesting their identification with the electron and positron particles with a naked ring essential singularity. Their background CP(3) formulation bypasses the Hawking-Penrose singularity theorems. The massless LCR-manifold does not have a charge, suggesting its identification with the neutrino. The LCR-structure formalism provides the particles separated into left and right handed chiral parts, the left and right columns of the homogeneous coordinates of the grassmannian G(4,2). The electron LCR-tetrad explicitly provides its gravitational and electroweak potentials (dressings). Their distributional nature permit us to use the Bogoliubov causal perturbative approach (improved by Epstein-Glaser and Scharf et. al. techniques) as a pure mathematical harmonic expansion in the Gelfand rigged Hilbert-Fock space of tempered distributions of the Poincare representations (corresponding free fields). This S-matrix computational procedure in the proper Gelfand triplet, provides the standard model lagrangian for the electromagnetic, weak and Higgs interactions. The interacting terms and the relation between the masses and the coupling constants are implied by the Scharf et. al. operational algorithm on the free fields. In PCFT the computed gluon potential (static quark dressing) cannot be treated with the Bogoliubov procedure. Possible solutions of the dark matter and neutrino mixing problems are discussed.

physics.gen-ph↗

arXiv2022

From 2-d Polyakov Action to the 4-d Pseudo-Conformal Field Theory

The characteristic property of the 2-dimensional Polyakov action is its independence on the metric tensor, without being topological. A renormalizable 4-dimensional action is found satisfying this fundamental property. The fundamental quantity of this pseudo-conformal field theory (PCFT) is the lorentzian Cauchy-Riemann (LCR) structure. This action describes all current phenomenology: 1) The Poincaré group is determined. 2) Stable solitonic LCR-tetrads are found, which belong to representations of the Poincaré group and they are determined by the irreducible and reducible algebraic quadratic surfaces of CP3. 3) The static (irreducible) LCR-structure implies the Kerr-Newman manifold with g=2 gyromagnetic ratio and it is identified with the electron. The stationary (reducible) LCR-structure is identified with the neutrino. The antiparticles have conjugate LCR-structures. The Hawking-Penrose singularity theorems are bypassed in the electron LCR-manifold. 4) The LCR-tetrad defines Einstein's metric and the U(2) electroweak connection. 5) An effective leptonic standard model action is derived using the Bogoliubov-Scharf recursive procedure. 6) The three generations of flavors are implied by the limited number (for curved spacetime) of permitted algebraic surfaces of CP3. 7) For every LCR-structure there exists a solitonic distributional gauge field configuration, identified with the corresponding quark, which explains the lepton-quark correspondence. It is explicitly computed for the static LCR-structure. 8) The derivation of a proper geometric SU(3) Cartan connection opens up the possibility to achieve Einstein's goal to derive all interactions from the pure geometric LCR-structure.

hep-th↗

arXiv2020

Hadronic Sector in the 4-d Pseudo-Conformal Field Theory

The pseudo-conformal field theory (PCFT) is a 4-d action, which depends on the lorentzian Cauchy-Riemann (LCR) structure. Like the 2-d linearized string action, it does not depend on the metric tensor. But the invariance under the pseudo-conformal transformations imposes in the action the existence of a gauge field instead of the scalar field of the string action. The tetrad of the LCR-structure defines a class of metrics and a corresponding class of self dual 2-forms. Soliton and multisoliton point of view of PCFT is described and related to the Einstein derivation of the equations of motion. After the expansion of the action around the static LCR-structure soliton, the quadratic part of the Yang-Mills-like term implies a linear partial differential equation (PDE). I solve this PDE using the Teukolsky method for the solution of the electromagnetic field in the background of the Kerr black hole. The angular and radial ODEs are different from the corresponding Teukolsky master equations. The exact gauge field PDEs are also solved, solved, using the fundamental property of LCR-structure coordinates. The found solutions have colored sources, which could be identified with the quarks.

hep-th↗

arXiv2015

Lorentzian CR structures

The mathematics of a 4-dimensional renormalizable generally covariant lagrangian model (with first order derivatives) is reviewed. The lorentzian CR manifolds are totally real submanifolds of 4(complex)-dimensional complex manifolds determined by four special conditions. The defining tetrad permits the definition of a class of lorentzian metrics which admit two geodetic and shear free congruences. These metrics permit the classification of the structures using the Weyl tensor and the Flaherty pseudo-complex structure. The Cartan procedure permits the definition of three relative invariants. Viewed as a pair of two hypersurface-type 3-dimensional CR structures, the lorentzian CR structures may be osculated on the basis of SU(1,2) group. An osculation on the basis of SU(2,2) group reveals the Poincare group which may be identified with the observed group in nature. Examples of static axially symmetric lorentzian CR structures are computed. For every lorentzian CR manifold, a class of Kaehler metrics of the ambient complex manifold is found, which induce the class of compatible lorentzian metrics on the submanifold. Then the lorentzian CR manifold becomes a lagrangian submanifold in the corresponding ambient (Kaehler) symplectic manifold. The lorentzian CR manifolds may be considered as dynamical processes in the context of the Einstein-Infeld-Hofman derivation of the equations of motion.

