publication . Preprint . 2016

The Continuum Limit of Causal Fermion Systems

Finster, Felix;
Open Access English
  • Published: 16 May 2016
Abstract
This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting cases and is therefore a candidate for a unified physical theory. From the mathematical perspective, causal fermion systems provide a general framework for describing and analyzing non-smooth geometries and "quantum geometries." The dynamics is described by a novel variational principle, called the causal action principle. In addition to the basics, the book provides all the necessary mathematical background and explains how t...
Subjects
free text keywords: General Relativity and Quantum Cosmology, Mathematical Physics, High Energy Physics - Theory
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147 references, page 1 of 10

[BF] C. Bar and K. Fredenhagen (eds), Quantum Field Theory on Curved Spacetimes, Lecture Notes in Physics, vol. 786, Springer Verlag, Berlin, 2009.

[Ba] H. Baumgartel, Analytic Perturbation Theory for Matrices and Operators, Operator Theory: Advances and Applications, vol. 15, Birkhauser Verlag, Basel, 1985.

[BF] Y. Bernard and F. Finster, On the structure of minimizers of causal variational principles in the non-compact and equivariant settings, arXiv:1205.0403 [math-ph], Adv. Calc. Var. 7 (2014), no. 1, 27{57.

[BD] J.D. Bjorken and S.D. Drell, Relativistic Quantum Mechanics, McGraw-Hill Book Co., New York, 1964.

[B1] V.I. Bogachev, Measure theory. Vol. I, Springer-Verlag, Berlin, 2007.

[B2] J. Bognar, Inde nite Inner Product Spaces, Springer-Verlag, New York, 1974, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 78.

[BLMS] L. Bombelli, J. Lee, D. Meyer, and R.D. Sorkin, Space-time as a causal set, Phys. Rev. Lett. 59 (1987), no. 5, 521{524.

[BDF] R. Brunetti, M. Dutsch, and K. Fredenhagen, Perturbative algebraic quantum eld theory and the renormalization groups, arXiv:0901.2038 [math-ph], Adv. Theor. Math. Phys. 13 (2009), no. 5, 1541{1599.

[Ch] S.M. Christensen, Vacuum expectation value of the stress tensor in an arbitrary curved background: the covariant point-separation method, Phys. Rev. D (3) 14 (1976), no. 10, 2490{2501.

[CL] E.A. Coddington and N. Levinson, Theory of Ordinary Di erential Equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955.

[C1] J.C. Collins, Renormalization, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1984.

[C2] A. Connes, Noncommutative Geometry, Academic Press Inc., San Diego, CA, 1994.

[DDMS] D.-A. Deckert, D. Durr, F. Merkl, and M. Schottenloher, Time-evolution of the external eld problem in quantum electrodynamics, arXiv:0906.0046v2 [math-ph], J. Math. Phys. 51 (2010), no. 12, 122301, 28.

[DFS] A. Diethert, F. Finster, and D. Schiefeneder, Fermion systems in discrete space-time exemplifying the spontaneous generation of a causal structure, arXiv:0710.4420 [math-ph], Int. J. Mod. Phys. A 23 (2008), no. 27/28, 4579{4620.

[D1] J. Dieudonne, Foundations of Modern Analysis, Academic Press, New York-London, 1969, Enlarged and corrected printing, Pure and Applied Mathematics, Vol. 10-I.

147 references, page 1 of 10
Abstract
This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting cases and is therefore a candidate for a unified physical theory. From the mathematical perspective, causal fermion systems provide a general framework for describing and analyzing non-smooth geometries and "quantum geometries." The dynamics is described by a novel variational principle, called the causal action principle. In addition to the basics, the book provides all the necessary mathematical background and explains how t...
Subjects
free text keywords: General Relativity and Quantum Cosmology, Mathematical Physics, High Energy Physics - Theory
Download from
147 references, page 1 of 10

[BF] C. Bar and K. Fredenhagen (eds), Quantum Field Theory on Curved Spacetimes, Lecture Notes in Physics, vol. 786, Springer Verlag, Berlin, 2009.

[Ba] H. Baumgartel, Analytic Perturbation Theory for Matrices and Operators, Operator Theory: Advances and Applications, vol. 15, Birkhauser Verlag, Basel, 1985.

[BF] Y. Bernard and F. Finster, On the structure of minimizers of causal variational principles in the non-compact and equivariant settings, arXiv:1205.0403 [math-ph], Adv. Calc. Var. 7 (2014), no. 1, 27{57.

[BD] J.D. Bjorken and S.D. Drell, Relativistic Quantum Mechanics, McGraw-Hill Book Co., New York, 1964.

[B1] V.I. Bogachev, Measure theory. Vol. I, Springer-Verlag, Berlin, 2007.

[B2] J. Bognar, Inde nite Inner Product Spaces, Springer-Verlag, New York, 1974, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 78.

[BLMS] L. Bombelli, J. Lee, D. Meyer, and R.D. Sorkin, Space-time as a causal set, Phys. Rev. Lett. 59 (1987), no. 5, 521{524.

[BDF] R. Brunetti, M. Dutsch, and K. Fredenhagen, Perturbative algebraic quantum eld theory and the renormalization groups, arXiv:0901.2038 [math-ph], Adv. Theor. Math. Phys. 13 (2009), no. 5, 1541{1599.

[Ch] S.M. Christensen, Vacuum expectation value of the stress tensor in an arbitrary curved background: the covariant point-separation method, Phys. Rev. D (3) 14 (1976), no. 10, 2490{2501.

[CL] E.A. Coddington and N. Levinson, Theory of Ordinary Di erential Equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955.

[C1] J.C. Collins, Renormalization, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1984.

[C2] A. Connes, Noncommutative Geometry, Academic Press Inc., San Diego, CA, 1994.

[DDMS] D.-A. Deckert, D. Durr, F. Merkl, and M. Schottenloher, Time-evolution of the external eld problem in quantum electrodynamics, arXiv:0906.0046v2 [math-ph], J. Math. Phys. 51 (2010), no. 12, 122301, 28.

[DFS] A. Diethert, F. Finster, and D. Schiefeneder, Fermion systems in discrete space-time exemplifying the spontaneous generation of a causal structure, arXiv:0710.4420 [math-ph], Int. J. Mod. Phys. A 23 (2008), no. 27/28, 4579{4620.

[D1] J. Dieudonne, Foundations of Modern Analysis, Academic Press, New York-London, 1969, Enlarged and corrected printing, Pure and Applied Mathematics, Vol. 10-I.

147 references, page 1 of 10
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