Abstract
In the last century, our theoretical knowledge of key physical processes has experienced an impressively large and fast growth thanks to the birth and to the development of new theories.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
R. Brunetti, M. Duetsch, K. Fredenhagen, Perturbative Algebraic Quantum Field Theory and the Renormalization Groups. Adv. Theor. Math. Phys. 13(5), 1541 (2009). arXiv:0901.2038 [math-ph]
R. Brunetti, C. Dappiaggi, K. Fredenhagen, J. Yngvason, Advances in algebraic quantum field theory (Springer, 2015), pp. 453
M. Benini, C. Dappiaggi, S. Murro, Radiative observables for linearized gravity on asymptotically flat spacetimes and their boundary induced states. J. Math. Phys. 55, 082301 (2014). arXiv:1404.4551 [gr-qc]
R. Brunetti, K. Fredenhagen, Quantum Field Theory on Curved Backgrounds. Lecture Notes in Physics, vol. 786 (2009), pp. 129. arXiv:0901.2063 [gr-qc]
R. Brunetti, K. Fredenhagen, M. Köhler, The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes. Commun. Math. Phys. 180, 633 (1996). arXiv:gr-qc/9510056
R. Brunetti, K. Fredenhagen, R. Verch, The generally covariant locality principle: a new paradigm for local quantum field theory. Commun. Math. Phys. 237, 31 (2003). arXiv: math-ph/0112041
B. Chilian, K. Fredenhagen, The time slice axiom in perturbative quantum field theory on globally hyperbolic spacetimes. Commun. Math. Phys. 287, 513 (2009). arXiv:0802.1642 [math-ph]
B.S. De Witt, R.W. Brehme, Radiation damping in a gravitational field. Ann. Phys. 9, 220 (1960)
C. Dappiaggi, T.P. Hack, N. Pinamonti, Approximate KMS states for scalar and spinor fields in Friedmann-Robertson-Walker spacetimes. Ann. Henri Poincaré 12, 1449–1489 (2011). arXiv:1009.5179 [gr-qc]
C. Dappiaggi, V. Moretti, N. Pinamonti, Rigorous steps towards holography in asymptotically flat spacetimes. Rev. Math. Phys. 18, 349 (2006). arXiv:gr-qc/0506069
C. Dappiaggi, V. Moretti, N. Pinamonti, Cosmological horizons and reconstruction of quantum field theories. Commun. Math. Phys. 285, 1129 (2009). arXiv:0712.1770 [gr-qc]
C. Dappiaggi, V. Moretti, N. Pinamonti, Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property. J. Math. Phys. 50, 062304 (2009). arXiv:0812.4033 [gr-qc]
C. Dappiaggi, V. Moretti, N. Pinamonti, Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime. Adv. Theor. Math. Phys. 15(2), 355 (2011). arXiv:0907.1034 [gr-qc]
C. Dappiaggi, D. Siemssen, Hadamard States for the Vector Potential on Asymptotically Flat Spacetimes. Rev. Math. Phys. 25, 1350002 (2013). arXiv:1106.5575 [gr-qc]
K. Fredenhagen, K. Rejzner, QFT on curved spacetimes: axiomatic framework and examples. J. Math. Phys. 57, 031101 (2016)
S.A. Fulling, F.J. Narcowich, R.M. Wald, Singularity structure of the two-point function in quantum field theory in curved spacetime II. Ann. Phys. 136, 243 (1981)
I.M. Gelfand, M.A. Naimark, On the imbedding of normed rings into the ring of operators on a Hilbert space. Matematicheskii Sbornik 12, 197–217 (1943)
C. Gérard, M. Wrochna, Construction of Hadamard states by pseudo-differential calculus. Commun. Math. Phys. 325, 713 (2014). arXiv:1209.2604 [math-ph]
C. Gérard, M. Wrochna, Construction of Hadamard states by characteristic cauchy problem. Anal. PDE 9, 111 (2016). arXiv:1409.6691 [math-ph]
L. Hörmander, The Analysis of Linear Partial Differential Operators, vol. 1, (Springer, 1989)
R. Haag, D. Kastler, An algebraic approach to quantum field theory. J. Math. Phys. 5, 848–861 (1964)
B.S. Kay, R.M. Wald, Theorems on the uniqueness and thermal properties of stationary, nonsingular, quasifree states on space-times with a bifurcate killing horizon. Phys. Rept. 207, 49 (1991)
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. Commun. Math. Phys. 268, 727 (2006). arXiv:gr-qc/0512049
V. Moretti, Quantum ground states holographically induced by asymptotic flatness: invariance under spacetime symmetries, energy positivity and Hadamard property. Commun. Math. Phys. 279, 31 (2008). arXiv:gr-qc/0610143
M.J. Radzikowski, Micro-local approach to the hadamard condition in quantum field theory on curved space-time. Commun. Math. Phys. 179, 529 (1996)
I.E. Segal, Irreducible representations of operator algebras. Bull. Am. Math. Soc. 53, 73–88 (1947)
D. Siemssen, Quantization of the electromagnetic potential in asymptotically flat spacetimes. Diploma Thesis, University of Hamburg, (2011)
S. Waldmann, Deformation Quantization: Observable Algebras, States And Representation Theory. arXiv:hep-th/0303080
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 The Author(s)
About this chapter
Cite this chapter
Dappiaggi, C., Moretti, V., Pinamonti, N. (2017). Introduction. In: Hadamard States from Light-like Hypersurfaces. SpringerBriefs in Mathematical Physics, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-64343-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-64343-4_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-64342-7
Online ISBN: 978-3-319-64343-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)