In General > s.a. modified
coherent states [thermal].
@ References: Sarris & Proto PhyA(07)
[from metric phase space]; Massar & Spindel PRL(08)-a0710 [for
discrete Fourier transform].
Gravity-Motivated Generalized Forms > s.a. locality; quantum-gravity
phenomenology.
* Generalized Uncertainty
Principle (GUP):
Motivated by the quantum-gravity idea that there is a smallest possible
x
lP,
xi
pj
(
/2)
(1 +
2 lP2
pi2/
2)
ij .
* Extended Uncertainty Principle (EUP): Motivated by physics in anti-de Sitter space (one can also have both terms present, EGUP),
xi
pj
(
/2)
(1 +
2
xi2/lh2)
ij .
* Remark: Taking into
account quantum-gravity effects, one tends to get larger uncertainties than
in standard quantum mechanics, related by
x
p
(
/2)
(1+...), while fixed, discrete spacetime tends to give smaller ones, related
by
x
p
(
/2)
(1–...).
@ And Lorentz-invariance: Kim qp/97-in;
Sasakura PTP(99)ht,
JHEP(00)ht;
Molotkov qp/02 [for
photons]; Kim & Noz AIP(07)qp/06.
@ In curved spaces: Golovnev & Prokhorov JPA(04);
Bambi & Urban CQG(08)-a0709 [particle
in de Sitter space]; Park PLB(08)-a0709;
Cooperstock & Dupre a0904 [in
terms of spacetime energy-momentum]; Mignemi a0909 [in (anti-)de Sitter
space].
@ And general relativity, quantum gravity: Doplicher et al PLB(94);
Amelino-Camelia MPLA(97)gq,
et al PAN(98)ht/97 [
-deformed
covariant phase space]; Adler & Santiago
MPLA(99)gq, ht/99;
Yoneya PTP(00)ht,
IJMPA(01)ht/00 [string
theory];
Camacho
GRG(02)gq [from
non-conformal metric fluctuations]; Shalyt-Margolin & Tregubovich gq/02 [and
mixed states]; Dragovich
ht/04-in
[p-adic, adelic]; Bambi CQG(08)-a0804 [departures
linear in lP]; > s.a. black-hole
entropy, information and thermodynamics.
@ With characteristic length: Kempf et al PRD(95)ht/94;
Kempf & Mangano PRD(97)ht/96 [regularization];
Brau JPA(99)
[harmonic oscillator, H atom]; Cortés & Gamboa PRD(05)ht/04 [in
DSR];
Brau & Buisseret PRD(06)ht [and
gravitational quantum well]; Mu et al a0909 [and extra dimensions]; > s.a. quantum
oscillator.
@ Black holes: Brout et al PRD(99)ht/98;
Scardigli PLB(99)ht [micro-black
holes]; Xiang & Shen MPLA(04)
[thermodynamics];
Maziashvili PLB(06)
[remnants]; > s.a. specific
types.
@ Inflation: Hassan & Sloth NPB(03)ht/02;
Nozari & Akhshabi IJMPD-a0910.
@ Other cosmological models: Rama PLB(01);
Nozari & Fazlpour GRG(06)gq [early-universe
thermodynamics]; Battisti & Montani PLB(09)-a0808 [mixmaster universe]; Shalyt-Margolin a0807 [for
cosmological-constant–spacetime-volume]; Vakili IJMPD(09)-a0811 [effects
on classical and quantum dS/AdS]; Zhu et al PLB(09)-a0811 [thermodynamics].
@ Related topics: Lindner et al PLA(96)
[particle number-phase]; Hogan ap/07 [holographic
uncertainty principle].
From Deformed Algebras > s.a. Commutation
Relations; modified
lorentz symmetry; modified quantum theory; poincaré group.
* Idea: One can
obtain modified uncertainty relations from a deformation of the Poincaré and/or
Heisenberg
algebra, using a prescription that can be derived from the Schwarz inequality
xi
pj
(1/2)
|
[xi ,
pj]
|
.
* Examples: From the symmetry algebra of AdS one obtaines the EUP above; In string theory one gets the modified commutation relations
[xi, pj]
= i
[(1 +
p2)
ij +
' pi pj]
.
@ General references: Maggiore PLB(93)ht.
@ String theory: Konishi et al PLB(90);
Capozziello et al IJTP(00)gq/99;
Benczik et al PRD(02)ht;
Hossenfelder
et al PLB(03)ht.
@ Non-commutative geometry: Carlen & Vilela Mendes PLA(01);
Brandenberger & Ho PRD(02)ht;
Bolonek & Kosinski PLB(02)ht, APPB(03)ht/02 [non-commutative
quantum mechanics].
@ In deformation quantization: Zhang PLA(99)ht/03;
Przanowski & Turrubiates JPA(02)m.QA;
Gerstenhaber JMP(07).
Other Minimal-Length Phenomenology > s.a. fine-structure
constant; modified
coherent states; modified
QED; types of quantum field theory.
@ General references: Ozawa PRA(03)qp/02 [measurement
disturbance], PLA(03)qp/02 [limitations];
Slawny JMP(07) [position and length operators].
@ H atom:
Akhoury & Yao PLB(03)hp;
Benczik
et al PRA(05); Stetsko & Tkachuk PRA(06).
@ Other consequences: Nozari & Azizi GRG(06)qp/05 [free
particle + box]; Nozari
& Mehdipour GRG(05)qp [wave
packet dispersion], CSF(07)ht/06 [ideal
gas thermodynamics]; Quesne & Tkachuk SIGMA(07)qp/06;
Bang & Berger PRD(06)
[minimum uncertainty wave packets]; Das & Vagenas CJP(09)-a0901-in
[Lamb shift, reflection
and transmission coefficients, ...]; > s.a. discrete
spacetime.
main page – abbreviations – journals – comments – other
sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 12
nov
2009