Fetching the paper…
Reading the bibliography…
We review the construction of models of algebraic quantum field theory by renormalized perturbation theory.
E. C. G. Stückelberg and D. Rivier, “A propos des divergences en théorie des champs quantifiés,” Helv. Phys. Acta 23
1950
Earlier work this paper cites.
R. E. Peierls, The Commutation Laws of Relativistic Field Theory
1952
Earlier work this paper cites.
N. N. Bogoliubov and O. S. Parasiuk, “Über die Multiplikation der Kausalfunktionen in der Quantentheorie der Felder,” Acta Mathematica 97
1957
Earlier work this paper cites.
N. N. Bogoliubov and D. V. Shirkov, “Introduction to the Theory of Quantized Fields,” Interscience Publishers (1959)
1959
Earlier work this paper cites.
K. Hepp, “Proof of the Bogoliubov-Parasiuk Theorem on Renormalization,” Commun. Math. Phys. 2
1966
Earlier work this paper cites.
H. Araki, M. Shiraishi, “On quasifree states of the canonical commutation relations (I),” Publications of the Research Institute for Mathematical Sciences 7
1971
Earlier work this paper cites.
O. Steinmann, “Perturbation Expansions in Axiomatic Field Theory,” Lecture Notes in Physics 11
1971
Earlier work this paper cites.
H. Epstein and V. Glaser, “The Role of locality in perturbation theory,” Annales Poincare Phys. Theor. A 19
1973
Earlier work this paper cites.
F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, D. Sternheimer, “Deformation theory and quantization. I. Deformations of symplectic structures,” Annals of Physics 111
1978
Earlier work this paper cites.
F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, D. Sternheimer, “Deformation theory and quantization. II. Physical applications,”’ Annals of Physics 111
1978
Earlier work this paper cites.
V. A. Il’in and D. S. Slavnov, “Observable algebras in the S-matrix approach", Theor. Math. Phys. 36
1978
Earlier work this paper cites.
S. A. Fulling, F. J. Narcowich, and R. M. Wald, “Singularity structure of the two-point function in quantum field theory in curved spacetime, ii”, Annals of Physics 136
1981
Earlier work this paper cites.
J. M. Arms, J. E. Marsden, and V. Moncrief, “The structure of the space of solutions of Einstein’s equations II: several Killing fields and the Einstein-Yang-Mills equations,” Annals of Physics 144
1982
Earlier work this paper cites.
C. Crnkovic, E. Witten, “Covariant description of canonical formalism in geometrical theories”, in “Three hundred years of gravitation” (1987), pp. 676-684
1987
Cited alongside, same era.
B. S. Kay, R. M. Wald, “Theorems on the uniqueness and thermal properties of stationary, nonsingular, quasifree states on spacetimes with a bifurcate Killing horizon,” Physics Reports 207
1991
Cited alongside, same era.
G. Keller, C. Kopper and M. Salmhofer, “Perturbative renormalization and effective Lagrangians in phi**4 in four-dimensions,” Helv. Phys. Acta 65
1992
Cited alongside, same era.
O. Steinmann, “Perturbation theory of wigthman functions,” Commun. Math. Phys. 152
1993
Cited alongside, same era.
G. Scharf, “Finite QED: the causal approach,” Springer Verlag (1995)
1995
Cited alongside, same era.
S. Hollands, “The Operator product expansion for perturbative quantum field theory in curved spacetime,” Commun. Math. Phys. 273
2007
Later among the works it cites.
S. Hollands and R. M. Wald, “Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes,” Reviews in Mathematical Physics 17
2007
Later among the works it cites.
S. Waldmann, “Poisson-Geometrie und Deformationsquantisierung: Eine Einführung,” Springer-Verlag, Berlin, Heidelberg (2007)
2007
Later among the works it cites.
S. Hollands, “Renormalized Quantum Yang-Mills Fields in Curved Spacetime,” Rev. Math. Phys. 20
2008
Later among the works it cites.
K. Fredenhagen, Ch. Bär Quantum field theory on curved spacetimes
2009
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
O. Steinmann, “Perturbative quantum field theory at positive temperatures: An axiomatic approach,” Commun. Math. Phys. 170
1995
Cited alongside, same era.
M. J. Radzikowski, Micro-local approach to the Hadamard condition in quantum field theory on curved space-time
1996
Cited alongside, same era.
A. Kriegl, P. Michor, Convenient setting of global analysis
1997
Cited alongside, same era.
M. Duetsch and K. Fredenhagen, “A Local (perturbative) construction of observables in gauge theories: The Example of QED,” Commun. Math. Phys. 203
1999
Cited alongside, same era.
R. Brunetti and K. Fredenhagen, “Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds,” Commun. Math. Phys. 208
2000
Cited alongside, same era.
S. Hollands and R. M. Wald, “Local Wick polynomials and time ordered products of quantum fields in curved space-time,” Commun. Math. Phys. 223
2001
Cited alongside, same era.
L. Hörmander The analysis of linear partial differential operators I: Distribution theory and Fourier analysis
2003
Cited alongside, same era.
R. Brunetti, M. Duetsch and K. Fredenhagen, “Perturbative Algebraic Quantum Field Theory and the Renormalization Groups,” Adv. Theor. Math. Phys. 13
2009
Later among the works it cites.
B. Chilian and K. Fredenhagen, “The Time slice axiom in perturbative quantum field theory on globally hyperbolic spacetimes,” Commun. Math. Phys. 287
2009
Later among the works it cites.
J. ,C. Weise, “On the Algebraic Formulation of Classical General Relativity”, Diploma thesis, Hamburg 2011, http://www.desy.de/uni-th/theses/Dipl_Weise.pdf
2011
Later among the works it cites.
J. Dereziński, C. Gérard, “Mathematics of quantization and quantum fields,” Cambridge University Press (2013)
2013
Later among the works it cites.
K. Fredenhagen and K. Rejzner, “Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory,” Commun. Math. Phys. 317
2013
Later among the works it cites.
F. Lindner,“Perturbative Algebraic Quantum Field Theory at Finite Temperature,” PhD thesis, University of Hamburg 2013
2013
Later among the works it cites.
M. Duetsch, K. Fredenhagen, K. J. Keller and K. Rejzner, “Dimensional Regularization in Position Space, and a Forest Formula for Epstein-Glaser Renormalization,” J. Math. Phys. 55
2014
Later among the works it cites.
K. Fredenhagen and F. Lindner, “Construction of KMS States in Perturbative QFT and Renormalized Hamiltonian Dynamics,” Commun. Math. Phys. 332
2014
Later among the works it cites.