Loop transfer matrix and loop quantum mechanics

Journal of High Energy Physics

Volumn 4, Issue 9 PART B, 2000, Pages 1-26

  Savvidy, George K ^a,b  

^a INSTITUTE OF NANOSCIENCE AND NANOTECHNOLOGY   (Greece)

^b UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

Conformal Field Models in String Theory; Exact S Matrix; Models of Quantum Gravity; Statistical Methods

Indexed keywords

EID: 7044226430     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2000/09/044     Document Type: Article

References (69)

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8. D. Weingarten, Euclidean quantum gravity on a lattice, Nucl. Phys. B 210 (1982) 229; A. Maritan and C. Omero, The N → 0 limit of a nonabelian gauge theory: a model for selfavoiding random surfaces, Phys. Lett. B 109 (1982) 51; T. Sterling and J. Greensite, Entropy of selfavoiding surfaces on the lattice, Phys. Lett. B 121 (1983) 345; B. Durhuus, J. Fröhlich and T. Jonsson, Selfavoiding and planar random surfaces on the lattice, Nucl. Phys. B 225 (1983) 185; J. Ambjørn, B. Durhuus, J. Fröhlich and T. Jonsson, Regularized strings with extrinsic curvature, Nucl. Phys. B 290 (1987) 480; T. Hofsäss and H. Kleinert, Field theory of selfavoiding random surfaces, Phys. Lett. A 102 (1984) 420; M. Karowski and H.J. Thun, On the phase structure of systems of self avoiding surfaces, Phys. Rev. Lett. 54 (1985) 2556; F. David, O(N) gauge models and selfavoiding random surfaces in three-dimensions, Europhys. Lett. 9 (1989) 575.
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10. D. Gross, The size of random surfaces, Phys. Lett. B 138 (1984) 185; V.A. Kazakov, Bilocal regularization of models of random surfaces, Phys. Lett. B 150 (1985) 282; F. David, Planar diagrams, two-dimensional lattice gravity and surface models, Nucl. Phys. B 257 (1985) 45; J. Ambjørn, B. Durhuus and J. Fröhlich, Diseases of triangulated random surface models and possible cures, Nucl. Phys. B 257 (1985) 433; V.A. Kazakov, A.A. Migdal and I.K. Kostov, Critical properties of randomly triangulated planar random surfaces, Phys. Lett. B 157 (1985) 295.
11. D. Gross, The size of random surfaces, Phys. Lett. B 138 (1984) 185; V.A. Kazakov, Bilocal regularization of models of random surfaces, Phys. Lett. B 150 (1985) 282; F. David, Planar diagrams, two-dimensional lattice gravity and surface models, Nucl. Phys. B 257 (1985) 45; J. Ambjørn, B. Durhuus and J. Fröhlich, Diseases of triangulated random surface models and possible cures, Nucl. Phys. B 257 (1985) 433; V.A. Kazakov, A.A. Migdal and I.K. Kostov, Critical properties of randomly triangulated planar random surfaces, Phys. Lett. B 157 (1985) 295.
12. D. Gross, The size of random surfaces, Phys. Lett. B 138 (1984) 185; V.A. Kazakov, Bilocal regularization of models of random surfaces, Phys. Lett. B 150 (1985) 282; F. David, Planar diagrams, two-dimensional lattice gravity and surface models, Nucl. Phys. B 257 (1985) 45; J. Ambjørn, B. Durhuus and J. Fröhlich, Diseases of triangulated random surface models and possible cures, Nucl. Phys. B 257 (1985) 433; V.A. Kazakov, A.A. Migdal and I.K. Kostov, Critical properties of randomly triangulated planar random surfaces, Phys. Lett. B 157 (1985) 295.
13. D. Gross, The size of random surfaces, Phys. Lett. B 138 (1984) 185; V.A. Kazakov, Bilocal regularization of models of random surfaces, Phys. Lett. B 150 (1985) 282; F. David, Planar diagrams, two-dimensional lattice gravity and surface models, Nucl. Phys. B 257 (1985) 45; J. Ambjørn, B. Durhuus and J. Fröhlich, Diseases of triangulated random surface models and possible cures, Nucl. Phys. B 257 (1985) 433; V.A. Kazakov, A.A. Migdal and I.K. Kostov, Critical properties of randomly triangulated planar random surfaces, Phys. Lett. B 157 (1985) 295.
