publication . Preprint . Book . 2016

The Continuum Limit of Causal Fermion Systems

Felix Finster;
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: Mathematical Physics, General Relativity and Quantum Cosmology, High Energy Physics - Theory, Relationship between string theory and quantum field theory, Theory of everything, Unified field theory, Classical mechanics, Physics, Causal fermion system, Group field theory, Quantum gravity, Fundamental interaction, Quantization (physics)
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. [OpenAIRE]

[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. [OpenAIRE]

[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: Mathematical Physics, General Relativity and Quantum Cosmology, High Energy Physics - Theory, Relationship between string theory and quantum field theory, Theory of everything, Unified field theory, Classical mechanics, Physics, Causal fermion system, Group field theory, Quantum gravity, Fundamental interaction, Quantization (physics)
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. [OpenAIRE]

[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. [OpenAIRE]

[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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publication . Preprint . Book . 2016

The Continuum Limit of Causal Fermion Systems

Felix Finster;