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arXiv · 2307.12379

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

Jerzy Lukierski·Anna Pachoł
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Abstract

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.

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Jerzy Lukierski, Anna Pachoł. 2023-07-23. $\hbar$-perturbative solutions of quantum Snyder and Yang models with parameters describing spontaneous symmetry breaking. https://doi.org/10.22323/1.436.0327

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