Topological symmetry breaking of self-interacting fractional Klein-Gordon field theories on toroidal spacetime

Journal of Physics A: Mathematical and Theoretical

Volumn 41, Issue 14, 2008, Pages

  Lim, S C ^a   Teo, L P ^a  

^a MULTIMEDIA UNIVERSITY   (Malaysia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 43949122962     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/14/145403     Document Type: Article

References (81)

1. Mandelbrot B B 1983 The Fractal Geometry of Nature (San Francisco: Freeman)
2. Feynman R P and Hibbs A R 1965 Quantum Mechanics and Path Integrals (New York: McGraw-Hill)
3. Abbot L F and Wise M B 1981 Dimension of a quantum-mechanical path Am. J. Phys. 49 37-9
4. Nelson E 1966 Derivation of Schrödinger equation from Newtonian mechanics Phys. Rev. 150 1079-85
5. Nelson E 1985 Quantum Fluctuations (Princeton, NJ: Princeton University Press)
6. Kroger H 2000 Fractal geometry in quantum mechanics, field theory and spin systems Phys. Rep. 323 81-181
7. Rothe H J 2005 Lattice Gauge Theories: An introduction 3rd edn (Singapore: World Scientific)
8. Durhuus B J and Ambjorn J 1997 Quantum Geometry: A Statistical Field Theory Approach (Cambridge: Cambridge University Press)
9. Lauscher O and Reuter M 2005 Fractal spacetime structure in asymptotically safe gravity Preprint hep-th/0508202
10. Miller K S and Ross B 1993 An Introduction to the Fractional Calculus and Fractional Differential Equations (New York: Wiley)
11. Samko S, Kilbas A A and Maritchev D I 1993 Integrals and Derivatives of the Fractional Order and Some of Their Applications (Armsterdam: Gordon and Breach)
12. Podlubny I 1999 Fractional Differential Equations (New York: Academic)
13. Kilbas A A, Srivastava H M and Trujillo J J 2006 Theory and Applications of Fractional Differential Equations (Amsterdam: Elsevier)
14. Hilfer R (ed) 2000 Applications of Fractional Calculus in Physics (Singapore: World Scientific)
15. West B J, Bologna M and Grigolini P 2003 Physics of Fractal Operators (New York: Springer)
16. Metzler R and Klafter J 2004 The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics J. Phys. A: Math. Gen. 37 R161-208
17. Zelenyi L M and Milovanov A V 2004 Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics Phys.-Usp. 47 749-88
18. Zaslavsky G M 2005 Hamiltonian Chaos and Fractional Dynamics (Oxford: Oxford University Press)
19. Hu Y and Kallianpur G 2000 Schrödinger equation with fractional Laplacian Appl. Math. Optim. 42 281-90
20. Laskin N 2000 Fractals and quantum mechanics Chaos 10 780-90
21. Laskin N 2002 Fractional Schrödinger equation Phys. Rev. E 66 056108
22. Naber M 2004 Time fractional Schrödinger equation J. Math. Phys. 45 3339-52
23. Guo X and Xu M 2006 Some applications of fractional Schrödinger equation J. Math. Phys. 47 082104
24. Wong S and Xu M 2007 Generalized fractional Schrödinger equation with space-time fractional derivatives J. Math. Phys. 48 043502
25. Dong J and Xu M 2007 Some solutions to the space fractional Schrödinger equation using momentum representation method J. Math. Phys. 48 072105
26. Baleanu D and Muslih S I 2005 About fractional supersymmetric quantum mechanics Czech. J. Phys. 55 1063-6
27. Bollini C G and Giambiagi J J 1993 Arbitrary powers of D'Alembertian and the Huygens' principle J. Math. Phys. 34 610-21
28. Lammerzahl C 1993 The pseudodifferential operator square root of the Klein-Gordon equation J. Math. Phys. 34 3918-32
29. Plyushchay M S and Traubenberg M R de 2000 Cubic root of Klein-Gordon equation Phys. Lett. B 477 276-84
30. Namsrai Kh and Geramb H V von 2001 Square-root operator quantization and nonlocality: a review Int. J. Theor. Phys. 40 1929-2010
31. Raspini A 2001 Simple solution of fractional Dirac equation of order 2/3 Phys. Scr. 64 20-2
32. Zavada P 2002 Relativistic wave equations with fractional derivatives and pseudo-differential operators J. Appl. Math. 2 163-97
33. Amaral R L P G do and Marino E C 1992 Canonical quantization of theories containing fractional powers of the D'Alembertian operator J. Phys. A: Math. Gen. 25 5183-200
34. Barci D G, Oxman L E and Rocca M 1996 Canonical quantization of non-local field equations Int. J. Mod. Phys. A 11 2111-26
35. Lim S C and Muniandy S V 2004 Stochastic quantization of nonlocal fields Phys. Lett. A 324 396-405
36. Albeverio S, Gottschalk H and Wu J-L 1996 Convoluted generalized white noise, Schwinger functions and their analytic continuation to Wightman functions Rev. Math. Phys. 8 763-817
37. Grothaus M and Streit L 1999 Construction of relativistic quantum fields in the framework of white noise analysis J. Math. Phys. 40 5387-405
38. Lim S C 2006 Fractional derivative quantum fields at positive temperature Physica A 363 269-81
39. Eab C H, Lim S C and Teo L P 2007 Finite temperature Casimir effect for a massless fractional Klein-Gordon field with fractional Neumann conditions J. Math. Phys. 48 082301
