Skip to main content
Springer Nature Link
Log in

Loop Quantum Gravity and planck Scale Phenomenology

  • Chapter
  • First Online:
Planck Scale Effects in Astrophysics and Cosmology

Part of the book series: Lecture Notes in Physics ((LNP,volume 669))

  • 408 Accesses

  • 9 Citations

Abstract

Of the different approaches to quantum gravity, the best developed, from the point of view of addressing the key theoretical questions a quantum theory of gravity must answer, is loop quantum gravity1. While string theory appears to better address the issue of uni.cation, at least so far, it fails to provide a background independent approach to the quantum mechanics of spacetime geometry-a necessary condition for any quantum theory of gravity. Moreover, many key conjectures remain unproven, including perturbative finiteness and consistency, which have not been demonstrated for any string theory past second order in perturbation theory2. By contrast, loop quantum gravity appears to provide a consistent and finite background independent approach to quantum gravity. There is recent progress on several issues, including accounting for the black hole entropy [8], and giving a precise quantum mechanical description of the earliest phases of the evolution of the universe [9, 10]. Furthermore, it gives unique predictions of novel quantum gravitational phenomena, such as the discreteness of area, volume and other observables.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, books and news in related subjects, suggested using machine learning.

References

  1. C. Rovelli, Living Rev. Rel. 1 (1998) 1, gr-qc/9710008.

    Google Scholar 

  2. A. Ashtekar, New perspectives in canonical gravity (Bibliopolis, Naples, 1988); Lectures on non-perturbative canonical gravity, Advanced Series in Astrophysics and Cosmology-Vol. 6 (World Scientific, Singapore, 1991).

    Google Scholar 

  3. R. Gambini and J. Pullin, Loops, knots, gauge theories and quantum gravity, Cambridge University Press, 1996.

    Google Scholar 

  4. L. Smolin: in Quantum Gravity and Cosmology, eds J Perez-Mercader et al., World Scientific, Singapore 1992; “The future of spin networks” gr-qc/9702030 in the Penrose Festschrift.

    Google Scholar 

  5. L. Smolin, “Quantum gravity with a positive cosmological constant,” hep-th/0209079.

    Google Scholar 

  6. L. Smolin, “How far are we from the quantum theory of gravity?,” hep-th/0303185.

    Google Scholar 

  7. A. Ashtekar and J. Lewandowski, “Background independent quantum gravity: a status report,” gr-qc/0404018.

    Google Scholar 

  8. O. Dreyer, “Ln(3) and Black Hole Entropy,” gr-qc/0404055; “Quasinormal Modes, the Area Spectrum, and Black Hole Entropy,” Phys. Rev. Lett. 90 (2003) 081301, gr-qc/0211076.

    Google Scholar 

  9. Martin Bojowald, “Isotropic Loop Quantum Cosmology”, Class. Quant. Grav. 19 (2002) 2717-2742, gr-qc/0202077; “Inflation from Quantum Geometry”, gr-qc/0206054; “The Semiclassical Limit of Loop Quantum Cosmology”, gr-qc/0105113, Class. Quant. Grav. 18 (2001) L109-L116; “Dynamical Initial Conditions in Quantum Cosmology”, gr-qc/0104072, Phys. Rev. Lett. 87 (2001) 121301.

    Google Scholar 

  10. S. Tsujikawa, P. Singh, and R. Maartens, “Loop quantum gravity effects on inflation and the CMB,” astro-ph/0311015

    Google Scholar 

  11. G. Amelino-Camelia et al., Int. J. Mod. Phys. A12:607-624,1997; G. Amelino-Camelia et al. Nature 393:763-765,1998; J. Ellis et al., Astrophys. J. 535:139-151, 2000; J. Ellis, N.E. Mavromatos and D. Nanopoulos, Phys. Rev. D63:124025,2001; ibidem astro-ph/0108295.

    Google Scholar 

  12. G. Amelino-Camelia and T. Piran, Phys. Rev. D64 (2001) 036005.

    Article  Google Scholar 

  13. Tomasz J. Konopka, Seth A. Major, “Observational Limits on Quantum Geometry Effects”, New J. Phys. 4 (2002) 57. hep-ph/0201184; Ted Jacobson, Stefano Liberati, David Mattingly, “TeV Astrophysics Constraints on Planck Scale Lorentz Violation”, hep-ph/0112207.

