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It is an article of folklore that the collection of ideas identified as Euclidean quantum gravity may be derived from ordinary Lorentzian signature gravity by the procedure of Wick rotation.
J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields
1965
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S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time
1977
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P. Candelas and D. J. Raine, “Feynman propagator in curved space-time”, Phys. Rev. D 15
1977
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G. W. Gibbons, “The Einstein action of Riemannian metrics and its relation to quantum gravity and thermodynamics”, Phys. Lett. A 61
1977
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C. Itzykson and J.-B. Zuber, Quantum Field Theory
1980
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R. L. Bishop and S. I. Goldberg, Tensor Analysis on Manifolds
1980
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J. Glimm and A. Jaffe, Quantum Physics: A Functional Integral Point of View
1987
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An overview of the status of formal developments in Euclidean quantum gravity may be gleaned from: S. W. Hawking and W. Israel, General Relativity: An Einstein Centenary Survey
1987
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V.D. Ivashchuk, “Regularization by ϵ \epsilon -metric: I”, Izvestiya Akademii Nauk Moldavskoi SSR. Ser. Fiziko-tekhnicheskih i matematicheskih nauk. No. 3, p. 8-17 (1987). [In Russian.]
1987
Cited alongside, same era.
P. O. Mazur and E. Mottola, “The gravitational measure, solution of the conformal factor problem, and stability of the ground state of quantum gravity”, Nuclear Physics B341
1988
Cited alongside, same era.
V.D. Ivashchuk. Regularization by ϵ \epsilon -metric: II. The limit ϵ = 0 + \epsilon=0^{+} ”, Izvestiya Akademii Nauk Moldavskoi SSR. Ser. Fiziko-tekhnicheskih i matematicheskih nauk. No. 1, p. 10-20 (1988). [In Russian.]
1988
Cited alongside, same era.
M. Visser, “Wormholes, Baby Universes and Causality”, Physical Review D41
1990
Cited alongside, same era.
J. Greensite, “Dynamical origin of the Lorentzian signature of space-time”, Phys. Lett. B 300
S. A. Hayward, “Complex lapse, complex action and path integrals”, Phys. Rev. D 53
1996
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J. F. Barbero G., “From Euclidean to Lorentzian general relativity: The real way”, Phys. Rev. D 54
1996
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V.D. Ivashchuk, “Wick rotation, regularization of propagators by a complex metric and multidimensional cosmology”, Grav. Cosmol. 3
1997
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B. P. Kosyakov, “Black holes: Interfacing the classical and the quantum”, Found. Phys. 38
2008
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2009
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1993
Cited alongside, same era.
A. Carlini and J. Greensite, “Why is space-time Lorentzian?”, Phys. Rev. D 49
1994
Cited alongside, same era.
J. Greensite, “Quantum mechanics of space-time signature”, Acta Phys. Polon. B 25
1994
Cited alongside, same era.
A. Carlini and J. Greensite, “Square root actions, metric signature, and the path integral of quantum gravity”, Phys. Rev. D 52
1995
Cited alongside, same era.
We choose our metric conventions such that the flat space Minkowski metric is η L = diag ( − 1 , + 1 , + 1 , + 1 ) \eta_{L}={\rm diag}(-1,+1,+1,+1) . The flat space Euclidean metric is taken to be positive definite, η E = diag ( + 1 , + 1 , + 1 , + 1 ) \eta_{E}={\rm diag}(+1,+1,+1,+1)
Cited in the paper.
This point has been forcefully made by Michael S. Morris, (private communication)
Cited in the paper.
I wish to thank Ian H. Redmount for bringing this example to my attention
Cited in the paper.
J. Greensite, “Stability and signature in quantum gravity”
Cited in the paper.
2010
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J. Samuel, “Wick Rotation in the Tangent Space”, Class. Quant. Grav. 33
2016
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Finnian Gray, “Black hole radiation, greybody factors, and generalised Wick rotation”, MSc thesis, 2016, Victoria University of Wellington. http://hdl.handle.net/10063/5148
2016
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