English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The relation between motion in $-1/r$ and $r^{2}$ potentials, known sinceNewton, can be demonstrated by the substitution $r\rightarrow r^{2}$ in theclassical/quantum radial equations of the Kepler/Hydrogen problems versus theharmonic oscillator. This suggests a duality-type relationship between thesesystems. However, when both radial and angular components of these systems areincluded the possibility of a true duality seems to be remote. Indeed,investigations that explored and generalized Newton's radial relation,including algebraic approaches based on noncompact groups such as SO(4,2), havenever exhibited a full duality consistent with Newton's. On the other hand,2T-physics predicts a host of dualities between pairs of a huge set of systemsthat includes Newton's two systems. These dualities take the form of rathercomplicated canonical transformations that relate the full phase spaces ofthese respective systems in all directions. In this paper we focus on Newton'scase by imposing his radial relation to find an appropriate basis for2T-physics dualities, and then construct the full duality. Using the techniquesof 2T-physics, we discuss the hidden symmetry of the actions (beyond thesymmetry of Hamiltonians) for the Hydrogen atom in $D$-dimensions and theharmonic oscillator in $\bar{D}$ dimensions. The symmetries lead us to find theone-to-one relation between the quantum states, including angular degrees offreedom, for specific values of $\left( D,\bar{D}\right) $, and construct theexplicit quantum canonical transformation in those special cases. We find thatthe canonical transformation has itself a hidden gauge symmetry that is crucialfor the respective phase spaces to be dual even when $D\neq\bar{D}$. In thisway we display the surprising beautiful symmetry of the full duality thatgeneralizes Newton's radial duality.

Duality Between Hydrogen Atom and Oscillator Systems via Hidden SO(d,2) Symmetry and 2T-physics