Conformal generation of an exotic rotationally invariant harmonic oscillator
نویسندگان
چکیده
An exotic rotationally invariant harmonic oscillator (ERIHO) is constructed by applying a non-unitary isotropic conformal bridge transformation (CBT) to free planar particle. It described the Hamiltonian supplemented Zeeman type term with real coupling constant $g$. The model reveals Euclidean ($|g|<1$) and Minkowskian ($|g|>1$) phases separated $g=+1$ $g=-1$ of Landau problem in symmetric gauge opposite orientation magnetic field. A hidden symmetry emerges system at rational values Its generators, together angular momentum produce non-linearly deformed $\mathfrak{u}(2)$ $\mathfrak{gl}(2,{\mathbb R})$ algebras cases $0<|g|<1$ $\infty>|g|>1$, which transmute one into another under inversion $g\rightarrow -1/g$. Similarly, true, $\mathfrak{u}(2)$, extended conformal, R})$, symmetries ($g=0$) interchange their roles ($|g|=\infty$), while two copies algebra analogous mutually phases. We show that ERIHO transformed peculiar unitary anisotropic generated, turn, CBT. relationship between subcritical harmonically problem, as well plane uniformly rotating reference frame, established.
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ژورنال
عنوان ژورنال: Physical review
سال: 2021
ISSN: ['0556-2813', '1538-4497', '1089-490X']
DOI: https://doi.org/10.1103/physrevd.103.106004