    Google Scholar 

  14. Subir Sarkar, “Possible astrophysical probes of quantum gravity”, Mod. Phys. Lett. A17 (2002) 1025-1036, gr-qc/0204092.

    Article  Google Scholar 

  15. J. Lukierski et al., “Q Deformation Of Poincar&x00027;e Algebra,” Phys. Lett. B264 (1991) 331.

    Article  Google Scholar 

  16. G. Amelino-Camelia, Nature 418 (2002) 34.

    Article  PubMed  Google Scholar 

  17. J. Magueijo and L. Smolin, Phys. Rev. Lett. (88) 190403, 2002.

    Article  PubMed  Google Scholar 

  18. J. Magueijo and L. Smolin, gr-qc/0207

    Google Scholar 

  19. N.R. Bruno, G. Amelino-Camelia, J. Kowalski-Glikman, Phys. Lett. B522:133-138,2001; J. Kowalski-Glikman and S. Nowak, hep-th/0203040;S. Judes, gr-qc/0205067; M. Visser, gr-qc/0205093; S. Judes, M. Visser, gr-qc/0205067; D. V. Ahluwalia and M. Kirchbach, qr-qc/0207004.

    Google Scholar 

  20. Achucarro and Townsend, “A Chern-Simons Action For Three-Dimensional Anti-De Sitter Supergravity Theories,” Phys. Lett. B180 (1986) 89; E. Witten, “(2+1)-Dimensional Gravity As An Exactly Soluble System,” Nucl. Phys. B311 (1988) 46.

    Google Scholar 

  21. A. Ashtekar, V. Husain, C. Rovelli, J. Samuel and L. Smolin, “2+1 quantum gravity as a toy model for the 3+1 theory,” Class. and Quantum Grav. L185-L193 (1989); L. Smolin, “Loop representation for quantum gravity in 2+1 dimensions,” in the proceedings of the John';s Hopkins Conference on Knots, Tolopoly and Quantum Field Theory ed. L. Lusanna (World Scientific, Singapore, 1989) .

    Google Scholar 

  22. Laurent Freidel, Jerzy Kowalski-Glikman, Lee Smolin, “2+1 gravity and Doubly Special Relativity,” hep-th/0307085, Phys. Rev. D69 (2004) 044001.

    Google Scholar 

  23. Hans-Juergen Matschull, Max Welling, “Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity,” gr-qc/9708054, Class. Quant. Grav. 15 (1998) 2981; Hans-Juergen Matschull, “The Phase Space Structure of Multi Particle Models in 2+1 Gravity,” gr-qc/0103084, Class. Quant. Grav. 18 (2001) 3497; F. A. Bais, N. M. Muller, B. J. Schroers, “Quantum group symmetry and particle scattering in (2+1)-dimensional quantum gravity,” hep-th/0205021, Nucl. Phys. B640 (2002) 3.

    Google Scholar 

  24. Giovanni Amelino-Camelia, Lee Smolin, Artem Starodubtsev, “Quantum symmetry, the cosmological constant and Planck scale phenomenology,” hep-th/0306134.

    Google Scholar 

  25. J.E. Nelson, R.F. Picken, “Quantum Holonomies in (2+1)-Dimensional Gravity,” Phys. Lett. B471 (2000) 367; J.E. Nelson, T. Regge, “Quantisation of 2+1 gravity for genus 2,” Phys. Rev. D50 (1994) 5125, gr-qc/9311029

    Google Scholar 

  26. E. Buffenoir, K. Noui, P. Roche, “Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group,” hep-th/0202121, Class. Quant. Grav. 19 (2002) 4953; Karim Noui, Philippe Roche, “Cosmological Deformation of Lorentzian Spin Foam Models,” gr-qc/0211109, Class. Quant. Grav. 20 (2003) 3175-3214.

    Google Scholar 

  27. L. Smolin, “Linking topological quantum field theory and nonperturbative quantum gravity,” J. Math. Phys. 36(1995)6417, gr-qc/9505028.