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16. W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch. C28 (1973) 693; J. Phys. (Paris) 46 (1985) 1263; L. Peliti and S. Leibler, Effects of thermal fluctuations on systems with small surface tension, Phys. Rev. Lett. 54 (1985) 1690; A. Polykov, Fine structure of strings, Nucl. Phys. B 268 (1986) 406; D. Forster, On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes, Phys. Lett. A 114 (1986) 115; H. Kleinert, The membrane properties of condensing strings, Phys. Lett. B 174 (1986) 335; T.L. Curtright, G.I. Ghandour, C.B. Thorn and C.K. Zachos, Trajectories of strings with rigidity, Phys. Rev. Lett. 57 (1986) 799; T. Curtright, G. Ghandour and C. Zachos, Classical dynamics of strings with rigidity, Phys. Rev. D 34 (1986) 3811; F. David, Rigid surfaces in a space with large dimensionality, Europhys. Lett. 2 (1986) 577; P.O. Mazur and V.P. Nair, Strings in QCD and theta vacua, Nucl. Phys. B 284 (1987) 146; E. Braaten and C.K. Zachos, Instability of the static solution to the closed string with rigidity, Phys. Rev. D 35 (1987) 1512; E. Braaten, R.D. Pisarski and S.-M. Tse, The static potential for smooth strings, Phys. Rev. Lett. 58 (1987) 93; P. Olesen and S.-K. Yang, Static potential in a string model with extrinsic curvatures, Nud. Phys. B 283 (1987) 73; R.D. Pisarski, Perturbative stability of smooth strings, Phys. Rev. Lett. 58 (1987) 1300.
17. W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch. C28 (1973) 693; J. Phys. (Paris) 46 (1985) 1263; L. Peliti and S. Leibler, Effects of thermal fluctuations on systems with small surface tension, Phys. Rev. Lett. 54 (1985) 1690; A. Polykov, Fine structure of strings, Nucl. Phys. B 268 (1986) 406; D. Forster, On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes, Phys. Lett. A 114 (1986) 115; H. Kleinert, The membrane properties of condensing strings, Phys. Lett. B 174 (1986) 335; T.L. Curtright, G.I. Ghandour, C.B. Thorn and C.K. Zachos, Trajectories of strings with rigidity, Phys. Rev. Lett. 57 (1986) 799; T. Curtright, G. Ghandour and C. Zachos, Classical dynamics of strings with rigidity, Phys. Rev. D 34 (1986) 3811; F. David, Rigid surfaces in a space with large dimensionality, Europhys. Lett. 2 (1986) 577; P.O. Mazur and V.P. Nair, Strings in QCD and theta vacua, Nucl. Phys. B 284 (1987) 146; E. Braaten and C.K. Zachos, Instability of the static solution to the closed string with rigidity, Phys. Rev. D 35 (1987) 1512; E. Braaten, R.D. Pisarski and S.-M. Tse, The static potential for smooth strings, Phys. Rev. Lett. 58 (1987) 93; P. Olesen and S.-K. Yang, Static potential in a string model with extrinsic curvatures, Nud. Phys. B 283 (1987) 73; R.D. Pisarski, Perturbative stability of smooth strings, Phys. Rev. Lett. 58 (1987) 1300.
