nach oben

Erschienen in:

2014 | OriginalPaper | Buchkapitel

Physical Ageing and New Representations of Some Lie Algebras of Local Scale-Invariance

verfasst von : Malte Henkel, Stoimen Stoimenov

Erschienen in: Lie Theory and Its Applications in Physics

Verlag: Springer Japan

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

Indecomposable but reducible representations of several Lie algebras of local scale-transformations, including the Schrödinger and conformal Galilean algebras, and their applications in physical ageing are reviewed. The physical requirement of the decay of co-variant two-point functions for large distances is related to analyticity properties in the coordinates dual to the physical masses or rapidities.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Modular Double of the Quantum Group

Nächstes Kapitel New Type of Supersymmetric Mechanics

In the context of asymptotically flat 3D gravity, an isomorphic Lie algebra is known as BMS algebra, \(\mathfrak{b}\mathfrak{m}\mathfrak{s}_{3} \equiv \text{CGA}(1)\) [6‐9].

The only previously known example of this had been obtained for the ageing algebra, where time-translations are excluded, see (24).

Aizawa, N.: Some representations of plane Galilean conformal algebra. In: Dobrev, V. (ed.) “Lie theory and its applications in physics”, Springer Proc. Math. Stat. 36, 301 (2013). arxiv:1212.6288

Akhiezer, N.I.: Lectures on Integral Transforms. Translations of Mathematical Monographs, vol. 70. Kharkov University 1984/American Mathematical Society, Providence (1988)

Andrzejewski, K., Gonera, J., Kijanka-Dec, A.: Nonrelativistic conformal transformations in Langrangian formalism. Phys. Rev. D86, 065009 (2013). arxiv:1301.1531

Bagchi, A., Mandal, I.: On representations and correlation functions of Galilean conformal algebras. Phys. Lett. B675, 393 (2009). arXiv:0903.4524

Bagchi, A., Gopakumar, R., Mandal, I., Miwa, A.: CGA in 2d. J. High Energy Phys. 1008, 004 (2010). arXiv:0912.1090

Bagchi, A., Detournay, S., Grumiller, D.: Flat-space chiral gravity. Phys. Rev. Lett. 109, 151301 (2012). arxiv:1208.1658

Bagchi, A., Detournay, S., Fareghbal, R., Simón, J.: Holographies of 3D flat cosmological horizons. Phys. Rev. Lett. 110, 141302 (2013). arxiv:1208.4372

Barnich, G., Compère, G.: Class. Quant. Grav. 24, F15 (2007); 24, 3139 (2007). gr-qc/0610130

Barnich, G., Gomberoff, A., González, H.A.: Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field-theories as the flat limit of Liouville theory. Phys. Rev. D87, 124032 (2007). arxiv:1210.0731

10.

Bray, A.J.: Theory of phase-ordering. Adv. Phys. 43, 357 (1994); Bray, A.J., Rutenberg, A.D.: Growth laws for phase-ordering. Phys. Rev. E49, R27 (1994)

11.

Chakraborty, S., Dey, P.: Wess-Zumino-Witten model for Galilean conformal algebra. Mod. Phys. Lett. A28, 1350176 (2013). arxiv:1209.0191

12.

Cherniha, R., Henkel, M.: The exotic conformal Galilei algebra and non-linear partial differential equations. J. Math. Anal. Appl. 369, 120 (2010). arxiv:0910.4822

13.

Duval, C., Horváthy, P.A.: Non-relativistic conformal symmetries and Newton-Cartan structures. J. Phys. A Math. Theor. 42, 465206 (2009). arxiv:0904.0531

14.

Gainutdinov, A., Ridout, D., Runkel, I.: Logarithmic conformal field-theory. J. Phys. A Math. Theor. 46, 490301 (2013) and the other reviews in that issue

15.

Galajinsky, A.V.: Remark on quantum mechanics with conformal Galilean symmetry. Phys. Rev. D78, 087701 (2008). arxiv:0808.1553

16.

Giulini, D.: On Galilei-invariance in quantum mechanics and the Bargman superselection rule. Ann. Phys. 249, 222 (1996). quant-ph/9508002

17.

Gurarie, V.: Logarithmic operators in conformal field theory. Nucl. Phys. B410, 535 (1993). arXiv:9303160

18.

Havas, P., Plebanski, J.: Conformal extensions of the Galilei group and their relation to the Schrödinger group. J. Math. Phys. 19, 482 (1978)CrossRefMATHMathSciNet

19.

Henkel, M.: Schrödinger-invariance in strongly anisotropic critical systems. J. Stat. Phys. 75, 1023 (1994). hep-th/9310081

20.

Henkel, M.: Local scale invariance and strongly anisotropic equilibrium critical systems. Phys. Rev. Lett. 78, 1940 (1997). cond-mat/9610174

21.

Henkel, M.: Phenomenology of local scale-invariance: from conformal invariance to dynamical scaling. Nucl. Phys. B641, 405 (2002). hep-th/0205256

22.

Henkel, M.: On logarithmic extensions of local scale-invariance. Nucl. Phys. B869[FS], 282 (2013). arXiv:1009.4139

23.

Henkel, M., Pleimling, M.: Nonequilibrium Phase Transitions. Ageing and Dynamical Scaling Far from Equilibrium, vol. 2. Springer, Heidelberg (2010)

24.

Henkel, M., Rouhani, S.: Logarithmic correlators or responses in non-relativistic analogues of conformal invariance. J. Phys. A Math. Theor. 46, 494004 (2013). arXiv:1302.7136

25.

