Triviality of higher derivative theories

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

Volumn 577, Issue 3-4, 2003, Pages 137-142

  Rivelles, Victor O ^a,b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; QUANTUM MECHANICS; QUANTUM THEORY; VACUUM;

EID: 0344872609     PISSN: 03702693     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physletb.2003.10.039     Document Type: Article

References (39)

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4. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
5. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
6. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
7. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
8. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
9. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
10. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
11. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
12. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
13. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
14. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
15. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
16. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
17. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
18. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
19. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
20. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
21. See the following papers for earlier references: J. Lukierski, Acta Phys. Pol. 32 (1967) 771; N. Nakanishi, Prog. Theor. Phys. Suppl. 51 (1972) 1; K.S. Stelle, Gen. Relativ. Gravit. 9 (1978) 353; H. Narnhofer, W. Thirring, Phys. Lett. B 76 (1978) 428; M. Mintchev, J. Phys. A 13 (1980) 1841; E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201 (1982) 469; P. Broadbridge, J. Phys. A 16 (1983) 3271; N.H. Barth, S.M. Christensen, Phys. Rev. D 28 (1983) 1876; U. Moschella, J. Math. Phys. 31 (1990) 2480; I.L. Buchbinder, S.D. Odintsov, I.L. Shapiro, Effective Action in Quantum Gravity, IOP, Bristol, 1992; M. Asorey, J.L. Lopez, I.L. Shapiro, Int. J. Mod. Phys. A 12 (1997) 5711, hep-th/9610006; F.J. de Urries, J. Julve, E.J. Sanchez, J. Phys. A 34 (2001) 8919, hep-th/0105301; S.W. Hawking, T. Hertog, Phys. Rev. D 65 (2002) 103515, hep-th/0107088; T.C. Cheng, P.M. Ho, M.C. Yeh, Nucl. Phys. B 625 (2002) 151, hep-th/0111160; A. Accioly, A. Azeredo, H. Mukai, J. Math. Phys. 43 (2002) 473; E.J. Villasenor, J. Phys. A 35 (2002) 6169, hep-th/0203197; S. De Filippo, F. Maimone, AIP Conf. Proc. 643 (2003) 373, gr-qc/0207059; G. Magnano, L.M. Sokolowski, gr-qc/0209022; S. Nojiri, hep-th/0210056.
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