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In this review article we want to expose a systematic development of quantum field theory on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the QFT framework which also yields a new perspective for the theories on Minkowski space. The aim of the present work is to provide an almost self contained introduction into the framework, which should be accessible for both physicists and mathematicians.
[1] N. Afshordi, S. Aslanbeigi, and R. D. Sorkin, A distinguished vacuum state for a quantum field in a curved spacetime: formalism, features, and cosmology, Journal of High Energy Physics 2012 (2012), no. 8, 1-29.
[3] C. Bär, N. Ginoux, and F. Pfäffle, Wave equations on Lorentzian manifolds and quantization, European Mathematical Society, 2007.
[4] I. A. Batalin and G. A. Vilkovisky, Gauge algebra and quantization, Physics Letters B 102 (1981), no. 1, 27-31.
[5] C. Becker, A. Schenkel, and R. J. Szabo, Differential cohomology and locally covariant quantum field theory, (2014), [arXiv:math-ph/arXiv:1406.1514].
[10] A. N. Bernal and M. Sánchez, On smooth Cauchy hypersurfaces and Geroch's splitting theorem, Commun. Math. Phys. 243 (2003), no. 3, 461-470.
[11] N. Bogoliubov and D. Shirkov, Introduction to the Theory of Quantized Fields, Introduction to the Theory of Quantized Fields, Interscience, New York, 1959.
[13] F. Brennecke and M. Dütsch, Removal of violations of the master Ward identity in perturbative QFT, Reviews in Mathematical Physics 20 (2008), no. 02, 119-51.
[14] M. Brum and K. Fredenhagen, 'vacuum-like' Hadamard states for quantum fields on curved spacetimes, Classical and Quantum Gravity 31 (2014), no. 2, 025024.
[15] R. Brunetti, M. Dütsch, and K. Fredenhagen, Perturbative algebraic quantum field theory and the renormalization groups, Adv. Theor. Math. Phys. 13 (2009), no. 5, 1541-1599.
[16] R. Brunetti and K. Fredenhagen, Microlocal analysis and interacting quantum field theories, Commun. Math. Phys. 208 (2000), no. 3, 623-661.
[18] R. Brunetti, K. Fredenhagen, and K. Rejzner, Quantum gravity from the point of view of locally covariant quantum field theory, [arXiv:math-ph/1306.1058] (2013).
[25] C. Dappiaggi, V. Moretti, and N. Pinamonti, Cosmological horizons and reconstruction of quantum field theories, Commun. Math. Phys. 285 (2009), no. 3, 1129-1163.
[68] G. Popineau and R. Stora, A pedagogical remark on the main theorem of perturbative renormalization theory, unpublished preprint (1982).