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SUMMARY:Some Curious Consequences of the Minimal Length Uncertainty Relati
 on
DTSTART;VALUE=DATE-TIME:20120607T093000Z
DTEND;VALUE=DATE-TIME:20120607T103000Z
DTSTAMP;VALUE=DATE-TIME:20260613T212946Z
UID:indico-event-1859@indico.ific.uv.es
DESCRIPTION:In theories of quantum gravity\, it is expected that spacetime
  distances smaller than the Planck length would not be resolvable. In quan
 tum mechanical language\, gravitational effects are expected to deform the
  uncertainty relation between position and momentum from the canonical Hei
 senberg form to Delta (x) >= (hbar/2) (1/Delta(p) + beta Delta(p))\, which
  would imply that Delta (x) is bounded from below by Delta (x) (min) = hba
 r \\sqrt{beta}. Indeed\, this "minimal length uncertainty relation" has be
 en shown to hold in perturbative string theory\, which is the top candidat
 e theory of quantum gravity.\nCanonical non-relativistic quantum mechanics
 \, on the other hand\, is completely oblivious of the existence of this mi
 nimal length\, even though we expect it to be the infrared limit of quantu
 m gravity (or string theory\, if it is indeed the theory of everything). O
 ne way to incorporate the "minimal length" into non-relativistic quantum m
 echanics is to deform the commutation relation between position and moment
 um to [x\,p]= i hbar (1+beta p^2). In this talk\, I will discuss the conse
 quences of this deformation on the eigenstates and eigenvalues of the harm
 onic oscillator hamiltonian\, and present several curious puzzles that hav
 e been uncovered.\n\nhttps://indico.ific.uv.es/event/1859/
LOCATION:Edf. Institutos de Investigación Sala Seminarios IFIC
URL:https://indico.ific.uv.es/event/1859/
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