40. Peskin M E and Schroeder D V 1995 An Introduction to Quantum Field Theory (Reading, MA: Addison-Wesley)
41. Kolb E W and Turner M S 1990 The Early Universe (Reading, MA: Addison-Wesley)
42. Zinn-Justin J 2002 Quantum Field Theory and Critical Phenomena 4th edn (Oxford: Clarendon)
43. Dauxois T and Peyrard M 2006 Physics of Solitons (Cambridge: Cambridge University Press)
44. Ford L H and Yoshimura T 1979 Mass generation by self-interaction in non-Minkowskian spacetimes Phys. Lett. A 70 89-91
45. Toms D J 1980 Symmetry breaking and mass generation by space-time topology Phys. Rev. D 21 2805-17
46. 3 Nucl. Phys. B 169 514-26
47. Actor A 1980 Topological generation of gauge field mass by toroidal spacetime Class. Quantum Grav. 7 663-83
48. Kirsten K 1993 Topological gauge field mass generation by toroidal spacetime J. Phys. A: Math. Gen. 26 2421-35
49. Elizalde E and Kirsten K 1994 Topological symmetry breaking in self-interacting theories on toroidal space-time J. Math. Phys. 35 1260-73
50. Hawking S W 1977 Zeta function regularization of path integrals in curved space time Commun. Math. Phys. 55 139-70
51. Elizalde E, Odintsov S D, Romeo A, Bytsenko A A and Zerbini S 1994 Zeta Regularization Techniques with Applications (River Edge, NJ: World Scientific)
52. Elizalde Emilio 1995 Ten Physical Applications of Spectral Zeta Functions (Berlin: Springer)
53. Kirsten K 2002 Spectral Functions in Mathematics and Physics (Boca Raton, FL: CRC Press)
54. Elizalde E, Kirsten K and Zerbini S 1995 Applications of the Mellin-Barnes integral representation J. Phys. A: Math. Gen. 28 617-29
55. Lim S C and Teo L P 2007 Finite temperature Casimir energy in closed rectangular cavities: a rigorous derivation based on zeta function technique J. Phys. A: Math. Theor. 40 11645-74
56. Lim S C and Teo L P On the minima and convexity of Epstein Zeta function (in preparation)
57. Sebastian K L 1995 Path integral representation for fractional Brownian motion J. Phys. A: Math. Gen. 28 4305
58. Eab C H and Lim S C 2006 Path integral representation of fractional harmonic oscillator Physica A 371 303-16
59. Lim S C, Li M and Teo L P 2007 Locally self-similar fractional oscillator processes Fluct. Noise Lett. 7 L169-79
60. Lim S C and Eab C H 2006 Riemann-Liouville and Weyl fractional oscillator processes Phys. Lett. A 335 87-93
61. Peltier R and Vehel J Levy 1995 Multifractional Brownian motion: definition and preliminary results INRIA Report 2645
62. Benassi A, Jaffard S and Roux D 1997 Elliptic Gaussian random processes Rev. Mat. Ibroamericana 13 19-90
63. Lacaux C 2004 Real harmonizable multifractional Levy motions Ann. Inst. Henri Poincare 40 259-77
64. Lim S C and Teo L P 2007 Weyl and Riemann-Liouville multifractional Ornstein-Uhlenbeck processes J. Phys. A: Theo. Gen. 40 6035-60
65. Epstein P 1903 Zur Theorie allgemeiner Zetafunktionen Math. Ann. 56 615-44
66. Epstein P 1907 Zur Theorie allgemeiner Zetafunktionen II Math. Ann. 65 205-16
67. Jorgenson J and Lang S 1993 Complex analytic properties of regularized products (Lect. Notes Math. 1564) (Berlin: Springer)
68. Sarnak P 1987 Determinants of Laplacians Commun. Math. Phys. 110 113-20
69. Spreafico M 2006 Zeta functions, special functions and the Lerch formula Proc. R. Soc. Ed. 136A 865-89
70. Vardi I 1988 Determinants of Laplacians and multiple Gamma functions SIAM J. Math. Anal. 19 493-507
71. Voros A 1987 Spectral functions, special functions and the Selberg zeta function Commun. Math. Phys. 110 439-65
72. Elizalde E and Romeo A 1989 Regularization of general multidimensional Epstein zeta-functions Rev. Math. Phys. 1 113-28
73. Kirsten K 1991 Inhomogeneous multidimensional Epstein zeta functions J. Math. Phys. 32 3008-14
74. Kirsten K 1994 Generalized multidimensional Epstein zeta functions J. Math. Phys. 35 459-70
75. Elizalde E 1994 An extension of the Chowla-Selberg formula useful in quantizing with the Wheeler-DeWitt equation J. Phys. A: Math. Gen. 27 3775-85
76. Elizalde E 1995 Extension of the Chowla-Selberg Formula and Applications Group Theoretical Methods in Physics (Toyonaka, 1994) (River Edge, NJ: World Scientific) pp 191-4
77. Elizalde E 1998 Multidimensional extension of the generalized Chowla-Selberg formula Commun. Math. Phys. 198 83-95
78. Elizalde E 2000 Zeta functions: formulas and applications J. Comput. Appl. Math. 118 125-42 Higher transcendental functions and their applications
79. Elizalde E 2001 Explicit zeta functions for bosonic and fermionic fields on a non-commutative toroidal spacetime J. Phys. A: Math. Gen. 34 3025-35
80. Chowla S and Selberg A 1949 On Epstein's zeta function. I Proc. Nat. Acad. Sci. USA 35 371-4
81. Selberg A and Chowla S 1967 On Epstein's zeta-function J. Reine Angew. Math. 227 86-110