    Article  Google Scholar 

  28. J. Baez, “Spin foammodels,”Class.Quant. Grav. 15 (1998) 1827-1858, gr-qc/9709052; “An introduction to spin foam models of quantum gravity and BF theory,” Lect. Notes Phys., 543:2594, 2000.

    Google Scholar 

  29. S. Major and L. Smolin, “Quantum deformation of quantum gravity,” Nucl. Phys. B473, 267(1996), gr-qc/9512020; R. Borissov, S. Major and L. Smolin, “The geometry of quantum spin networks,” Class. and Quant. Grav.12, 3183(1996), gr-qc/9512043.

    Google Scholar 

  30. Artem Starodubtsev, “Topological excitations around the vacuum of quantum gravity I: The symmetries of the vacuum,” hep-th/0306135.

    Google Scholar 

  31. A. Ashtekar, C. Rovelli and L. Smolin,“Weaving a classical geometry with quantum threads,” Phys. Rev. Lett. 69 (1992) 237 hep-th/9203079; Luca Bombelli, “Statistical geometry of random weave states,” gr-qc/0101080; A. Corichi, J.M. Reyes, “A Gaussian Weave for Kinematical Loop Quantum Gravity,” gr-qc/0006067, Int. J. Mod. Phys. D10 (2001) 325-338.

    Google Scholar 

  32. Rodolfo Gambini, Jorge Pullin, “Nonstandard optics from quantum spacetime”, Phys. Rev. D59 (1999) 124021, gr-qc/9809038;

    Article  Google Scholar 

  33. Jorge Alfaro, Hugo A. Morales-Tžcotl, Luis F. Urrutia, “Loop quantum gravity and light propagation,” Phys. Rev. D65 (2002) 103509, hep-th/0108061; “Quantum gravity and spin 1/2 particles effective dynamics,” hep-th/0208192, Phys. Rev. D66:124006,2002.

    Google Scholar 

  34. Hanno Sahlmann, Thomas Thiemann, “Towards the QFT on Curved Spacetime Limit of QGR. I: A General Scheme,” gr-qc/0207030; “Towards the QFT on Curved Spacetime Limit of QGR. II: A Concrete Implementation,” gr-qc/0207031.

    Google Scholar 

  35. H. Kodama, Prog. Theor. Phys. 80, 1024(1988); Phys. Rev. D42(1990)2548.

    Google Scholar 

  36. L. Smolin and C. Soo, “The Chern-Simons Invariant as the Natural Time Variable for Classical and Quantum Cosmology,” Nucl. Phys. B449 (1995) 289, gr-qc/9405015.

    Article  Google Scholar 

  37. A. Ashtekar, private communication.

    Google Scholar 

  38. A. Sen, “On the existence of neutrino zero modes in vacuum spacetime,” J. Math. Phys. 22 (1981) 1781, “Gravity as a spin system,” Phys. Lett. B11 (1982) 89.

    Google Scholar 

  39. Abhay Ashtekar, “New variables for classical and quantum gravity," Phys. Rev. Lett. 57(18), 2244-2247 (1986).

    Article  Google Scholar 

  40. C. Soo, “Wave function of the Universe and Chern-Simons Perturbation Theory,” gr-qc/0109046.

    Google Scholar 

  41. P. A. M. Dirac, Lectures on Quantum Mechanics Belfer Graduate School of Science Monographs, no. 2 (Yeshiva University Press, New York,1964).

    Google Scholar 

  42. J. Stachel, “Einstein';s search for general covariance, 1912-15” in Einstein and the History of General Relativity vol 1 of Einstein Studies eds. D. Howard and J. Stachel. (Birkhauser, Boston, 1989).

    Google Scholar 

  43. L. Smolin Three Roads to Quantum Gravity (Weidenfeld and Nicolson and Basic Books, London and New York, 2001)

    Google Scholar 

  44. Y. Ling and L. Smolin, “Supersymmetric spin networks and quantum supergravity,” Phys. Rev. D61, 044008(2000), hep-th/9904016; “Holographic Formulation of Quantum Supergravity,” hep-th/0009018, Phys. Rev. D63 (2001) 064010.

