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UID:20250915T190248EDT-0136MuUD4m@132.216.98.100
DTSTAMP:20250915T230248Z
DESCRIPTION:The quantum n-body problem in dimension d &#8805\; n-1: the gro
 und state.\n\nWe employ generalized Euler coordinates for the n body syste
 m in d ≥ n − 1 dimensional space\, which consist of the centre-of-mass vec
 tor\, relative (mutual) distances r_ij and angles as remaining coordinates
 . We prove that the kinetic energy of the quantum n-body problem for d ≥ n
  − 1 can be written as the sum of three terms: (i) kinetic energy of centr
 e-of-mass\, (ii) the second order differential operator D_1 which depends 
 on relative distances alone and (iii) the differential operator D_2 which 
 annihilates any angle-independent function. The operator D_1 has a large r
 eflection symmetry group (a direct sum of n(n-1)/2 copies of Z_2) and in ρ
 _ij = r_{ij}^2 variables is the algebraic operator with hidden algebra sl(
 n(n−1)/2 + 1\, R). Thus\, it is the Hamiltonian of quantum Euler-Arnold sl
 (n(n−1)/2 + 1\, R) top in a constant magnetic field. It is conjectured tha
 t for any n similarity-transformed D_1 is the Laplace-Beltrami operator pl
 us (effective) potential\, thus\, it describes a n(n−1)/2-dimensional quan
 tum particle in curved space\, it was verified for n = 2\, 3\, 4. After de
 -quantization similarity-transformed D_1 becomes the Hamiltonian of the cl
 assical top with variable tensor of inertia in external potential. Work do
 ne with W. Miller\, Jr. and A. Escobar-Ruiz.\n\n \n\n\n	 \n\n	CRM\, UdeM\, P
 avillon André-Aisenstadt\, 2920\, ch. de la Tour\, salle 4336\n\n\n \n
DTSTART:20171003T193000Z
DTEND:20171003T203000Z
LOCATION:Room 4336\, CA\, QC\, Montreal\, Pav. André-Aisenstadt\, 2920\, ch
 . de la Tour
SUMMARY:Alexander Turbiner\, UNAM\, México
URL:/mathstat/channels/event/alexander-turbiner-unam-m
 exico-270699
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