18. W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch. C28 (1973) 693; J. Phys. (Paris) 46 (1985) 1263; L. Peliti and S. Leibler, Effects of thermal fluctuations on systems with small surface tension, Phys. Rev. Lett. 54 (1985) 1690; A. Polykov, Fine structure of strings, Nucl. Phys. B 268 (1986) 406; D. Forster, On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes, Phys. Lett. A 114 (1986) 115; H. Kleinert, The membrane properties of condensing strings, Phys. Lett. B 174 (1986) 335; T.L. Curtright, G.I. Ghandour, C.B. Thorn and C.K. Zachos, Trajectories of strings with rigidity, Phys. Rev. Lett. 57 (1986) 799; T. Curtright, G. Ghandour and C. Zachos, Classical dynamics of strings with rigidity, Phys. Rev. D 34 (1986) 3811; F. David, Rigid surfaces in a space with large dimensionality, Europhys. Lett. 2 (1986) 577; P.O. Mazur and V.P. Nair, Strings in QCD and theta vacua, Nucl. Phys. B 284 (1987) 146; E. Braaten and C.K. Zachos, Instability of the static solution to the closed string with rigidity, Phys. Rev. D 35 (1987) 1512; E. Braaten, R.D. Pisarski and S.-M. Tse, The static potential for smooth strings, Phys. Rev. Lett. 58 (1987) 93; P. Olesen and S.-K. Yang, Static potential in a string model with extrinsic curvatures, Nud. Phys. B 283 (1987) 73; R.D. Pisarski, Perturbative stability of smooth strings, Phys. Rev. Lett. 58 (1987) 1300.
19. W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch. C28 (1973) 693; J. Phys. (Paris) 46 (1985) 1263; L. Peliti and S. Leibler, Effects of thermal fluctuations on systems with small surface tension, Phys. Rev. Lett. 54 (1985) 1690; A. Polykov, Fine structure of strings, Nucl. Phys. B 268 (1986) 406; D. Forster, On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes, Phys. Lett. A 114 (1986) 115; H. Kleinert, The membrane properties of condensing strings, Phys. Lett. B 174 (1986) 335; T.L. Curtright, G.I. Ghandour, C.B. Thorn and C.K. Zachos, Trajectories of strings with rigidity, Phys. Rev. Lett. 57 (1986) 799; T. Curtright, G. Ghandour and C. Zachos, Classical dynamics of strings with rigidity, Phys. Rev. D 34 (1986) 3811; F. David, Rigid surfaces in a space with large dimensionality, Europhys. Lett. 2 (1986) 577; P.O. Mazur and V.P. Nair, Strings in QCD and theta vacua, Nucl. Phys. B 284 (1987) 146; E. Braaten and C.K. Zachos, Instability of the static solution to the closed string with rigidity, Phys. Rev. D 35 (1987) 1512; E. Braaten, R.D. Pisarski and S.-M. Tse, The static potential for smooth strings, Phys. Rev. Lett. 58 (1987) 93; P. Olesen and S.-K. Yang, Static potential in a string model with extrinsic curvatures, Nud. Phys. B 283 (1987) 73; R.D. Pisarski, Perturbative stability of smooth strings, Phys. Rev. Lett. 58 (1987) 1300.
20. W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch. C28 (1973) 693; J. Phys. (Paris) 46 (1985) 1263; L. Peliti and S. Leibler, Effects of thermal fluctuations on systems with small surface tension, Phys. Rev. Lett. 54 (1985) 1690; A. Polykov, Fine structure of strings, Nucl. Phys. B 268 (1986) 406; D. Forster, On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes, Phys. Lett. A 114 (1986) 115; H. Kleinert, The membrane properties of condensing strings, Phys. Lett. B 174 (1986) 335; T.L. Curtright, G.I. Ghandour, C.B. Thorn and C.K. Zachos, Trajectories of strings with rigidity, Phys. Rev. Lett. 57 (1986) 799; T. Curtright, G. Ghandour and C. Zachos, Classical dynamics of strings with rigidity, Phys. Rev. D 34 (1986) 3811; F. David, Rigid surfaces in a space with large dimensionality, Europhys. Lett. 2 (1986) 577; P.O. Mazur and V.P. Nair, Strings in QCD and theta vacua, Nucl. Phys. B 284 (1987) 146; E. Braaten and C.K. Zachos, Instability of the static solution to the closed string with rigidity, Phys. Rev. D 35 (1987) 1512; E. Braaten, R.D. Pisarski and S.-M. Tse, The static potential for smooth strings, Phys. Rev. Lett. 58 (1987) 93; P. Olesen and S.-K. Yang, Static potential in a string model with extrinsic curvatures, Nud. Phys. B 283 (1987) 73; R.D. Pisarski, Perturbative stability of smooth strings, Phys. Rev. Lett. 58 (1987) 1300.
