早期量子宇宙中的空间、物质和相互作用Part II：超代数与顶点代数
Space, Matter and Interactions in a Quantum Early Universe. Part II : Superalgebras and Vertex Algebras
摘要：
In our investigation on quantum gravity , we introduce an infinite dimensional complex Lie algebra $\textbf{$ { \mathfrak g}_{ \mathsf u} $}$ that extends $\mathbf{e_9}$ . It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn $\textbf{$ { \mathfrak g}_{ \mathsf u} $}$ into a Lie superalgebra $\textbf{$ \mathfrak {sg}_{ \mathsf u} $}$ with no superpartners, in order to comply with the Pauli exclusion principle . There is a natural action of the Poincaré group on $\textbf{$ \mathfrak {sg}_{ \mathsf u} $}$ , which is an automorphism in the massive sector. We introduce a mechanism for scattering that includes decays as particular { \it resonant scattering}. Finally, we complete the model by merging the local $\textbf{$ \mathfrak {sg}_{ \mathsf u} $}$ into a vertex-type algebra.
英文摘要：
In our investigation on quantum gravity, we introduce an infinite dimensional complex Lie algebra $\textbf{${\mathfrak g}_{\mathsf u}$}$ that extends $\mathbf{e_9}$. It is defined through a symmetric Cartan matrix of a rank 12 Borcherds algebra. We turn $\textbf{${\mathfrak g}_{\mathsf u}$}$ into a Lie superalgebra $\textbf{$\mathfrak {sg}_{\mathsf u}$}$ with no superpartners, in order to comply with the Pauli exclusion principle. There is a natural action of the Poincaré group on $\textbf{$\mathfrak {sg}_{\mathsf u}$}$, which is an automorphism in the massive sector. We introduce a mechanism for scattering that includes decays as particular {\it resonant scattering}. Finally, we complete the model by merging the local $\textbf{$\mathfrak {sg}_{\mathsf u}$}$ into a vertex-type algebra.
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