The zeta function method and the harmonic oscillator propagator

American Journal of Physics

Volumn 69, Issue 2, 2001, Pages 232-235

  Barone, F A ^a   Farina, C ^a  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035587542     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1311784     Document Type: Article

References (15)

1. Barry R. Holstein, "The harmonic oscillator propagator," Am. J. Phys. 66, 583-589 (1998).
2. J. Schwinger, "Gauge invariance and vacuum polarization," Phys. Rev. 82, 664 (1951).
3. L. C. Albuquerque, C. Farina, and S. Rabello, "Schwinger's method for computing determinants," Am. J. Phys. 66, 524-528 (1998).
4. H. Boschi-Filho, C. Farina, and A. de Souza Dutra, "Green function approach for computing non-relativistic determinants," Rio de Janeiro, preprint (1994).
5. H. Boschi-Filho, C. Farina, and A. de Souza Dutra, "Partition function for an anyon-like oscillator," J. Phys. A 28, L7-L12 (1995).
6. A. Salam and J. Strahdee, "Transition electromagnetic fields in particle physics," Nucl. Phys. B 90, 203-220 (1975); J. S. Dowker and R. Critchley, "Effective Lagrangian and energy-momentum tensor in de Sitter space," Phys. Rev. D 13, 3224-3232 (1976); S. W. Hawking, "Zeta Function Regularization of Path Integrals in Curved Spacetime," Commun. Math. Phys. 55, 133-148 (1977); G. W. Gibbons, "Thermal Zeta Functions," Phys. Lett. 60A, 385-386 (1977).
7. A. Salam and J. Strahdee, "Transition electromagnetic fields in particle physics," Nucl. Phys. B 90, 203-220 (1975); J. S. Dowker and R. Critchley, "Effective Lagrangian and energy-momentum tensor in de Sitter space," Phys. Rev. D 13, 3224-3232 (1976); S. W. Hawking, "Zeta Function Regularization of Path Integrals in Curved Spacetime," Commun. Math. Phys. 55, 133-148 (1977); G. W. Gibbons, "Thermal Zeta Functions," Phys. Lett. 60A, 385-386 (1977).
8. A. Salam and J. Strahdee, "Transition electromagnetic fields in particle physics," Nucl. Phys. B 90, 203-220 (1975); J. S. Dowker and R. Critchley, "Effective Lagrangian and energy-momentum tensor in de Sitter space," Phys. Rev. D 13, 3224-3232 (1976); S. W. Hawking, "Zeta Function Regularization of Path Integrals in Curved Spacetime," Commun. Math. Phys. 55, 133-148 (1977); G. W. Gibbons, "Thermal Zeta Functions," Phys. Lett. 60A, 385-386 (1977).
9. A. Salam and J. Strahdee, "Transition electromagnetic fields in particle physics," Nucl. Phys. B 90, 203-220 (1975); J. S. Dowker and R. Critchley, "Effective Lagrangian and energy-momentum tensor in de Sitter space," Phys. Rev. D 13, 3224-3232 (1976); S. W. Hawking, "Zeta Function Regularization of Path Integrals in Curved Spacetime," Commun. Math. Phys. 55, 133-148 (1977); G. W. Gibbons, "Thermal Zeta Functions," Phys. Lett. 60A, 385-386 (1977).
10. E. Elizalde, S. D. Odintsov, A. Romeo, A. A. Bitsenko, and S. Zerbini, Zeta Regularization Techniques with Applications (World Scientific, Singapore, 1994).
11. J. Ambjorn and S. Wolfram, "Properties of the Vacuum. I. Mechanical and Thermodynamic," Ann. Phys. (Leipzig) 147, 1-32 (1983).
12. George Arfken, Mathematical Methods for Physicists (Academic, New York, 1970).
13. J. Schwinger, "Casimir Effect in Source Theory. II," Lett. Math. Phys. 24, 59-61 (1992).
14. H. B. G. Casimir, "On the Attraction Between Two Perfectly Conducting Planes," Proc. K. Ned. Akad. Wet. 51, 793-795 (1948).
15. E. Elizalde and A. Romeo, "Essentials of the Casimir Effect and its Computation," Am. J. Phys. 59, 711-719 (1991).