The time-dependent quantum harmonic oscillator revisited: Applications to quantum field theory

Annals of Physics

Volumn 324, Issue 6, 2009, Pages 1360-1385

  Vergel, Daniel Gómez ^a   Villaseñor, Eduardo J S ^a,b  

^a INSTITUTO DE ESTRUCTURA DE LA MATERIA   (Spain)

^b UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

Quantum field theory; Schr dinger representation; Time dependent harmonic oscillator

Indexed keywords

EID: 65049088673     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2009.03.003     Document Type: Article

References (72)

1. Glauber R.J. Phys. Rev. Lett. 10 (1963) 84
2. Glauber R.J. Phys. Rev. 130 (1963) 2529
3. Glauber R.J. Phys. Rev. 131 (1963) 2766
4. Paul W. Rev. Mod. Phys. 62 (1990) 531
5. Brown L.S. Phys. Rev. Lett. 66 (1991) 527
6. Cirac J.I., Garay L.J., Blatt R., Parkins A.S., and Zoller P. Phys. Rev. A 49 (1994) 421-432
7. Hagedorn G.A., Loss M., and Slawny J. J. Phys. A: Math. Gen. 19 (1986) 521-531
8. Gadella M., Gracia-Bondi{dotless}́a J.M., Nieto L.M., and Várilly J.C. J. Phys. A: Math. Gen. 22 (1989) 2709-2738
9. Liu W.S., and Li X.P. Europhys. Lett. 58 (2002) 669
10. Abeverio S., and Mazzucchi S. J. Funct. Anal. 238 (2006) 471
11. Lewis Jr. H.R. Phys. Rev. Lett. 18 (1967) 510-636
12. Lewis Jr. H.R., and Riesenfeld W.B. J. Math. Phys. 10 (1969) 1458
13. Birrell N.D., and Davies P.C.W. Quantum Fields in Curved Space (1984), Cambridge University Press
14. Wald R.M. Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (1994), The University of Chicago Press, USA
15. Beetle C. Adv. Theor. Math. Phys. 2 (1998) 471-495
16. Mena Marugán G.A. Phys. Rev. D 56 (1997) 907
17. Pierri M. Int. J. Mod. Phys. D 11 (2002) 135
18. J.F. Barbero G., D.G. Vergel, E.J.S. Villaseñor, Class. Quant. Grav. 24 (2007) 5945.
19. Ermakov V.P. Univ. Izv. Kiev. 20 (1880) 1
20. V.P. Ermakov, see Appl. Anal. Discrete Math. 2, 123-145 (2008) for an English translation of Ermakov's original paper.
21. Pinney E. Proc. Am. Math. Soc. 1 (1950) 681
22. Leach P.G.L., and Andriopoulos K. Appl. Anal. Discrete Math. 2 (2008) 146-157
23. Lewis H.R., and Leach P.G.L. J. Math. Phys. 23 (1982) 165-175 2371-2374
24. Lewis H.R., and Leach P.G.L. Ann. Phys. 164 (1985) 47-76
25. Fernández Guasti M., and Moya-Cessa H. J. Phys. A: Math. Gen. 36 (2003) 2069-2076
26. Khandekar D.C., and Lawande S.V. J. Math. Phys. 16 (1973) 384-388
27. Dhara A.K., and Lawande S.V. Phys. Rev. A 30 (1984) 560-567
28. Gowdy R.H. Phys. Rev. Lett. 27 (1971) 826
29. Gowdy R.H. Ann. Phys. 83 (1974) 203
30. Corichi A., Cortez J., and Mena Marugán G.A. Phys. Rev. D 73 (2006) 084020
31. J.F. Barbero G., D.G. Vergel, E.J.S. Villaseñor, Phys. Rev. D 74 (2006) 024003.
32. J.F. Barbero G., D.G. Vergel, E.J.S. Villaseñor, Class. Quant. Grav. 25 (2008) 085002.
33. Lewis Jr. H.R. J. Math. Phys. 9 (1968) 1976
34. Lutzky M. Phys. Lett. A 68 (1978) 3