    Google Scholar 

  45. M. Atiyah, “Topological quantum field theory” Publ. Math. IHES 68 (1989) 175; The Geometry and Physics of Knots, Lezion Lincee (Cambridge University Press, Cambridge, 1990); G. Segal, Conformal field theory Oxford preprint (1988).

    Google Scholar 

  46. R. Floreanini and R. Percacci, Phys. Lett. B224 (1989) 291-294; B231:119-124, 1989. V.V. Fock, N.A. Nekrasov, A.A. Rosly, K.G. Selivanov “What we think about the higher dimensional Chern-Simons theories” (Moscow, ITEP). ITEP-91-70, July 1991. 7pp. in Sakharov Conf.1991:465-472 (QC20:I475:1991)

    Google Scholar 

  47. M. Banados, M. Henneaux, C. Iannuzzo and C. M. Viallet, “A note on the gauge symmetries of pure Chern-Simons theory with p-form gauge fields” gr-qc/9703061; Max Banados, Luis J. Garay and Marc Henneaux, Nucl. Phys. B476:611-635,1996, hep-th/9605159; Phys. Rev. D53:593-596,1996, hep-th/9506187.

    Google Scholar 

  48. Y. Ling and L. Smolin, “Eleven dimensional supergravity as a constrained topological field theory,” hep-th/0003285, Nucl. Phys. B601 (2001) 191-208.

    Article  Google Scholar 

  49. J. Ambjorn, A. Dasgupta, J. Jurkiewiczcy and R. Loll, “A Lorentzian cure for Euclidean troubles”, hep-th/0201104; J. Ambjorn and R. Loll, Nucl. Phys. B536 (1998) 407 [hep-th/9805108]; J. Ambjorn, J. Jurkiewicz and R. Loll, Phys. Rev. Lett. 85 (2000) 924 [hepth/ 0002050]; Nucl. Phys. B610 (2001) 347 [hep-th/0105267]; R. Loll, Nucl. Phys. B (Proc. Suppl.) 94 (2001) 96 [hep-th/0011194]; J. Ambjorn, J. Jurkiewicz and R. Loll, Phys. Rev. D64 (2001) 044011 [hep-th/0011276]; JHEP 09 (2001) 022 [hep-th/0106082].

    Google Scholar 

  50. T. Jacobson and L. Smolin, Phys. Lett. B 196 (1987) 39; Class. and Quant. Grav. 5 (1988) 583; J. Samuel, Pramana-J Phys. 28 (1987) L429.

    Google Scholar 

  51. J.F. Plebanski. “On the separation of Einsteinian” J. Math. Phys., 18:2511, 1977.

    Article  Google Scholar 

  52. R. Capovilla, J. Dell and T. Jacobson, Phys. Rev. Lett. 21, 2325(1989); Class. Quant. Grav. 8, 59(1991); R. Capovilla, J. Dell, T. Jacobson and L. Mason, Class. and Quant. Grav. 8, 41(1991).

    Google Scholar 

  53. J. Barbero, “Real Ashtekar variables for Lorentzian signature spacetime,” Phys. Rev. D51 (1995) 5507.

    Google Scholar 

  54. T. Thiemann, “Quantum Spin Dynamics (QSD) I & II,” Class. Quant. Grav. 15 (1998) 839-905, gr-qc/9606089, gr-qc/9606090.

    Article  Google Scholar 

  55. K. Krasnov, “On Quantum Statistical Mechanics of a Schwarzschild Black Hole,” grqc/9605047, Gen. Rel. Grav. 30 (1998) 53-68; C. Rovelli, “Black hole entropy from loop quantum gravity," grqc/9603063.

    Google Scholar 

  56. A. Ashtekar, J. Baez, K. Krasnov, “Quantum Geometry of Isolated Horizons and Black Hole Entropy,” gr-qc/0005126; A. Ashtekar, J. Baez, A. Corichi, K. Krasnov, “Quantum geometry and black hole entropy,” gr-qc/9710007, Phys. Rev. Lett. 80 (1998) 904-907.

