Two-Component Spinorial Formalism Using Quaternions for Six-Dimensional Spacetimes

Venâncio, Joás; Batista, Carlos

doi:10.1007/s00006-021-01172-1

Cited by 5 publications

(2 citation statements)

References 48 publications

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“…An old (1950) paper by Podolanski [55] studies unified field theory in six dimensions, and in fact the abstract starts by saying 'The geometry of the Dirac equation is actually six-dimensional'. An elegant (2020) paper by Venancio and Batista [56] analyses 'Two-Component spinorial formalism using quaternions for six-dimensional Spacetimes'. An insightful (1993) work by Boyling and Cole [57] studies the six-dimensional (3+3) Dirac equation and shows that particles have spatial spin-1/2 and temporal spin-1/2.…”

Section: Overview Of the Octonionic Theorymentioning

confidence: 99%

An $E_8 \otimes E_8$ Unification of the Standard Model with Pre-Gravitation, on an Exceptional Lie algebra - Valued Space

KAUSHIK,

VAIBHAV,

SINGH

2024

Preprint

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We propose an $E_8 \otimes E_8$ unification of the standard model with pre-gravitation, on an exceptional Lie algebra-valued space . Each of the $E_8$ has in its branching an $SU(3)$ for space-time and an $SU(3)$ for three fermion generations. The first $E_8$ further branches to the standard model $SU(3)_c \otimes SU(2)_L \otimes U(1)_Y$ and describes the gauge bosons, Higgs and the left chiral fermions of the standard model. The second $E_8$ further branches into a right-handed counterpart (pre-gravitation) $SU(3)_{grav}\otimes SU(2)_R \otimes U(1)_g$ of the standard model, and describes right chiral fermions, a Higgs, and twelve gauge bosons associated with pre-gravitation, from which general relativity is emergent. We account for 208 out of the 496 degrees of freedom of $E_8 \otimes E_8$ and propose an interpretation for the remaining 288, motivated by the trace dynamics Lagrangian of our theory. We explain how the two copies of $SU(3)_{spacetime}$ together give rise to a 6D spacetime with signature $(3,3)$ which upon symmetry breaking gives rise to our 4D spacetime and to a second 4D anti-spacetime with flipped signature.

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Section: Overview Of the Octonionic Theorymentioning

confidence: 99%

An $E_8 \otimes E_8$ Unification of the Standard Model with Pre-Gravitation, on an Exceptional Lie algebra - Valued Space

KAUSHIK,

VAIBHAV,

SINGH

2024

Preprint

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“…Further information about quaternions will be given in the next section, but we anticipate that quaternions are hyper-complex numbers comprising four real components that can be used to model several applications of physical interest, such as Lorentz transformations [2,3,4,5], vector calculus [6], the Dirac equation [7,8,9], and several other [10,11,12,13]. However, these are simply different ways of solving wellknown problems.…”

Section: Introductionmentioning

confidence: 99%

Quaternionic scalar field in the real Hilbert space

Giardino

2022

Preprint

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Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and charge operators. Conversely to the complex case, the quaternionic quantization admits two quantization schemes, concerning either two or four components. Therefore, the quaternionic field permits a richer structure of states, if compared to the complex scalar field case. Moreover, the quaternionic theory admits as a further novel feature a non-associative algebraic structure in their complex components, something not observed in the complex case.

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Twistorial cohomotopy implies Green–Schwarz anomaly cancellation

2022

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We characterize the integral cohomology and the rational homotopy type of the maximal Borel-equivariantization of the combined Hopf/twistor fibration, and find that subtle relations satisfied by the cohomology generators are just those that govern Hořava–Witten’s proposal for the extension of the Green–Schwarz mechanism from heterotic string theory to heterotic M-theory. We discuss how this squares with the Hypothesis H that the elusive mathematical foundation of M-theory is based on charge quantization in tangentially twisted unstable Cohomotopy theory.

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Two-Component Spinorial Formalism Using Quaternions for Six-Dimensional Spacetimes

Cited by 5 publications

References 48 publications

An $E_8 \otimes E_8$ Unification of the Standard Model with Pre-Gravitation, on an Exceptional Lie algebra - Valued Space

An $E_8 \otimes E_8$ Unification of the Standard Model with Pre-Gravitation, on an Exceptional Lie algebra - Valued Space

Quaternionic scalar field in the real Hilbert space

Twistorial cohomotopy implies Green–Schwarz anomaly cancellation

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