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4 - An Introduction to Quantum Field Theory on Curved Spacetimes

Published online by Cambridge University Press:  21 December 2017

Christian Gérard
Affiliation:
Université de Paris XI
Thierry Daudé
Affiliation:
Université de Cergy-Pontoise
Dietrich Häfner
Affiliation:
Université Grenoble Alpes
Jean-Philippe Nicolas
Affiliation:
Université de Bretagne Occidentale
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Publisher: Cambridge University Press
Print publication year: 2018

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References

[1] C., Bär, K., Fredenhagen, editors. Quantum Field Theory on Curved Spacetimes, Springer Lecture Notes in Physics, Springer, 2009.
[2] C., Bär, N., Ginoux, F., Pfäffle: Wave Equations on Lorentzian Manifolds and Quantization, ESI Lectures in Mathematics and Physics, Springer, 2007.
[3] Bjorken, J.D., Drell, S.D. Relativistic Quantum Mechanics, McGraw-Hill, 1964.Google Scholar
[4] C., Dappiaggi, V., Moretti and N., Pinamonti, Distinguished Quantum States in a Class of Cosmological Spacetimes and their Hadamard Property, J., Math. Phys. 50, 2009, 062304.
[5] C., Dappiaggi, V.Moretti and N., Pinamonti, Rigorous Construction and Hadamard Property of the Unruh State in Schwarzschild Spacetime, Adv. Theor. Math. Phys. 15, 2011, 355.
[6] C., Dappiaggi, D., Siemssen, Hadamard States for the Vector Potential on Asymptotically Flat Spacetimes, Rev. Math. Phys. 25, 2013, 1350002.
[7] J., Derezinski, C., Gérard. Mathematics of Quantization and Quantum Fields, Cambridge Monographs on Mathematical Physics, Cambridge University Press, 2013.Google Scholar
[8] Duistermaat, J.J., Hörmand er, L. Fourier Integral Operators. II. Acta Math. 128, 183–269, 1972.
[9] Friedland er, F.G. The Wave Equation on a Curved Space-time Cambridge University Press, 1975.Google Scholar
[10] S., Fulling. Aspects of Quantum Field Theory in Curved Space-Time, London Mathematical Society Student Texts, Cambridge University Press, 1989.Google Scholar
[11] Fulling, S.A., Narcowich, F.J., Wald, R.M. Singularity Structure of the Two-point Function in Quantum Field Theory in Curved Space-time, II, Annals of Physics, 136, 243–272, 1981.
[12] C., Gérard, M., Wrochna, Construction of Hadamard States by Pseudo-differential Calculus, Comm. Math. Phys. 325, 713–755, 2014.
[13] C., Gérard, M., Wrochna, Hadamard States for the Linearized Yang-Mills Equation on Curved Spacetime, arXiv:1403.7153, 2014.
[14] C., Gérard, M., Wrochna, Construction of Hadamard States by Characteristic Cauchy Problem, arXiv:1409.6691, 2014.
[15] L., Hörmand er, A Remark on the Characteristic Cauchy Problem, J. Funct. Anal. 93, 270–277, 1990.
[16] V., Moretti, Uniqueness Theorem for BMS-invariant States of Scalar QFT on the Null Boundary of Asymptotically Flat Spacetimes and Bulk-boundary Observable Algebra Correspondence, Comm. Math. Phys. 268, 727–756, 2006.
[17] V., Moretti, Quantum Out-states Holographically Induced by Asymptotic Flatness: Invariance under Space-time Symmetries, Energy Positivity and Hadamard Property, Comm. Math. Phys. 279, 31–75, 2008.
[18] Sahlmann, H., Verch, R. Passivity and Microlocal Spectrum Condition, Comm. Math. Phys. 214, 705–731, 2000.

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