Quantum groups, gravity and the generalized uncertainty principle

Maggiore, Michele

doi:10.1103/PhysRevD.49.5182

Quantum groups, gravity and the generalized uncertainty principle

Michele Maggiore
(
- INFN, Pisa and
- Pisa U.
)

May, 1993

6 pages

Published in:

Phys.Rev.D 49 (1994) 5182-5187

e-Print:

hep-th/9305163 [hep-th]

DOI:

10.1103/PhysRevD.49.5182

Report number:

IFUP-TH-19-93

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Abstract: (arXiv)

We investigate the relationship between the generalized uncertainty principle in quantum gravity and the quantum deformation of the Poincar\'e algebra. We find that a deformed Newton-Wigner position operator and the generators of spatial translations and rotations of the deformed Poincar\'e algebra obey a deformed Heisenberg algebra from which the generalized uncertainty principle follows. The result indicates that in the

\kappa

-deformed Poincar\'e algebra a minimal observable length emerges naturally.

Note:

13 pages, IFUP-TH 19/93, May 1993 (revised Nov. 1993)

quantum gravity
quantum algebra: Poincare
algebra: deformation
uncertainty relations

References(49)

Figures(0)

[1]

On the Nature of quantum geometrodynamics

John A. Wheeler
(
- Princeton U.
)

- Annals Phys. 2 (1957) 604-614
•
DOI:
- 10.1016/0003-4916(57)90050-7

[2]

Action Integrals and Partition Functions in Quantum Gravity

G.W. Gibbons
(
- Cambridge U.
)
,
S.W. Hawking
(
- Cambridge U.
)

- Phys.Rev.D 15 (1977) 2752-2756
•
DOI:
- 10.1103/PhysRevD.15.2752

[2]

in General Relativity An Einstein Centenary Survey, edited by S.W. Hawking and W. Israel

S.W. Hawking

[3]

A Stringy Nature Needs Just Two Constants

G. Veneziano
(
- CERN
)

- EPL 2 (1986) 199
•
DOI:
- 10.1209/0295-5075/2/3/006

[4]

Can Space-Time Be Probed Below the String Size?

D. Amati
(
- SISSA, Trieste and
- INFN, Trieste
)
,
M. Ciafaloni
(
- Florence U. and
- INFN, Florence
)
,
G. Veneziano
(
- CERN and
- Boston U.
)

- Phys.Lett.B 216 (1989) 41-47
•
DOI:
- 10.1016/0370-2693(89)91366-X

[5]

Superstring Collisions at Planckian Energies

- Phys.Lett.B 197 (1987) 81,
- In *Caneschi, L. (ed.): Regge theory of low-p(T) hadronic interactions* 188-195. (Phys. Lett. B197 (1987) 81-88) and CERN Geneva - TH. 4782 (87,rec.Aug.) 13 p. (see Book Index)
•
DOI:
- 10.1016/0370-2693(87)90346-7

[5]

Classical and Quantum Gravity Effects from Planckian Energy Superstring Collisions

D. Amati
(
- SISSA, Trieste and
- INFN, Trieste
)
,
M. Ciafaloni
(
- CERN
)
,
G. Veneziano
(
- CERN
)

- Int.J.Mod.Phys.A 3 (1988) 1615-1661,
- INT. J. MOD. PHYS. A3 (1988) 1615-1661 AND CERN GENEVA - TH. 4886 (87,REC.JAN.88) 55p
•
DOI:
- 10.1142/S0217751X88000710

[5]

- Nucl.Phys.B 347 530

[6]

The High-Energy Behavior of String Scattering Amplitudes

David J. Gross
(
- Princeton U.
)
,
Paul F. Mende
(
- Princeton U.
)

- Phys.Lett.B 197 (1987) 129-134
•
DOI:
- 10.1016/0370-2693(87)90355-8

[6]

String Theory Beyond the Planck Scale

David J. Gross
(
- Princeton U.
)
,
Paul F. Mende
(
- Princeton U.
)

- Nucl.Phys.B 303 (1988) 407-454
•
DOI:
- 10.1016/0550-3213(88)90390-2

[7]

Planckian scattering beyond the eikonal approximation

Marcello Ciafaloni
(
- Florence U. and
- INFN, Florence
)

- Erice Theor.Phys.1992:249-261

[8]