21. W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch. C28 (1973) 693; J. Phys. (Paris) 46 (1985) 1263; L. Peliti and S. Leibler, Effects of thermal fluctuations on systems with small surface tension, Phys. Rev. Lett. 54 (1985) 1690; A. Polykov, Fine structure of strings, Nucl. Phys. B 268 (1986) 406; D. Forster, On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes, Phys. Lett. A 114 (1986) 115; H. Kleinert, The membrane properties of condensing strings, Phys. Lett. B 174 (1986) 335; T.L. Curtright, G.I. Ghandour, C.B. Thorn and C.K. Zachos, Trajectories of strings with rigidity, Phys. Rev. Lett. 57 (1986) 799; T. Curtright, G. Ghandour and C. Zachos, Classical dynamics of strings with rigidity, Phys. Rev. D 34 (1986) 3811; F. David, Rigid surfaces in a space with large dimensionality, Europhys. Lett. 2 (1986) 577; P.O. Mazur and V.P. Nair, Strings in QCD and theta vacua, Nucl. Phys. B 284 (1987) 146; E. Braaten and C.K. Zachos, Instability of the static solution to the closed string with rigidity, Phys. Rev. D 35 (1987) 1512; E. Braaten, R.D. Pisarski and S.-M. Tse, The static potential for smooth strings, Phys. Rev. Lett. 58 (1987) 93; P. Olesen and S.-K. Yang, Static potential in a string model with extrinsic curvatures, Nud. Phys. B 283 (1987) 73; R.D. Pisarski, Perturbative stability of smooth strings, Phys. Rev. Lett. 58 (1987) 1300.
22. W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch. C28 (1973) 693; J. Phys. (Paris) 46 (1985) 1263; L. Peliti and S. Leibler, Effects of thermal fluctuations on systems with small surface tension, Phys. Rev. Lett. 54 (1985) 1690; A. Polykov, Fine structure of strings, Nucl. Phys. B 268 (1986) 406; D. Forster, On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes, Phys. Lett. A 114 (1986) 115; H. Kleinert, The membrane properties of condensing strings, Phys. Lett. B 174 (1986) 335; T.L. Curtright, G.I. Ghandour, C.B. Thorn and C.K. Zachos, Trajectories of strings with rigidity, Phys. Rev. Lett. 57 (1986) 799; T. Curtright, G. Ghandour and C. Zachos, Classical dynamics of strings with rigidity, Phys. Rev. D 34 (1986) 3811; F. David, Rigid surfaces in a space with large dimensionality, Europhys. Lett. 2 (1986) 577; P.O. Mazur and V.P. Nair, Strings in QCD and theta vacua, Nucl. Phys. B 284 (1987) 146; E. Braaten and C.K. Zachos, Instability of the static solution to the closed string with rigidity, Phys. Rev. D 35 (1987) 1512; E. Braaten, R.D. Pisarski and S.-M. Tse, The static potential for smooth strings, Phys. Rev. Lett. 58 (1987) 93; P. Olesen and S.-K. Yang, Static potential in a string model with extrinsic curvatures, Nud. Phys. B 283 (1987) 73; R.D. Pisarski, Perturbative stability of smooth strings, Phys. Rev. Lett. 58 (1987) 1300.
23. W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch. C28 (1973) 693; J. Phys. (Paris) 46 (1985) 1263; L. Peliti and S. Leibler, Effects of thermal fluctuations on systems with small surface tension, Phys. Rev. Lett. 54 (1985) 1690; A. Polykov, Fine structure of strings, Nucl. Phys. B 268 (1986) 406; D. Forster, On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes, Phys. Lett. A 114 (1986) 115; H. Kleinert, The membrane properties of condensing strings, Phys. Lett. B 174 (1986) 335; T.L. Curtright, G.I. Ghandour, C.B. Thorn and C.K. Zachos, Trajectories of strings with rigidity, Phys. Rev. Lett. 57 (1986) 799; T. Curtright, G. Ghandour and C. Zachos, Classical dynamics of strings with rigidity, Phys. Rev. D 34 (1986) 3811; F. David, Rigid surfaces in a space with large dimensionality, Europhys. Lett. 2 (1986) 577; P.O. Mazur and V.P. Nair, Strings in QCD and theta vacua, Nucl. Phys. B 284 (1987) 146; E. Braaten and C.K. Zachos, Instability of the static solution to the closed string with rigidity, Phys. Rev. D 35 (1987) 1512; E. Braaten, R.D. Pisarski and S.