Abstract
It’s created a canonical Lie algebra in electrodynamics with all the “nice” algebraic and geometrical properties of an universal enveloping algebra with the goal of can to obtain generalizations in quantum electrodynamics theory of the TQFT, and the Universe based in lines and twistor bundles to the obtaining of irreducible unitary representations of the Lie groups SO(4) andO(3,1), based in admissible representations of U(1), and SU(n) . The obtained object haves the advantages to be an algebraic or geometrical space at the same time. This same space of ￡-modules can explain and model different electromagnetic phenomena in superconductor and quantum processes where is necessary an organized transformation of the electromagnetic nature of the space- time and obtain nanotechnologies of the space-time and their elements.
Highlights
Construction of E ⊗ H, with E, and H, L -ModulesLet M, be the space-time whose causal structure [1] (Segal, 1974), is defined by the space{ } ( ) ( ) C= σt X p ∈ End Tp (M ) t ∈ R, X p ∈Tp (M )Let the Lorentz group{ } ( ) L = ξ ∈ GL R4 g (ξ p, ξ q) =g ( p, q),∀p, q ∈ R4 where ∀p ∈ M, and to a local coordinates system {x, y, z},1( ) g ( p) = ds2 = dt2 − dx2 + dy2 + dz2Is the pseudo Riemannian metric of the manifold M
Induced for the orientation of M, σt, results to be an endomorphism of a subspace V, of Tp ( M ), with the property to be an affine connection in the space-time
To demonstrate that H, is a L -module, we consider the coordinate system transformation ( B' )b = ιξ∗∂ ∂tξ ∗F = ξ ∗ (ι∂ ∂tF ) = ξ ∗Bb ◆ Let (⊗E), be the tensor algebra generated by the elements F1 ⊗ F2 − F2 ⊗ F1, ∀F1, F2 ∈ Ω2 ( M )
Summary
Let M , be the space-time whose causal structure [1] (Segal, 1974), is defined by the space.
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