$\hbar$-perturbative solutions of quantum Snyder and Yang models with parameters describing spontaneous symmetry breaking

Autor:	Lukierski, Jerzy, Pachoł, Anna
Rok vydání:	2023
Předmět:	High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics
Zdroj:	PoS(CORFU2022)327
Druh dokumentu:	Working Paper
DOI:	10.22323/1.436.0327
Popis:	We introduce the perturbative $\hbar$-power series ($\hbar$ = Planck constant) providing the algebraic solutions of $D=4$ quantum Snyder and Yang models which describe relativistic quantum space-times and Lorentz-covariant quantum phase spaces. We argue that if in these series the zero order ($\hbar $-independent) terms are non-vanishing they describe the spontaneous symmetry breaking (SSB) parameters of Lie-algebraic symmetries which characterize the considered models ($D=4$ dS symmetry in Snyder and $D=5$ dS symmetry in Yang cases). The consecutive terms in $\hbar$-power series can be calculated explicitly if we supplement the SSB order parameters (Nambu-Goldstone or NG modes) by dual set of commutative momenta, which together define the canonical tensorial Heisenberg algebra. Comment: Contribution to PoS Corfu 2022
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2307.12379 Zobrazit plný text záznamu View this record from Arxiv