Quantum cosmological multidimensional Einstein-Yang-Mills model in an <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="bold">R</mi><mo>×</mo><mrow><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow><mo>×</mo><mrow><msup><mrow><mi>S</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></math></span> topology

O. Bertolami; P. D. Fonseca; P. V. Moniz

doi:10.1103/PhysRevD.56.4530

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Quantum cosmological multidimensional Einstein-Yang-Mills model in an $R \times S^{3} \times S^{d}$ topology

O. Bertolami

P. D. Fonseca

P. V. Moniz

Instituto Superior Técnico, Departamento de Fı ´sica, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal

Instituto Superior Técnico, Departamento de Matemática, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal

University of Cambridge, DAMTP, Silver Street, Cambridge CB3 9EW, United Kingdom

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Phys. Rev. D 56, 4530 – Published 15 October, 1997

DOI: https://doi.org/10.1103/PhysRevD.56.4530

Abstract

The quantum cosmological version of the multidimensional Einstein-Yang-Mills model in an $R \times S^{3} \times S^{d}$ topology is studied in the framework of the Hartle-Hawking proposal. In contrast with previous work in the literature, we consider Yang-Mills field configurations with nonvanishing time-dependent components in both $S^{3}$ and $S^{d}$ spaces. We obtain stable compactifying solutions that do correspond to extrema of the Hartle-Hawking wave function of the Universe. Subsequently, we also show that the regions where the 4-dimensional metric behaves classically or quantum mechanically (i.e., regions where the metric is Lorentzian or Euclidean) will depend on the number $d$ of compact space dimensions.

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[c4] O. Bertolami, Yu. A. Kubyshin, and J. M. Mourão, Phys. Rev. D 45, 3405 (1992).

[c5] J. B. Hartle and S. W. Hawking, Phys. Rev. D 28, 2960 (1983).

[c6] S. W. Hawking, Nucl. Phys. B239, 257 (1984).

[c7] O. Bertolami and J. M. Mourão, Class. Quantum Grav. 8, 1271 (1991).

[c8] O. Bertolami and P. V. Moniz, Nucl. Phys. B439, 259 (1995).

[c9] P. V. Moniz, Int. J. Mod. Phys. A 11, 4321 (1996).

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[c11] J. J. Halliwell, Nucl. Phys. B266, 228 (1986).

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[c14] O. Bertolami, J. M. Mourão, R. F. Picken, and I. P. Volobujev, Int. J. Mod. Phys. A 6, 4149 (1991).

[c15] U. Bleyer, in Proceedings of the First Iberian Meeting on Gravity, edited by M.C. Bento, O. Bertolami, J.M. Mourão, and R.F. Picken (World Scientific, Singapore 1993); V. D. Ivashchuk, and V. N. Melnikov, Int. J. Mod. Phys. D 3, 795 (1994); Phys. Lett. B 384, 58 (1996); U. Bleyer and V. D. Ivashchuk, 332, 292 (1994); U. Bleyer, V. D. Ivashchuk, V. N. Melnikov, and A. Zhuk, Nucl. Phys. B429, 177 (1994); V. D. Ivashchuk and V. N. Melnikov, Class. Quantum Grav. 12, 809 (1995); V. R. Gavrilov, V. D. Ivashchuk, and V. N. Melnikov, 13, 3039 (1996).

[c16] E. Cremmer and J. Scherk, Nucl. Phys. B118, 61 (1977); J. F. Luciani, B135, 111 (1978).

[c17] M. C. Bento, O. Bertolami, P. V. Moniz, J. M. Mourão, and P. M. Sá, Class. Quantum Grav. 10, 285 (1993).

[c18] P. V. Moniz and J. M. Mourão, Class. Quantum Grav. 8, 1815 (1991); P. V. Moniz, J. M. Mourão, and P. M. Sá, 10, 517 (1993).

[c19] J.J. Halliwell, in Proceedings of the Jerusalem Winter School in Physics: Quantum Cosmology and Baby Universes, edited by T. Piran (World Scientific, Singapore, 1990).

[c20] P. Chmielowski, Phys. Rev. D 41, 1835 (1990).

[c21] J. J. Halliwell and J. Louko, Phys. Rev. D 42, 3997 (1990).

[c22] J. Louko, Phys. Lett. B 202, 201 (1988).

[c23] A. Vilenkin, Phys. Rev. D 39, 1116 (1989).

[c24] R.E. Stong, Notes on Cobordism, Mathematical Notes (Princeton University Press, Princeton, 1968); J.W. Milner and J.D. Stasheff, Characteristic Classes, Annals of the Mathematical Studies (Princeton University Press, Princeton, 1974); F.P. Peterson, Lectures in Cobordism Theory, Lecture Notes in Mathematics, Vol. 1 (K-inokunyo Press, Tokyo, 1961).

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Quantum cosmological multidimensional Einstein-Yang-Mills model in an $R \times S^{3} \times S^{d}$ topology

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Quantum cosmological multidimensional Einstein-Yang-Mills model in an R×S3×Sd topology

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References (24)

Quantum cosmological multidimensional Einstein-Yang-Mills model in an $R \times S^{3} \times S^{d}$ topology