35. Abraham R., and Marsden J.E. Foundations of Mechanics. second ed. (1978), Benjamin, New York
36. von Neumann J. Mathematical Foundations of Quantum Mechanics (1964), Princeton University Press
37. Prugovečki E. Quantum Mechanics in Hilbert Space. second ed. (1981), Academic Press, New York
38. Felsager B. Geometry Particles and Fields (1981), Odense University Press
39. Rezende J. J. Math. Phys. 25 (1984) 3264-3269
40. Cheng B.K., and Chan F.T. J. Phys. A: Math. Gen. 20 (1987) 3771-3775
41. Landovitz L.F., Levine A.M., and Schreiber W.M. J. Math. Phys. 21 (1980) 2159-2163
42. Parker L. Phys. Rev. 183 (1969) 5
43. Pilch K., and Warner N. Class. Quant. Grav. 4 (1987) 1183
44. Hartley J.G., and Ray J.R. Phys. Rev. D 25 (1982) 382-386
45. José J.V., and Saletan E.J. Classical Dynamics: A Contemporary Approach (1998), Cambridge University Press
46. Mathieu E. J. Mathematiques Pures et Appliquees 13 (1868) 137203
47. McLachlan N.W. Theory and Application of Mathieu Functions (1965), Dover
48. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (1964), Dover
49. Corichi A., Cortez J., Mena Marugán G.A., and Velhinho J.M. Class. Quant. Grav. 23 (2006) 6301
50. Shale D. Trans. Am. Math. Soc. 103 (1962) 149
51. Torre C.G. Phys. Rev. D 66 (2002) 084017
52. Simon B. Functional Integration and Quantum Physics (1974), Academic Press, New York
53. Glimm J., and Jaffe A. Quantum Physics. A Functional Integral Point of View (1987), Springer, New York
54. Gel'fand I.M., and Shilov G.E. Generalized Functions. Applications of Harmonic Analysis vol. 4 (1964), Academic Press, New York
55. Corichi A., Cortez J., and Quevedo H. Phys. Rev. D66 (2002) 085025
56. Corichi A., Cortez J., and Quevedo H. Class. Quant. Grav. 20 (2003) L83
57. Corichi A., Cortez J., and Quevedo H. Ann. Phys. 313 (2004) 446-478
58. Torre C.G. Class. Quant. Grav. 24 (2007) 1
59. Corichi A., Cortez J., Mena Marugán G.A., and Velhinho J.M. Phys. Rev. D 76 (2007) 124031
60. Vergel D.G. Class. Quant. Grav. 25 (2008) 175016
61. Yamasaki Y. Measures on Infinite Dimensional Spaces (1985), World Scientific, Singapore
62. Vergel D.G., and Villaseñor E.J.S. Class. Quant. Grav. 25 (2008) 145008
63. Reed M., and Simon B. Methods of Modern Mathematical Physics vol. I (1980), Academic Press, New York
64. Rezende J. Lett. Math. Phys. 7 (1983) 75
65. Glauber R.J. Phys. Rev. 130 (1963) 2529
66. Ashtekar A. Phys. Rev. Lett. 77 (1996) 4864-4867
67. Angulo M.E., and Mena Marugán G.A. Int. J. Mod. Phys. D 9 (2000) 669-686
68. J.F. Barbero G., I. Garay, E.J.S. Villaseñor, Class. Quant. Grav. 25 (2008) 205013.
69. Husain V. Class. Quant. Grav. 4 (1987) 1587
70. Cariñena J.F., Grabowski J., and Marmo G. Rept. Math. Phys. 60 (2007) 237-258
71. Cariñena J.F., de Lucas J., and Rañada M.F. J. Phys. A: Math. Theor. 41 (2008) 304029
72. J.F. Cariñena, J. de Lucas, A. Ramos, Int. J. Theor. Phys. (2008), doi:10.1007/s10773-008-9909-5. Available from: arXiv:0811.4386v1.