Quantum perturbative solutions of extended Snyder and Yang models with spontaneous symmetry breaking

Abstract

We propose $\hslash$-expansions as perturbative solutions of quantum extended Snyder and Yang models, with $\hslash$-independent classical zero-th order terms responsible for the spontaneous breaking of $D=4$ and $D=5$ de Sitter symmetries. In such models, with algebraic basis spanned by $\hat{o}(D,1)$ Lie algebra generators, we relate the vacuum expectation values (VEV) of the spontaneously broken generators with the Abelian set of ten (Snyder, $D=4$) or fifteen (Yang, $D=5$) antisymmetric tensorial generalized coordinates, which are also used as zero order input for obtaining the perturbative solutions of quantum extended Snyder and Yang models. In such a way we will attribute to these Abelian generalized coordinates the physical meaning of the order parameters describing spontaneous symmetry breaking (SSB). It appears that the consecutive terms in $\hslash$-power series can be calculated explicitly if we supplement the SSB order parameters by the dual set of tensorial commutative momenta.

arXiv comment11 pages; published version

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Cited by in corpus (5)

• From Snyder space-times to doubly $\kappa$-dependent Yang quantum phase spaces and their generalizations
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• Yang model revisited
• $\hslash$-perturbative solutions of quantum Snyder and Yang models with parameters describing spontaneous symmetry breaking
• Realizations of the Extended Snyder Model