De Donder-Weyl theory and a hypercomplex extension of quantum mechanics to field theory

Reports on Mathematical Physics

Volumn 43, Issue 1-2, 1999, Pages 157-170

  Kanatchikov, Igor V ^a  

^a INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033074624     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0034-4877(99)80024-x     Document Type: Article

References (23)

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2. Th. De Donder: Theorie Invariantive du Calcul des Variations, Nouv. éd., Gauthier-Villars, Paris 1935; H. Weyl: Ann. Math. (2) 36 (1935), 607; for a review see: H. Rund: The Hamilton-Jacobi Theory in the Calculus of Variations, D. van Nostrand, Toronto 1966.
3. Th. De Donder: Theorie Invariantive du Calcul des Variations, Nouv. éd., Gauthier-Villars, Paris 1935; H. Weyl: Ann. Math. (2) 36 (1935), 607; for a review see: H. Rund: The Hamilton-Jacobi Theory in the Calculus of Variations, D. van Nostrand, Toronto 1966.
4. M. J. Gotay, J. Isenberg And J. Marsden: Momentum Maps and Classical Relativistic Fields (various versions are known since 1985 as the GIMMSY paper), Part I: Covariant Field Theory, physics/9801019.
5. G. Giachetta, L. Mangiarotti and G. Sardanashvily: New Lagrangian and Hamiltonian Methods in Field Theory, World Scientific, Singapore 1997.
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8. I. V. Kanatchikov: Int. J. Theor. Phys. 37 (1998), 333, quant-ph/9712058; see also I. V. Kanatchikov: Hypercomplex Wave Functions and the Born-Weyl Quantization in Field Theory, preprint March 1996, 16 pp. (presented as a part of a poster at the GROUP21 Colloquium, Goslar, Germany 1996), unpublished.
9. I. V. Kanatchikov: Int. J. Theor. Phys. 37 (1998), 333, quant-ph/9712058; see also I. V. Kanatchikov: Hypercomplex Wave Functions and the Born-Weyl Quantization in Field Theory, preprint March 1996, 16 pp. (presented as a part of a poster at the GROUP21 Colloquium, Goslar, Germany 1996), unpublished.
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16. I. M. Benn and R. W. Tucker: An Introduction to Spinors and Geometry with Applications in Physics, Adam Hilger, Bristol 1987; see also: P. Becher and H. Joos: Z. Phys. C 15 (1982), 343; I. M. Benn and R. W. Tucker: Commun. Math. Phys. 89 (1983), 341; N. A. Salingaros and G. P. Wene: Acta Appl. Math. 4 (1985), 271.
17. I. M. Benn and R. W. Tucker: An Introduction to Spinors and Geometry with Applications in Physics, Adam Hilger, Bristol 1987; see also: P. Becher and H. Joos: Z. Phys. C 15 (1982), 343; I. M. Benn and R. W. Tucker: Commun. Math. Phys. 89 (1983), 341; N. A. Salingaros and G. P. Wene: Acta Appl. Math. 4 (1985), 271.
18. I. M. Benn and R. W. Tucker: An Introduction to Spinors and Geometry with Applications in Physics, Adam Hilger, Bristol 1987; see also: P. Becher and H. Joos: Z. Phys. C 15 (1982), 343; I. M. Benn and R. W. Tucker: Commun. Math. Phys. 89 (1983), 341; N. A. Salingaros and G. P. Wene: Acta Appl. Math. 4 (1985), 271.
19. I. M. Benn and R. W. Tucker: An Introduction to Spinors and Geometry with Applications in Physics, Adam Hilger, Bristol 1987; see also: P. Becher and H. Joos: Z. Phys. C 15 (1982), 343; I. M. Benn and R. W. Tucker: Commun. Math. Phys. 89 (1983), 341; N. A. Salingaros and G. P. Wene: Acta Appl. Math. 4 (1985), 271.
20. B. Hatfield: Quantum Field Theory of Point Particles and Strings, Addison-Wesley, Redwood City 1992; see also: S. S. Schweber: An Introduction to Relativistic Quantum Field Theory, Harper and Row, New York 1961; P. Mansfield, M. Sampaio and J. Pachos: Short Distance Properties from Large Distance Behavior, hep-th/9702072 (and reference cited therein).
21. B. Hatfield: Quantum Field Theory of Point Particles and Strings, Addison-Wesley, Redwood City 1992; see also: S. S. Schweber: An Introduction to Relativistic Quantum Field Theory, Harper and Row, New York 1961; P. Mansfield, M. Sampaio and J. Pachos: Short Distance Properties from Large Distance Behavior, hep-th/9702072 (and reference cited therein).
22. B. Hatfield: Quantum Field Theory of Point Particles and Strings, Addison-Wesley, Redwood City 1992; see also: S. S. Schweber: An Introduction to Relativistic Quantum Field Theory, Harper and Row, New York 1961; P. Mansfield, M. Sampaio and J. Pachos: Short Distance Properties from Large Distance Behavior, hep-th/9702072 (and reference cited therein).
23. M. Navarro: Toward a Finite Dimensional Formulation of Quantum Field Theory, quant-ph/9805010.