On Rational Physics: a Basic Formalism for Relativistic Physics – and "A Unique Mathematical Derivation of the Fundamental Laws of Nature Based on a New Algebraic Approach"

Ramin Zahedi (1)

1 Hokkaido University [Sapporo, Japan]

In Part I (pp. 1-10) of this article, I provide a general analysis of a number of current discontinuous approaches to fundamental physics. In Part II (the main part, pp. 11-99, Ref. [37]), as a new mathematical approach to the origin of basic laws of nature, using a new algebraic axiomatic (matrix) formalism based on the ring theory and Clifford algebras (presented in Sec.2), "it is shown that certain mathematical forms of the fundamental laws of nature, including laws governing the fundamental forces of nature (represented by a set of two definite classes of general covariant massive field equations, with new matrix formalisms), are derived uniquely from only a very few axioms"; where in agreement with the rational Lorentz group, it is also basically assumed that the components of relativistic energy-momentum can only take rational values. Based on the definite mathematical formalism of this axiomatic approach, along with the C, P and T symmetries (represented by the corresponding quantum matrix operators) of the fundamentally derived field equations, it is concluded that the universe could be realized solely with the (1+2) and (1+3)-dimensional space-times. On the basis of these discrete symmetries of the derived field equations, it has been also shown that only left-handed particle fields (along with their complementary right-handed fields) could be coupled to the corresponding (any) source currents. Moreover, it is shown that the (1+3)-dimensional cases of uniquely determined two classes of general covariant field equations, represent, respectively, new massive forms of the bispinor fields of spin-2, and spin-1 particles; and (1+2)-dimensional cases of these equations represent new massive forms of the bispinor fields of spin-3/2 and spin-1/2 particles, respectively.
As a particular consequence, it is shown that a certain massive formalism of general relativity – with a definite form of torsion field appeared originally as the generator of gravitational field’s invariant mass – is obtained only by first quantization (followed by a basic procedure of minimal coupling to space-time geometry) of a certain set of special relativistic algebraic matrix equations. It has been also proved that Lagrangian densities specified for the originally derived new massive forms of the Maxwell, Yang-Mills and Dirac field equations, are also gauge invariant, where the invariant mass of each field is generated solely by the corresponding torsion field. In addition, in agreement with recent astronomical data, a new form of massive gauge boson is identified (compatible with U(1) symmetry group) with invariant mass: "m_γ ≈ 4.90571×10^-50kg", which generated by a coupled torsion field of the background space-time geometry.
Moreover, based on the definite mathematical formalism of this axiomatic approach, along with the C, P and T symmetries (represented basically by the corresponding quantum operators) of the fundamentally derived field equations, it has been concluded that the universe could be realized solely with the (1+2) and (1+3)-dimensional space-times (where this conclusion, in particular, is based on the T-symmetry). It is proved that CPT is the only (unique) combination of C, P, and T symmetries that could be defined as a symmetry for interacting fields. In addition, on the basis of these discrete symmetries of derived field equations, it has been also shown that only left-handed particle fields (along with their complementary right-handed fields) could be coupled to the corresponding (any) source currents. Furthermore, it has been shown that the metric of background space-time is diagonalized for the uniquely derived fermion field equations (defined and expressed solely in (1+2)-dimensional space-time), where this property generates a certain set of additional symmetries corresponding uniquely to the "SU(2)_L⊗U(2)_R" symmetry group for spin-1/2 fermion fields (representing “1+3” generations of four fermions, including a group of eight leptons and a group of eight quarks), and also the "SU(2)_L⊗U(2)_R" gauge symmetry groups for spin-1 boson fields coupled to the spin-1/2 fermionic source currents. Hence, along with the known elementary particles, eight new elementary particles, including four new charge-less right-handed spin-1/2 fermions (two leptons and two quarks), a spin-3/2 fermion, and also three new spin-1 (massive) bosons are predicted axiomatically by this new mathematical approach (on a fundamental gauge-theoretic basis). As a particular result, based on the definite matrix formalism of the uniquely derived general covariant form of Maxwell (and also Yang-Mills) field equations, it has been also concluded that magnetic monopoles could not exist in nature.

