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Abstract
We show how Lorentz and SU(3) groups can be derived from the covariance principle conserving a Z3-graded three-form on a Z3-graded cubic algebra representing quarks endowed with non-standard commutation laws. This construction suggests that the geometry of space-time can be considered as a manifestation of symmetries of fundamental matter fields.
Highlights
We show how Lorentz and SU (3) groups can be derived from the covariance principle conserving a Z3-graded three-form on a Z3-graded cubic algebra representing quarks endowed with non-standard commutation laws
The Pauli exclusion principle, symmetry between particles and anti-particles, electric charge and baryonic number conservation belong to this category
Quantum mechanics itself can be formulated without any mention of space, as was shown by M
Summary
We show how Lorentz and SU (3) groups can be derived from the covariance principle conserving a Z3-graded three-form on a Z3-graded cubic algebra representing quarks endowed with non-standard commutation laws. Let us introduce N generators spanning a linear space over complex numbers, satisfying the following relations which are a cubic generalization of anti-commutation in the ususal (binary) case
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