Minimum Physical Length and the Generalized Uncertainty Principle in String Theory

Kenichi Konishi
(
- Genoa U. and
- INFN, Genoa and
- Pisa U. and
- INFN, Pisa
)
,
Giampiero Paffuti
(
- Genoa U. and
- INFN, Genoa and
- Pisa U. and
- INFN, Pisa
)
,
Paolo Provero
(
- Genoa U. and
- INFN, Genoa and
- Pisa U. and
- INFN, Pisa
)

- Phys.Lett.B 234 (1990) 276-284
•
DOI:
- 10.1016/0370-2693(90)91927-4

[8]

On the short distance behavior of string theories

Riccardo Guida
(
- Genoa U. and
- INFN, Genoa
)
,
K. Konishi
(
- Genoa U. and
- INFN, Genoa
)
,
P. Provero
(
- Genoa U. and
- INFN, Genoa
)

- Mod.Phys.Lett.A 6 (1991) 1487-1504
•
DOI:
- 10.1142/S0217732391001603

[9]

Particle Theories With Minimum Observable Length and Open String Theory

Mitsuhiro Kato
(
- LBL, Berkeley
)

- Phys.Lett.B 245 (1990) 43-47
•
DOI:
- 10.1016/0370-2693(90)90162-Y

[10]

A Generalized uncertainty principle in quantum gravity

Michele Maggiore
(
- INFN, Pisa and
- Pisa U.
)

- Phys.Lett.B 304 (1993) 65-69
•
e-Print:
- hep-th/9301067
•
DOI:
- 10.1016/0370-2693(93)91401-8

[11]

Particle Creation by Black Holes

S.W. Hawking
(
- Cambridge U., DAMTP and
- Caltech
)

- Commun.Math.Phys. 43 (1975) 199-220,
- Commun.Math.Phys. 46 (1976) 206 (erratum),
•
DOI:
- 10.1007/BF02345020

[12]

The Algebraic structure of the generalized uncertainty principle

Michele Maggiore
(
- INFN, Pisa and
- Pisa U.
)

- Phys.Lett.B 319 (1993) 83-86
•
e-Print:
- hep-th/9309034
•
DOI:
- 10.1016/0370-2693(93)90785-G

[13]

Proceedings of ICM, Berkeley, I986', A. M. Gleason (eds.) (American Mathematical Society, Berkeley,), p. 798

V.G. Drinfeld

[14]

A q difference analog of U(g) and the Yang-Baxter equation

Michio Jimbo
(
- Kyoto U., RIMS
)

- Lett.Math.Phys. 10 (1985) 63-69
•
DOI:
- 10.1007/BF00704588

[14]

A q Analog of u (Gl (n+1)), Hecke Algebra and the Yang-Baxter Equation

Michio Jimbo
(
- Kyoto U., RIMS
)

- Lett.Math.Phys. 11 (1986) 247
•
DOI:
- 10.1007/BF00400222

[15]

Reshetikhin, and L. A. Tskhtsjsn, in Algebraic Analysis, M. Kashiwara and T. Kswai (eds.) Boston,)

L.D. Fsddeev
,
N. Yu

[16]

Yu Montreal University Report No.

T. Manin

[17]

Compact matrix pseudogroups

S.L. Woronowicz
(
- Warsaw U., Math. Dept.
)

- Commun.Math.Phys. 111 (1987) 613-665
•
DOI:
- 10.1007/BF01219077

[18]

Differential calculus on compact matrix pseudogroups (quantum groups)

S.L. Woronowicz
(
- Warsaw U., Math. Dept.
)

- Commun.Math.Phys. 122 (1989) 125-170
•
DOI:
- 10.1007/BF01221411

[19]

Covariant Differential Calculus on the Quantum Hyperplane

Julius Wess
(
- Karlsruhe U.
)
,
Bruno Zumino
(
- UC, Berkeley and
- CERN
)

- Nucl.Phys.B Proc.Suppl. 18 (1991) 302-312,
- In *Annecy 1990, Proceedings, Recent advances in field theory* 302-312. (Nucl. Phys. B, Proc. Suppl. 18B (1990) 302-312) and CERN Geneva - TH. 5697 (90,rec.May) 21 p,
- In *Li, M. (ed.) et al.: Physics in non-commutative world, vol. 1* 63-73
•
DOI:
- 10.1016/0920-5632(91)90143-3

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