    Google Scholar 

  57. T. Jacobson and L. Smolin, Nucl. Phys. B 299 (1988) 295.

    Article  Google Scholar 

  58. C. Rovelli and L. Smolin, “Knot theory and quantum theory,” Phys. Rev. Lett 61(1988)1155; “Loop representation of quantum general relativity,” Nucl. Phys. B331(1990)80-152.

    Google Scholar 

  59. R. Gambini and A. Trias, Phys. Rev. D23 (1981) 553, Lett. al Nuovo Cimento 38 (1983) 497; Phys. Rev. Lett. 53 (1984) 2359; Nucl. Phys. B278 (1986) 436; R. Gambini, L. Leal and A. Trias, Phys. Rev. D39 (1989) 3127.

    Google Scholar 

  60. M. P. Reisenberger. “Worldsheet formulations of gauge theories and gravity,” in Proceedings of the 7th Marcel Grossman Meeting, ed. by R. Jantzen and G. MacKeiser, World Scientific, 1996; gr-qc/9412035; “A lattice worldsheet sum for 4-d Euclidean general relativity,” gr-qc/9711052.

    Google Scholar 

  61. M. P. Reisenberger and C. Rovelli. “Sum-over-surface form of loop quantum gravity,” gr-qc/9612035, Phys. Rev. D 56 (1997) 3490; “Spacetime as a Feynman diagram: the connection formulation,” Class. Quant. Grav., 18:121140, 2001; “Spin foams as Feynman diagrams,” gr-qc/0002083.

    Google Scholar 

  62. J. Barrett and L. Crane, “Relativistic spin networks and quantum gravity,” J. Math. Phys. 39 (1998) 3296-3302, gr-qc/9709028.

    Article  Google Scholar 

  63. J. Baez, “Spin foam models,” Class. Quant. Grav. 15 (1998) 1827-1858, gr-qc/9709052; “An introduction to spin foam models of quantum gravity and BF theory,” Lect. Notes Phys., 543:2594, 2000.

    Google Scholar 

  64. Fotini Markopoulou, “Dual formulation of spin network evolution,” gr-qc/9704013.

    Google Scholar 

  65. Fotini Markopoulou, Lee Smolin, “Quantum geometry with intrinsic local causality,” Phys. Rev. D58 (1998) 084032, gr-qc/9712067.

    Article  Google Scholar 

  66. J. Iwasaki, “A reformulation of the Ponzano-Regge quantum gravity model in terms of surfaces,” gr-qc/9410010; “A definition of the Ponzano-Regge quantum gravity model in terms of surfaces,” gr-qc/9505043, J. Math. Phys. 36 (1995) 6288; L. Freidel and K. Krasnov, “Spin foam models and the classical action principle,” Adv. Theor. Math. Phys., 2:11831247, 1999; R. De Pietri, L. Freidel, K. Krasnov, and C. Rovelli, “Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space,” Nucl. Phys. B, 574:785806, 2000.

    Google Scholar 

  67. B. Bruegmann, R. Gambini and J. Pullin, Phys. Rev. Lett. 68 (1992) 431-434; Rodolfo Gambini, Jorge Griego, Jorge Pullin, “Chern-Simons states in spin-network quantum gravity,” gr-qc/9703042, Phys. Lett. B413 (1997) 260-266; C. Di Bartolo, R. Gambini, J. Griego, J. Pullin, “Consistent canonical quantization of general relativity in the space of Vassiliev knot invariants,” gr-qc/9909063, Phys. Rev. Lett. 84 (2000) 2314-2317; “Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical structure,” gr-qc/9911009, Class. Quant. Grav. 17 (2000) 3211-3238.

    Google Scholar 

  68. R. Jackiw, Topological Investigations In Quantized Gauge Theories, p. 258, exercise 3.7, in S. B. Treiman et al. Current Algebra And Anomalies (World Scientific, 1985).

    Google Scholar 

  69. E. Witten, “A Note On The Chern-Simons And Kodama Wavefunctions,” gr-qc/0306083.

    Google Scholar 

  70. L. Freidel and L. Smolin, “The linearization of the Kodama state,” hep-th/ 0310224.

    Google Scholar 

  71. G. W. Gibbons and S. W. Hawking, “Cosmological Event Horizons, Thermodynamics, and Particle Creation,” Phys. Rev. D 15, 2738 (1977).

