Abstract
Quantum field theory is an extremely successful piece of theoretical physics. Based on few general principles, it describes with an incredibly good precision large parts of particle physics. But also in other fields, in particular in solid state physics, it yields important applications. At present, the only problem which seems to go beyond the general framework of quantum field theory is the incorporation of gravity. Quantum field theory on curved backgrounds aims at a step toward solving this problem by neglecting the back reaction of the quantum fields on the spacetime metric.
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References
Haag, R., Kastler, D.: An algebraic approach to quantum field theory. J. Math. Phys. 5, 848 (1964)
Haag, R.: Local Quantum Physics. 2nd edn. Springer-Verlag, Berlin, Heidelberg, New York (1996)
Peskin, M.E., Schröder, D.V.: An Introduction to Quantum Field Theory. Perseus (1995)
Brunetti, R., Fredenhagen, K., Verch, R.: The generally covariant locality principle – A new paradigm for local quantum physics, Commun. Math. Phys. 237, 31 (2003)
Radzikowski, M.: Micro-local approach to the Hadamard condition in quantum field theory in curved spacetime. Commun. Math. Phys. 179, 529 (1996)
Brunetti, R., Fredenhagen, K., Köhler, M.: The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes. Commun. Math. Phys. 180, 633–652 (1996)
Hollands, S., Wald, R.M.: Local wick polynomials and time-ordered-products of quantum fields in curved spacetime. Commun. Math. Phys. 223, 289 (2001)
Hamilton, R.S.: The inverse function theorem of Nash and Moser. Bull. (New Series) Am. Math. Soc. 7, 65 (1982)
Brunetti, R., Fredenhagen, K., Ribeiro, P.L.: work in progress.
Peierls, R.: The commutation laws of relativistic field theory. Proc. Roy. Soc. (London) A 214, 143 (1952)
Marolf, D.M.: The generalized Peierls brackets. Ann. Phys. 236, 392 (1994)
deWitt, B.S.: The spacetime approach to quantum field theory. In: B.S. deWitt, R. Stora, (eds.), Relativity, Groups and Topology II: Les Houches 1983, part 2, 381, North-Holland, New York (1984)
Buchholz, D., Porrmann, M., Stein, U.: Dirac versus Wigner: Towards a universal particle concept in local quantum field theory. Phys. Lett. B 267, 377 (1991)
Steinmann, O.: Perturbative Quantum Electrodynamics and Axiomatic Field Theory. Springer, Berlin, Heidelberg, New York (2000)
Buchholz, D., Ojima, I., Roos, H.: Thermodynamic properties of non-equilibrium states in quantum field theory. Ann. Phys. NY. 297, 219 (2002)
Brunetti, R., Dütsch, M., Fredenhagen, K.: Perturbative Algebraic Quantum Field Theory and the Renormalization Groups. Preprint http://arxiv.org/abs/0901.2038
Dirac, P.A.M.: Classical theory of radiating electrons. Proc. Roy. Soc. London A929, 148 (1938)
Brunetti, R., Fredenhagen, K.: Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds. Commun. Math. Phys. 208, 623 (2000)
Epstein, H., Glaser, V.: The role of locality in perturbation theory. Annales Poincare Phys. Theor. A 19, 211 (1973)
Hollands, S., Wald, R.M.: Existence of local covariant time-ordered-products of quantum fields in curved spacetime. Commun. Math. Phys. 231, 309 (2002)
Duetsch, M., Hurth, T., Krahe, F., Scharf, G.: Causal Construction of Yang-Mills Theories 1. Nuovo Cim. A 106, 1029 (1993)
Hollands, S.: Renormalized quantum yang-mills fields in curved spacetime. Rev. Math. Phys. 20, 1033 (2008)
Connes, A., Kreimer, D.: Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem. Commun. Math. Phys. 210, 249 (2000)
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Brunetti, R., Fredenhagen, K. (2009). Quantum Field Theory on Curved Backgrounds. In: Bär, C., Fredenhagen, K. (eds) Quantum Field Theory on Curved Spacetimes. Lecture Notes in Physics, vol 786. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02780-2_5
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DOI: https://doi.org/10.1007/978-3-642-02780-2_5
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