<i>U</i>(1) ×<i>SU</i>(2) from the tangent bundle

Vargas, Jose G.

doi:10.1088/1742-6596/474/1/012032

Cited by 3 publications

(12 citation statements)

References 18 publications

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“…The present paper becomes the fourth in a series [1], [2], [3] on idempotents that enter solutions with symmetry of exterior systems. This was first considered by É. Kähler [4], but only for only for idempotents involving only scalar-valued differential forms.…”

Section: Introductionmentioning

confidence: 93%

“…They play a privileged role. They constitute a commutative algebra under correlated products in the individual factor algebras that make that product structure [1], [2], [3].…”

Section: Idempotents In the Commutative Algebra Arising From Geometri...mentioning

confidence: 99%

“…In [1], we reproduced a little geometric calculation by É. Cartan [5]. It shows that modern differential geometry amounts to only a theory of moving frames.…”

Section: Introductionmentioning

confidence: 99%

“…The orthogonality of time-space frames that characterizes Special Relativity (SR) -and more generally the Lorentz transformations (LTs)-is not present in its associated space-propertime, which is to be viewed as the high energy physics (HEP) subspace. As argued in [1], there is a specific alternative to SR that preserves orthogonality in space-propertime at a most fundamental level, and still involves the LTs at a practical level. The role of these transformations in what might in principle be a non-relativistic context but with length contraction and time dilation has been known to philosophers of science and interested physicist for many decades, in the context of the issue of conventionality of synchronizations.…”

Section: Introductionmentioning

confidence: 99%

“…Because of that structural equivalence of relativistic time-space and PL space-propertime and in order to postpone anything controversial, we devel-oped mathematical theory in [2] and [3] as if we were dealing with the timespace of SR [We, however, dealt extensively with the physical differences in our paper "U(1) × SU(2) from the tangent bundle" [1]]. We connect here with those papers by first giving names (quarks, flavor, color, generations) to concepts that had previously emerged [3].…”

Section: Introductionmentioning

confidence: 99%

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Algebraic Quarks from the Tangent Bundle: Methodology

Vargas

2015

Preprint

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In a previous paper, we developed a table of components of algebraic solutions of a system of equations generated by an inhomogeneous proper-value equation involving Kähler's total angular momentum. This table looks as if it were a representation of real life quarks. We did not consider all options for solutions of the system of equations that gave rise to it. We shall not, therefore, claim that the present distribution of those components as a well ordered table has strict physical relevance. It, however, is of great interest for the purpose of developing methodology, which may then be used for other solutions.We insert into our present table concepts that parallel those of the phenomenology of high energy physics (HEP): generations, color, flavor, isospin, etc. Breaking then loose from that distribution, we consider simpler alternatives for algebraic "quarks" of primary color (The mathematics speaks of each generation having its own primary color). We use them to show how stoichiometric argument allows one to reach what appear to be esthetically appealing idempotent representation of particles for other than electrons and positrons (Kähler already provided these half a century ago with idempotents similar to our hypothetical quarks). We then use neutron decay to obtain formulas for also hypothetical algebraic neutrinos and the Z 0 , and use pair annihilation to obtain formulas for gamma particles.We finally go back to the aforementioned system of equations and start to develop an alternative option. We solve the system of equations for this new option but stop short of studying it along the lines of the present paper. This would thus be an easy entry point to this theory by HEP physicists. Their knowledge of the phenomenology will allow them to go faster and further.

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Section: Introductionmentioning

confidence: 93%

“…They play a privileged role. They constitute a commutative algebra under correlated products in the individual factor algebras that make that product structure [1], [2], [3].…”

Section: Idempotents In the Commutative Algebra Arising From Geometri...mentioning

confidence: 99%

“…In [1], we reproduced a little geometric calculation by É. Cartan [5]. It shows that modern differential geometry amounts to only a theory of moving frames.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Algebraic Quarks from the Tangent Bundle: Methodology

Vargas

2015

Preprint

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Leptons, Quarks, and Gauge from the Complex Clifford Algebra $$\mathbb {C}\ell _6$$ C ℓ 6

Stoica

2018

Adv. Appl. Clifford Algebras

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Helmholtz Theorem for Differential Forms in 3-D Euclidean Space

Vargas

2014

Preprint

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There are significant differences between Helmholtz and Hodge's decomposition theorems, but both share a common flavor. This paper is a first step to bring them together.We here produce Helmholtz theorems for differential 1−forms and 2−forms in 3-D Euclidean space, E 3 . We emphasize their common structure in order to facilitate the understanding of another paper, soon to be made public, where a Helmholtz theorem for arbitrary differential forms in arbitrary Euclidean space is presented and which allows one to connect (actually to derive from it) an improvement of Hodge's decomposition theorem.

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U(1) ×SU(2) from the tangent bundle

Cited by 3 publications

References 18 publications

Algebraic Quarks from the Tangent Bundle: Methodology

Algebraic Quarks from the Tangent Bundle: Methodology

Leptons, Quarks, and Gauge from the Complex Clifford Algebra $$\mathbb {C}\ell _6$$ C ℓ 6

Helmholtz Theorem for Differential Forms in 3-D Euclidean Space

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