Comments: 99 Pages. A summary of a submitted and accepted research project ("Foundations of Physics", "Investigation of the Origin of Space-Time", and "Ontology"), Japan, 2012 - 2015. Expanded and Presented Article's Version at "The 2016 GRavitational-Wave Astronomy International Conference in Paris, Institute d‘Astrophysique de Paris (IAP), Sorbonne University, 'Paris VI - UPMC, CNRS, LERU, EUA', Paris, France, 2016. 'Supported by the European Union's 7th Framework Program: FP7/PEOPLE-2011-CIG,‘ 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx)

This article has been invited and presented at the following international conferences:
-The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, 2016. (https://www.siam.org/meetings/ms16)
-The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, Engineering and Cognitive Sciences (ICMM), Linnaeus University, Sweden, 2016. (https://lnu.se/en/qb/)
-The 4th International Conference on New Frontiers in Physics, CERN Organized and Supported Conference (Europe), ICNFP-2015. (https://indico.cern.ch/e/icnfp2015/)
-The 2016 International Conference on Algebraic Geometry and Mathematical Physics, University of Tromsø, Norway, 2016. (https://site.uit.no/)
-The XXXVII Max Born International Symposium, International Conference on Non-commutative Geometry, Quantum Symmetries and Quantum Gravity (II), Wroclaw University, Poland, 2016. (http://ift.uni.wroc.pl/~mborn37/)
-The 2016 GRavitational-wave Astronomy International Conference in Paris, Institute d‘Astrophysique de Paris (IAP), The University of Paris VI - Sorbonne University, CNRS, LERU, EUA, Paris, France, 'Supported by the European Union's 7th Framework Program: FP7/PEOPLE-2011-CIG,‘ 2016.
(http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx)
-The 22nd Internnational Australian Institute of Physics Congress (AIP), University of Queensland, Brisbane, Australia, 2016. (http://appc-aip2016.org.au)
-The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016. (http://www.gr21.org)

External URLs (including preprints and earlier publications of this article):
https://cds.CERN.ch/record/1980381/, https://INSPIREHEP.net/record/1387680/,
https://eprints.lib.hokudai.ac.jp/dspace/handle/2115/59279/ , http://jairo.NII.ac.jp/0003/00047402/en/,
https://indico.CERN.ch/event/344173/session/22/contribution/422/attachments/1140145/1646101/R.a.Zahedi--OnDiscretePhysics-Jan.2015-signed.pdf,
https://CORE.ac.uk/display/41880261/, http://philsci-archive.PITT.edu/11497,
http://philpapers.cdp.UWO.ca/rec/zahotl/,
http://www.ijqf.org/archives/3495, http://ci.NII.ac.jp/naid/120005613576,
https://citeseerx.ist.PSU.edu/viewdoc/summary?doi=10.1.1.675.2202/,
https://LNU.se/contentassets/1489145f113348f382202fbf0d1d4094/qb-abstracts-compiled-160613.pdf,
http://mts-ncomms.Nature.com/ncomms_files/2017/07/10/00136200/00/136200_0_art_file_2445656_bsw9c4.pdf ,
https://indico.CERN.ch/event/344173/contribution/1740565/attachments/1140145/1726912/R.A.Zahedi--Forces.of.Nature.Laws-Jan.2015-signed.pdf .

Mots clés: "Fundamental Forces of Nature and their Axiomatic-Mathematical Representation; CPT Symmetry as the Only Combination of C - P and T Symmetries for the Interactiong Fields; Energy-Momentum as a Basic Rational-valued Physical Quantity; Mathematical Prediction of Eight New Elementary Particles including: Two Chargeless Leptons Two Chargeless Quarks - One Spin-3/2 Fermion and Three Spin-1 Bosons - Based on the Determined Certan Forms of Gauge Symmetry Groups; Ontology and Logical Origin of the Fundamental Laws of Nature; "

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique mathématique [math-ph]; Physique Quantique [quant-ph]; Philosophie; Physique des Hautes Energies - Théorie [hep-th]; Planète et Univers [physics]; Phénomènes cosmiques de haute energie [astro-ph.HE]

Ramin Zahedi. On Rational Physics: a Basic Formalism for Relativistic Physics – and "A Unique Mathematical Derivation of the Fundamental Laws of Nature Based on a New Algebraic Approach". Hokkaido University Collection of Scholarly and Academic Papers, 2015, 16 (2), pp.99. ⟨hal-01547739⟩