    Article  Google Scholar 

  72. L. N. Chang and C. Soo, “Ashtekar';s variables and the topological phase of quantum gravity,” Proceedings of the XXth. Conference on Differential Geometric Methods in Physics, (Baruch College, New York, 1991), edited by S. Catto and A. Rocha (World Scientific, 1992); Phys. Rev. D46 (1992) 4257; C. Soo and L. N. Chang, Int. J. Mod. Phys. D3 (1994) 529.

    Google Scholar 

  73. T. Jacobson, “New Variables for canonical supergravity,” Class. Quant. Grav.5(1988)923; D. Armand-Ugon, R. Gambini, O. Obregon, J. Pullin, “Towards a loop representation for quantum canonical supergravity,” hep-th/9508036, Nucl. Phys. B460 (1996) 615; L. F. Urrutia “Towards a loop representation of connection theories defined over a super-lie algebra,” hep-th/9609010; H. Kunitomo and T. Sano “The Ashtekar formulation for canonical N=2 supergravity,” Prog. Theor. Phys. suppl. (1993) 31; Takashi Sano and J. Shiraishi, “The Nonperturbative Canonical Quantization of the N=1 Supergravity,” Nucl. Phys. B410 (1993) 423, hep-th/9211104; “The Ashtekar Formalism and WKB Wave Functions of N = 1,2 Supergravities,” hep-th/9211103; T. Kadoyoshi and S. Nojiri, “N = 3 and N = 4 two form supergravities,” Mod. Phys. Lett. A12:1165-1174,1997, hep-th/9703149; K. Ezawa, “Ashtekar';s formulation for N = 1, N = 2 supergravities as constrained BF theories,” Prog. Theor. Phys. 95:863-882, 1996, hep-th/9511047.

    Google Scholar 

  74. Yi Ling, “Introduction to supersymmetric spin networks”, hep-th/0009020, J. Math. Phys. 43 (2002) 154-169

    Article  Google Scholar 

  75. T. Banks, “T C P, Quantum Gravity, The Cosmological Constant And All That”, Nucl. Phys. B249 (1985) 332.

    Article  Google Scholar 

  76. L. Smolin, in preparation.

    Google Scholar 

  77. A. Ashtekar, C. Rovelli and L. Smolin “Gravitons and Loops”, Phys. Rev. D 44 (1991) 1740-1755; J. Iwasaki, C. Rovelli, “Gravitons as embroidery on the weave,” Int. J. Mod. Phys. D 1 (1993) 533; “Gravitons from loops: non-perturbative loop-space quantum gravity contains the graviton-physics approximation,” Class. Quantum Grav. 11 (1994) 1653.

    Google Scholar 

  78. M. Spradlin, A. Strominger, A. Volovich, “Les Houches Lectures on de Sitter Space,” hep-th/0110007

    Google Scholar 

  79. G. Horowitz, “Exactly Soluble Diffeomorphism Invariant Theories”, Commun. Math. Phys. 125 (1989) 417; V. Husain, “Topological Quantum Mechanics”, Phys. Rev. D43 (1991) 1803.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Perimeter Institute for Theoretical Physics Waterloo Department of Physics, University of Waterloo, N2J2W9, Canada

    L. Smolin

Authors
  1. L. Smolin
    View author publications

    Search author on:PubMed Google Scholar

Editor information

Jurek Kowalski-Glikman Giovanni Amelino-Camelia

Rights and permissions

Reprints and permissions

About this chapter

Cite this chapter

Smolin, L. Loop Quantum Gravity and planck Scale Phenomenology. In: Kowalski-Glikman, J., Amelino-Camelia, G. (eds) Planck Scale Effects in Astrophysics and Cosmology. Lecture Notes in Physics, vol 669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11377306_11

Download citation

  • DOI: https://doi.org/10.1007/11377306_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25263-4

  • Online ISBN: 978-3-540-31527-8

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Keywords

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Publish with us

Policies and ethics