-M. Tse, The static potential for smooth strings, Phys. Rev. Lett. 58 (1987) 93; P. Olesen and S.-K. Yang, Static potential in a string model with extrinsic curvatures, Nud. Phys. B 283 (1987) 73; R.D. Pisarski, Perturbative stability of smooth strings, Phys. Rev. Lett. 58 (1987) 1300.
24. W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch. C28 (1973) 693; J. Phys. (Paris) 46 (1985) 1263; L. Peliti and S. Leibler, Effects of thermal fluctuations on systems with small surface tension, Phys. Rev. Lett. 54 (1985) 1690; A. Polykov, Fine structure of strings, Nucl. Phys. B 268 (1986) 406; D. Forster, On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes, Phys. Lett. A 114 (1986) 115; H. Kleinert, The membrane properties of condensing strings, Phys. Lett. B 174 (1986) 335; T.L. Curtright, G.I. Ghandour, C.B. Thorn and C.K. Zachos, Trajectories of strings with rigidity, Phys. Rev. Lett. 57 (1986) 799; T. Curtright, G. Ghandour and C. Zachos, Classical dynamics of strings with rigidity, Phys. Rev. D 34 (1986) 3811; F. David, Rigid surfaces in a space with large dimensionality, Europhys. Lett. 2 (1986) 577; P.O. Mazur and V.P. Nair, Strings in QCD and theta vacua, Nucl. Phys. B 284 (1987) 146; E. Braaten and C.K. Zachos, Instability of the static solution to the closed string with rigidity, Phys. Rev. D 35 (1987) 1512; E. Braaten, R.D. Pisarski and S.-M. Tse, The static potential for smooth strings, Phys. Rev. Lett. 58 (1987) 93; P. Olesen and S.-K. Yang, Static potential in a string model with extrinsic curvatures, Nud. Phys. B 283 (1987) 73; R.D. Pisarski, Perturbative stability of smooth strings, Phys. Rev. Lett. 58 (1987) 1300.
25. W. Helfrich, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforsch. C28 (1973) 693; J. Phys. (Paris) 46 (1985) 1263; L. Peliti and S. Leibler, Effects of thermal fluctuations on systems with small surface tension, Phys. Rev. Lett. 54 (1985) 1690; A. Polykov, Fine structure of strings, Nucl. Phys. B 268 (1986) 406; D. Forster, On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes, Phys. Lett. A 114 (1986) 115; H. Kleinert, The membrane properties of condensing strings, Phys. Lett. B 174 (1986) 335; T.L. Curtright, G.I. Ghandour, C.B. Thorn and C.K. Zachos, Trajectories of strings with rigidity, Phys. Rev. Lett. 57 (1986) 799; T. Curtright, G. Ghandour and C. Zachos, Classical dynamics of strings with rigidity, Phys. Rev. D 34 (1986) 3811; F. David, Rigid surfaces in a space with large dimensionality, Europhys. Lett. 2 (1986) 577; P.O. Mazur and V.P. Nair, Strings in QCD and theta vacua, Nucl. Phys. B 284 (1987) 146; E. Braaten and C.K. Zachos, Instability of the static solution to the closed string with rigidity, Phys. Rev. D 35 (1987) 1512; E. Braaten, R.D. Pisarski and S.-M. Tse, The static potential for smooth strings, Phys. Rev. Lett. 58 (1987) 93; P. Olesen and S.-K. Yang, Static potential in a string model with extrinsic curvatures, Nud. Phys. B 283 (1987) 73; R.D. Pisarski, Perturbative stability of smooth strings, Phys. Rev. Lett. 58 (1987) 1300.
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