Evaluation of the heat kernel in Riemann-Cartan space using the covariant Taylor expansion method

Classical and Quantum Gravity

Volumn 14, Issue 10, 1997, Pages 2853-2868

  Yajima, Satoshi ^a,b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b KUMAMOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031519325     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/14/10/012     Document Type: Article

References (47)

1. Schwinger J S 1951 Phys. Rev. 82 664
2. De Witt B S 1965 Dynamical Theory of Groups and Fields (New York: Gordon and Breach) De Witt BS 1975 Phys. Rep. 19 296 De Witt B S 1979 General Relativity ed S Hawking and W Israel (Cambridge: Cambridge University Press) De Witt B S 1984 Relativity, Groups and Topology II ed B S De Witt and R Stora (Amsterdam: North-Holland)
3. De Witt B S 1965 Dynamical Theory of Groups and Fields (New York: Gordon and Breach) De Witt BS 1975 Phys. Rep. 19 296 De Witt B S 1979 General Relativity ed S Hawking and W Israel (Cambridge: Cambridge University Press) De Witt B S 1984 Relativity, Groups and Topology II ed B S De Witt and R Stora (Amsterdam: North-Holland)
4. De Witt B S 1965 Dynamical Theory of Groups and Fields (New York: Gordon and Breach) De Witt BS 1975 Phys. Rep. 19 296 De Witt B S 1979 General Relativity ed S Hawking and W Israel (Cambridge: Cambridge University Press) De Witt B S 1984 Relativity, Groups and Topology II ed B S De Witt and R Stora (Amsterdam: North-Holland)
5. De Witt B S 1965 Dynamical Theory of Groups and Fields (New York: Gordon and Breach) De Witt BS 1975 Phys. Rep. 19 296 De Witt B S 1979 General Relativity ed S Hawking and W Israel (Cambridge: Cambridge University Press) De Witt B S 1984 Relativity, Groups and Topology II ed B S De Witt and R Stora (Amsterdam: North-Holland)
6. Avramidi I G 1989 Teor. Mat. Fiz. 79 219 Avramidi I G 1990 Phys. Lett. 238B 92 Avramidi I G 1991 Nucl. Phys. B 355 712 Avramidi I G 1987 The covariant methods for calculation of the effective action in quantum field theory and the investigation of higher-derivative quantum gravity Preprint hep-th/9510140 Avramidi I G 1997 Covariant techniques for computation of the heat kernel Preprint hep-th/9704166
7. Avramidi I G 1989 Teor. Mat. Fiz. 79 219 Avramidi I G 1990 Phys. Lett. 238B 92 Avramidi I G 1991 Nucl. Phys. B 355 712 Avramidi I G 1987 The covariant methods for calculation of the effective action in quantum field theory and the investigation of higher-derivative quantum gravity Preprint hep-th/9510140 Avramidi I G 1997 Covariant techniques for computation of the heat kernel Preprint hep-th/9704166
8. Avramidi I G 1989 Teor. Mat. Fiz. 79 219 Avramidi I G 1990 Phys. Lett. 238B 92 Avramidi I G 1991 Nucl. Phys. B 355 712 Avramidi I G 1987 The covariant methods for calculation of the effective action in quantum field theory and the investigation of higher-derivative quantum gravity Preprint hep-th/9510140 Avramidi I G 1997 Covariant techniques for computation of the heat kernel Preprint hep-th/9704166
9. Avramidi I G 1989 Teor. Mat. Fiz. 79 219 Avramidi I G 1990 Phys. Lett. 238B 92 Avramidi I G 1991 Nucl. Phys. B 355 712 Avramidi I G 1987 The covariant methods for calculation of the effective action in quantum field theory and the investigation of higher-derivative quantum gravity Preprint hep-th/9510140 Avramidi I G 1997 Covariant techniques for computation of the heat kernel Preprint hep-th/9704166
10. Avramidi I G 1989 Teor. Mat. Fiz. 79 219 Avramidi I G 1990 Phys. Lett. 238B 92 Avramidi I G 1991 Nucl. Phys. B 355 712 Avramidi I G 1987 The covariant methods for calculation of the effective action in quantum field theory and the investigation of higher-derivative quantum gravity Preprint hep-th/9510140 Avramidi I G 1997 Covariant techniques for computation of the heat kernel Preprint hep-th/9704166
11. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
12. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
13. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
14. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
15. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
16. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
17. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
18. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
19. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
20. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
21. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
22. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
23. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
24. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
25. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
26. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
27. Vilkovisky G A 1983 Quantum Gravity ed S Christensen (Bristol: Hilger) Barvinsky A O and Vilkovisky GA 1985 Phys. Rep. 119 1 Barvinsky A O and Vilkovisky G A 1987 Nucl. Phys. B 282 163 Barvinsky A O and Vilkovisky GA 1990 Nucl. Phys. B 333 471 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3525 Barvinsky A O, Gusev Yu V, Vilkovisky G A and Zhytnikov V V 1994 J. Math. Phys. 35 3543 Frolov V P and Zelonikov A I 1984 Phys. Rev. D 29 1057 Jack I and Osborn H 1982 Nucl. Phys. B 207 474 Jack I and Osborn H 1984 Nucl. Phys. B 234 331 Osborn T A and Molzahn FH 1986 Phys. Rev. A 34 1696 Camporesi 1990 Phys. Rep. 196 1 Ketov S V and Moch S O 1994 Class. Quantum Grav. 11 11 Gusynin V P 1995 Heat Kernel Techniques and Quantum Gravity (Discourses in Mathematics and Its Application 4) ed S A Fulling (Texas: College station) Saledo L L and Ruiz Arriola E 1996 Ann. Phys., NY 250 1 Ichinose S and Ikeda N 1996 Phys. Rev. D 53 5932 Bellisai D 1996 Nucl. Phys. B 467 127 Mukku C 1997 J. Math. Phys. D 38 668
28. Elizalde E, Odintsov S D, Romeo A, Bytsenko A A and Zerbini S 1994 Zeta Regularization Techniques with Applications (Singapore: World Scientific)
29. Birrell N D and Davies PCW 1982 Quantum Fields in Curved Space (Cambridge: Cambridge University Press) Kimura T 1969 Prog. Theor. Phys. 42 1191 Alvarez-Gaumé L and Witten E 1984 Nucl. Phys. B 234 269 Nieh H T 1984 Phys. Rev. Lett. 53 2219
30. Birrell N D and Davies PCW 1982 Quantum Fields in Curved Space (Cambridge: Cambridge University Press) Kimura T 1969 Prog. Theor. Phys. 42 1191 Alvarez-Gaumé L and Witten E 1984 Nucl. Phys. B 234 269 Nieh H T 1984 Phys. Rev. Lett. 53 2219
31. Birrell N D and Davies PCW 1982 Quantum Fields in Curved Space (Cambridge: Cambridge University Press) Kimura T 1969 Prog. Theor. Phys. 42 1191 Alvarez-Gaumé L and Witten E 1984 Nucl. Phys. B 234 269 Nieh H T 1984 Phys. Rev. Lett. 53 2219
32. Birrell N D and Davies PCW 1982 Quantum Fields in Curved Space (Cambridge: Cambridge University Press) Kimura T 1969 Prog. Theor. Phys. 42 1191 Alvarez-Gaumé L and Witten E 1984 Nucl. Phys. B 234 269 Nieh H T 1984 Phys. Rev. Lett. 53 2219
33. Obukhov Yu N 1983 Nucl. Phys. B 212 237
34. van Nieuwenhuizen P 1981 Phys. Rep. 68 189
35. Nielsen N K 1978 Nucl. Phys. B 140 499 Kallosh R E 1978 Nucl. Phys. B 141 141 Hata H and Kugo T 1979 Nucl. Phys. B 158 357 Endo R and Kimura T 1980 Prog. Theor. Phys. 63 683 Endo R and Takao M 1985 Phys. Lett. 161B 155
36. Nielsen N K 1978 Nucl. Phys. B 140 499 Kallosh R E 1978 Nucl. Phys. B 141 141 Hata H and Kugo T 1979 Nucl. Phys. B 158 357 Endo R and Kimura T 1980 Prog. Theor. Phys. 63 683 Endo R and Takao M 1985 Phys. Lett. 161B 155
37. Nielsen N K 1978 Nucl. Phys. B 140 499 Kallosh R E 1978 Nucl. Phys. B 141 141 Hata H and Kugo T 1979 Nucl. Phys. B 158 357 Endo R and Kimura T 1980 Prog. Theor. Phys. 63 683 Endo R and Takao M 1985 Phys. Lett. 161B 155
38. Nielsen N K 1978 Nucl. Phys. B 140 499 Kallosh R E 1978 Nucl. Phys. B 141 141 Hata H and Kugo T 1979 Nucl. Phys. B 158 357 Endo R and Kimura T 1980 Prog. Theor. Phys. 63 683 Endo R and Takao M 1985 Phys. Lett. 161B 155
39. Nielsen N K 1978 Nucl. Phys. B 140 499 Kallosh R E 1978 Nucl. Phys. B 141 141 Hata H and Kugo T 1979 Nucl. Phys. B 158 357 Endo R and Kimura T 1980 Prog. Theor. Phys. 63 683 Endo R and Takao M 1985 Phys. Lett. 161B 155
40. Goldthorpe WH 1980 Nucl. Phys. B 170 307 Nieh H T and Yan M L 1982 Ann. Phys., NY 138 237 Barth N H 1987 J. Phys. A: Math. Gen. 20 857
41. Goldthorpe WH 1980 Nucl. Phys. B 170 307 Nieh H T and Yan M L 1982 Ann. Phys., NY 138 237 Barth N H 1987 J. Phys. A: Math. Gen. 20 857
42. Goldthorpe WH 1980 Nucl. Phys. B 170 307 Nieh H T and Yan M L 1982 Ann. Phys., NY 138 237 Barth N H 1987 J. Phys. A: Math. Gen. 20 857
43. Cognola G and Zerbini S 1987 Phys. Lett. 195B 435 Cognola G and Zerbini S 1988 Phys. Lett. 214B 70
44. Cognola G and Zerbini S 1987 Phys. Lett. 195B 435 Cognola G and Zerbini S 1988 Phys. Lett. 214B 70
45. Yajima S 1996 Class. Quantum Grav. 13 2423
46. Gilkey P B 1975 J. Diff. Geom. 10 601
47. Yajima S 1988 Prog. Theor. Phys. 79 535