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UID:20251119T031940EST-8713bFfPvT@132.216.98.100
DTSTAMP:20251119T081940Z
DESCRIPTION:Title:Four-body problem in d-dimensional space: ground state.\n
 \nAbstract: In this talk\, we will consider aspects of the quantum and cla
 ssical dynamics of a 4-body system in $d$-dimensional space. The study is 
 restricted to solutions which are functions of mutual (relative) distances
  only. The ground state (and some other states) in the quantum case and so
 me trajectories in the classical case are of this type. We construct the q
 uantum Hamiltonian for which these states are eigenstates. For $d geq 3$\,
  this describes a six-dimensional quantum particle moving in a curved spac
 e while for $d=1$ it corresponds to a three-dimensional particle and coinc
 ides with the $A_3$ (4-body) rational Calogero model. The kinetic energy o
 f the system has a hidden $sl(7\,mathbb{R})$ Lie (Poisson) algebra structu
 re\, but for the special case $d=1$ it becomes degenerate with hidden alge
 bra $sl(4\,R)$. Based on the geometrical properties of the tetrahedron who
 se vertices correspond to the positions of the particles\, exactly-solvabl
 e potentials will be presented as well.\n
DTSTART:20190226T203000Z
DTEND:20190226T213000Z
LOCATION:Room 4336\, CA\, Pav. André-Aisenstadt\, 2920\, ch. de la Tour
SUMMARY:Adrian Escobar\, CRM
URL:/mathstat/channels/event/adrian-escobar-crm-294930
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