Henkel, M., Unterberger, J.: Schrödinger invariance and space-time symmetries. Nucl. Phys. B660, 407 (2003). hep-th/0302187; Henkel, M.: Causality from dynamical symmetry: an example from local scale-invariance. In: Makhlouf, A. et al. (eds.) Springer Proc. Math. Stat. 85, 511 (2014). arxiv:1205.5901

26.

Henkel, M., Enss, T., Pleimling, M.: On the identification of quasiprimary operators in local scale-invariance. J. Phys. A Math. Gen. 39, L589 (2006). cond-mat/0605211; Picone, A., Henkel, M.: Local scale-invariance and ageing in noisy systems. Nucl. Phys. B688[FS], 217 (2004). cond-mat/0402196

27.

Henkel, M., Noh, J.D., Pleimling, M.: Phenomenology of ageing in the Kardar-Parisi-Zhang equation. Phys. Rev. E85, 030102(R) (2012). arXiv:1109.5022

28.

Henkel, M., Hosseiny, A., Rouhani, S.: Logarithmic exotic conformal Galilean algebras. Nucl. Phys. B879[PM], 292 (2014). arxiv:1311.3457

29.

Hosseiny, A., Naseh, A.: On holographic realization of logarithmic Galilean conformal algebra. J. Math. Phys. 52, 092501 (2011). arxiv:1101.2126

30.

Hosseiny, A., Rouhani, S.: Logarithmic correlators in non-relativistic conformal field theory. J. Math. Phys. 51, 102303 (2010). arXiv:1001.1036

31.

Hosseiny, A., Rouhani, S.: Affine extension of galilean conformal algebra in 2+1 dimensions. J. Math. Phys. 51, 052307 (2010). arXiv:0909.1203

32.

Hotta, K., Kubota, T., Nishinaka, T.: Galilean conformal algebra in two dimensions and cosmological topologically massive gravity. Nucl. Phys. B838, 358 (2010). arxiv:1003.1203

33.

Kim, Y.-W., Myung, Y.S., Park, Y.-J.: Massive logarithmic gravition in the critical generalised massive gravity (2013). arxiv:1301.3604

34.

Knapp, A.W.: Representation Theory of Semisimple Groups: An Overview Based on Examples. Princeton University Press, Princeton (1986)MATH

35.

Kytölä, K., Ridout, D.: On staggered indecomposable Virasoro modules. J. Math. Phys. 50, 123503 (2009). arxiv:0905.0108

36.

Lee, K.M., Lee, S., Lee, S.: Nonrelativistic superconformal M2-Brane theory. J. High Energy Phys. 0909, 030 (2009). arxiv:0902.3857

37.

Lukierski, J.: Galilean conformal and superconformal symmetries. Phys. Atom. Nucl. 75, 1256 (2012). arxiv:1101.4202

38.

Lukierski, J., Stichel, P.C., Zakrzewski, W.J.: Exotic Galilean conformal symmetry and its dynamical realisations. Phys. Lett. A357, 1 (2006). arXiv:0511259

39.

Lukierski, J., Stichel, P.C., Zakrzewski, W.J.: Acceleration-extended galilean symmetries with central charges and their dynamical realizations. Phys. Lett. B650, 203 (2007). arXiv:0511259

40.

Martelli, D., Tachikawa, Y.: Comments on Galilean conformal field theories and their geometric realization. J. High Energy Phys. 1005, 091 (2010). arXiv:0903.5184

41.

Mathieu, P., Ridout, D.: From percolation to logarithmic conformal field theory. Phys. Lett. B657, 120 (2007). arxiv:0708.0802; Logarithmic \(\mathcal{M}(2,p)\) minimal models, their logarithmic coupling and duality. Nucl. Phys. B801, 268 (2008). arxiv:0711.3541

42.

Nakayama, Yu.: Universal time-dependent deformations of Schrödinger geometry. J. High Energy Phys. 04, 102 (2010). arxiv:1002.0615

43.

Negro, J., del Olmo, M.A., Rodríguez-Marco, A.: Nonrelativistic conformal groups, I & II. J. Math. Phys. 38, 3786, 3810 (1997)

44.

Rahimi Tabar, M.R., Aghamohammadi, A., Khorrami, M.: The logarithmic conformal field theories. Nucl. Phys. B497, 555 (1997). hep-th/9610168

45.

Ruelle, P.: Logarithmic conformal invariance in the Abelian sandpile model. J. Phys. A Math. Theor. 46, 494014 (2013). arxiv:1303.4310

46.

Saleur, H.: Polymers and percolation in two dimensions and twisted N = 2 supersymmetry. Nucl. Phys. B382, 486 (1992). hep-th/9111007

47.

Sastre, F., Henkel, M.: in preparation

48.

Stoimenov, S., Henkel, M.: Non-local representations of the ageing algebra in higher dimensions. J. Phys. A Math. Theor. 46, 245004 (2013). arxiv:1212.6156; On non-local representations of the ageing algebra. Nucl. Phys. B847, 612 (2011). arxiv:1011.6315

49.

Unterberger, J., Roger, C.: The Schrödinger-Virasoro Algebra. Springer, Heidelberg (2012)CrossRefMATH

Titel: Physical Ageing and New Representations of Some Lie Algebras of Local Scale-Invariance
verfasst von: Malte Henkel
Stoimen Stoimenov
Verlag: Springer Japan
Buch: Lie Theory and Its Applications in Physics
Print ISBN: 978-4-431-55284-0

Electronic ISBN: 978-4-431-55285-7

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-4-431-55285-7_4

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"