- 
								[1]
								R. Utiyama and B. S. DeWitt, J. Math. Phys., 3: 608 (1962) 
- 
								[2]
								S. DeWitt, Phys. Rep., 19C: 295 (1975) 
- 
								[3]
								R.P. Feynman and A. R. Hibbs, Quantum mechanics and path integration, McGraw-Hill, 1965 
- 
								[4]
								P. Candelas and D. J. Raine, Phys. Rev. D, 12: 965 (1975) 
- 
								[5]
								J. S. Dowker and R. Critchley, Phys. Rev. D, 13: 3224 (1976) 
- 
								[6]
								L. S. Brown, Phys. Rev. D, 15: 1469 (1977); 
 L. S. Brown and J. P. Cassidy, Phys. Rev. D, 15: 2810 (1977)
- 
								[7]
								T. S. Bunch, J. Phys. A: Math Gen., 11: 603 (1978); J. Phys. A: Math Gen., 12: 517 (1979) 
- 
								[8]
								S. M. Christensen, Phys. Rev. D, 14: 2490 (1976) 
- 
								[9]
								S. M. Christensen, Phys. Rev. D, 17: 946 (1978) 
- 
								[10]
								T. S. Bunch, S. M. Christensen, and S. A. Fulling, Phys. Rev. D, 18: 4435 (1978) 
- 
								[11]
								R. Wald, Phys. Rev. D, 17: 1477 (1978) 
- 
								[12]
								S. L. Adler, J. Lieberman, and Y. J.Ng, Ann. Phys. (N.Y.), 106: 279 (1977) 
- 
								[13]
								T. S. Bunch and P. C. W. Davies, Proc. R. Soc. Lond. A, 360: 117 (1978); Proc. R. Soc. Lond. A, 357: 381 (1977) 
- 
								[14]
								P. C. W. Davies, S. A. Fulling, S. M. Christensen et al., Ann. Phys. (N.Y.), 109: 108 (1977) 
- 
								[15]
								S. Hawking, Comm. Math. Phys., 55: 133 (1977) 
- 
								[16]
								K. Fujikawa, Phys. Rev. Lett., 44: 1733 (1980) 
- 
								[17]
								Y. Zhang, X. Ye, and B. Wang, Science China Physics, Mechanics & Astronomy, 63(5): 250411 (2020) 
- 
								[18]
								L. Parker and S. A. Fulling, Phys. Rev. D, 9: 341 (1974) 
- 
								[19]
								S. A. Fulling, L. Parker, and B. L. HuHu, Phys. Rev. D, 10: 3905 (1974) 
- 
								[20]
								B. L. Hu and L. Parker, Phys. Rev. D, 17: 933 (1978) 
- 
								[21]
								B. L. Hu, Phys. Rev. D, 18: 4460 (1978) 
- 
								[22]
								N. D. Birrell, Proc. R. Soc. Lond. B., 361: 513 (1978) 
- 
								[23]
								T. S. Bunch, J. Phys. A: Math. Gen., 11: 603 (1978) 
- 
								[24]
								T. S. Bunch and L. Parker, Phys. Rev. D, 20: 2499 (1979) 
- 
								[25]
								T. S. Bunch, J. Phys. A, 13: 1297 (1980) 
- 
								[26]
								P. R. Anderson and L. Parker, Phys. Rev. D, 36: 2963 (1987) 
- 
								[27]
								N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space, (Cambridge University Press, Cambridge, England, 1982) 
- 
								[28]
								L. Parker and D. J. Toms, Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity, (Cambridge University Press, Cambridge, England, 2009) 
- 
								[29]
								L. Parker, arXiv: hep-th/0702216 
- 
								[30]
								T. Markkanen, JCAP, 05: 001 (2018) 
- 
								[31]
								D. G. Wang, Y. Zhang, and J. W. Chen, Phys. Rev. D, 94: 044033 (2016) 
- 
								[32]
								Y. Zhang and B. Wang, JCAP, 11: 006 (2018) 
- 
								[33]
								G. N. Watson, Treatise on the theory of Bessel functions, (Cambridge U Press, 1958) 
- 
								[34]
								L. H. Ford and L. Parker, Phys. Rev. D, 16: 245 (1977) 
- 
								[35]
								A. Vilenkin and L. H. Ford, Phys. Rev. D, 26: 1231 (1982) 
- 
								[36]
								B. Wang and Y. Zhang, Phys. Rev. D, 98: 103522 (2017); Phys. Rev. D, 98: 123019 (2018); Phys. Rev. D, 99: 123008 (2019); Y. Zhang, F. Qin, and B. Wang, Phys. Rev. D, 98: 103523 (2017) 
- 
								[37]
								B. Chakraborty, J. Math. Phys., 14: 188 (1973)