hep-th↗

arXiv2013

A Renormalisable Cosmodynamic Model

The fermionic gyromagnetic ratio g= 2 of the Kerr-Newman spacetime cannot be a computational "coincidence". This naturally immerges in a four dimensional generally covariant modified Yang-Mills action, which depends on the lorentzian complex structure of spacetime and not its metric. This metric independence makes the model renormalizable. It is a counter example to the general belief that "string theory is the only selfconsistent quantum model which includes gravity". The other properties of the model are phenomenologically very interesting too. The modified Yang-Mills action generates a linear potential, instead of the Coulomb-like (1/r) potential of the ordinary action. Therefore the Yang-Mills excitations must be perturbatively confined. This separates the solutions of the model into the vacuum bosonic sector of the periodic configurations, the "leptonic" sector with fermionic solitons and their gauge field excitations, the "hadronic" sector. Simple integrability conditions of the pure geometric equations imply a limited number of "leptonic" and "hadronic" families. The geometric surfaces are generally inside the SU(2,2) classical domain. Soliton spin and gravity measure how much the surface penetrates inside the classical domain. The i0 point of infinity breaks the SU(2,2) symmetry down to the Poincare and dilation groups. A scaling breaking mechanism is presented. Hence the pure geometric modes and asymptotically flat solitons of the model must belong to representations of the Poincare group. The metrics compatible to the lorentzian complex structure are induced by a Kaehler metric and the spacetime is a totally real lagrangian submanifold of a Kaehler manifold. This opens up the possibility to use the geometric quantization directly to the solitonic surfaces of the model, considering their corresponding Kaehler symplectic manifold as their phase space.

hep-th↗

arXiv2012

A Renormalizable Quantum Field Theoretic Model with Gravity

A four dimensional generally covariant modified Yang-Mills action, which depends on the lorentzian complex structure of spacetime and not its metric, is presented. The extended Weyl symmetry, implied by the effective metric independence, makes the lagrangian model renormalizable. The modified Yang-Mills action generates a linear potential, instead of the Coulomb-like (1/r) potential of the ordinary action. Therefore the Yang-Mills excitations must be perturbatively confined. The metric, which admits an integrable lorentzian complex structure, can be extended to a Kaehler metric and the spacetime is a totally real CR manifold in $\mathbb{C}^4$. These surfaces are generally inside the SU(2,2) homogeneous domain. A non-real-analytic point, transferred to the U(2) characteristic boundary of the classical domain, spontaneously breaks the SU(2,2) symmetry down to its Poincare subgroup. Hence the pure geometric modes and solitons of the model must belong to representations of the Poincare group.

hep-th↗

arXiv2012

The gravitational content of lorentzian complex structures

The definition of a positive energy is investigated in a renormalizable 4-dimensional generally covariant model, which depends on the lorentzian complex structure and not the metric of spacetime. The gravitational content of the lorentzian complex structures is revealed by identifying the spacetime with special 4-dimensional surfaces of the G{2,2} Grassmannian manifold. The lorentzian complex structure is found to be a codimension-4 CR structure and its classification is studied using the Chern-Moser and Cartan methods. The spacetime metric is found to be a Fefferman-like metric of this codimension-4 CR structure. The open CR manifolds "hanging" from the points of the U(2) characteristic boundary of the SU(2,2) classical domain belong into representations of the Poincaré group and are related to the particle spectrum of the model.

hep-th↗

arXiv2010

Perturbative Confinement in a 4-d Lorentzian Complex Structure Dependent YM-like Model

I continue the study of a renormalizable four-dimensional generally covariant Yang-Mills-like action, which depends on the Lorentzian complex structure of spacetime and not its metric. The field equations and their integrability conditions are written down explicitly. The model is studied with the presence of two static external sources in the trivial cylindrical complex structure. The energy of two static "colored" sources is found to increase linearly with respect to their distance, providing an explicit proof of their perturbative confinement. In the present model, confinement is not a concequence of the non-Abelian character of the gauge group, but it is implied by the complex structure dependence of the model.

hep-th↗

arXiv2008

A Modified Y-M Action with Three Families of Fermionic Solitons and Perturbative Confinement

The dynamics of a four dimensional generally covariant modified SU(N) Yang-Mills action, which depends on the complex structure of spacetime and not its metric, is studied. A general solution of the complex structure integrability conditions is found in the context of the G{2,2) Grassmannian manifold, which admits a global SL(4,C) symmetry group. A convenient definition of the physical energy and momentum permits the study of the vacuum and soliton sectors. The model has a set of conformally SU(2,2) invariant vacua and a set of Poincare invariant vacua. An algebraic integrability condition of the complex structure classifies the solitonic surfaces into three classes (families). The first class (spacetimes with two principal null directions) contains the Kerr-Newman complex structure, which has fermionic (electron-like) properties. That is the correct fermionic gyromagnetic ratio (g=2) and it satisfies the correct electron equations of motion. The conjugate complex structure determines the antisoliton, which has the same mass and opposite charge. The fermionic solitons are differentiated from the complex structure bosonic modes by the periodicity condition on compactified spacetime. The non-periodicity of the found solitonic complex structures is proved. The modification of the Yang-Mills action has an essential consequence to the classical potential. It generates a linear static potential instead of the Coulomb-like (1/r) potential of the ordinary Yang-Mills action. This linear potential implies that for every pure geometric soliton there are N solitonic gauge field excitations, which are perturbatively confined. The present model advocates a solitonic unification scheme without supersymmetry and/or superstrings.

hep-th↗

arXiv2008

Renormalizability of a mofified generally covariant Yang-Mills action

A modified generally covariant Yang-Mills action, which depends on the complex structure of spacetime and not its metric, is proved to be renormalizable. This proof makes this Lagrangian model the unique known generally covariant four dimensional model to be renormalizable without higher order derivatives. The first order one-loop diagrams are computed in an appropriate gauge condition and they are found to be finite.

hep-th↗