Nonperturbative operator quantization of strongly nonlinear fields

Foundations of Physics Letters

Volumn 16, Issue 1, 2003, Pages 57-70

  Dzhunushaliev, V ^a  

^a KYRGYZ RUSSIAN SLAVIC UNIVERSITY   (Kyrgyzstan)

Author keywords

Non associative algebra; Non perturbative quantization; Nonlinear fields

Indexed keywords

EID: 0037757811     PISSN: 08949875     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1024102223722     Document Type: Article

References (17)

1. W. Heisenberg, "Zur Quantentheorie nichtrenormierbarer Wellengleichungen," Z. Naturforsch. 9a, 292 (1954). W. Heisenberg, F. Kortel and H. Mitter, "Zur Quantentheorie nichtlinear Wellengleichungen III," Z. Naturforsch. 10a, 425 (1955). W. Heisenberg, "Erweiterungen des Hilbert-Raums in der Quantentheorie der Wellenfelder," Z. Phys., 144, 1 (1956). P. Askoli and W. Heisenberg, "Zur Quantentheorie nichtlinear Wellengleichungen IV: Elektrodynamik," Z. Naturforsch. 12a, 177 (1957). W. Heisenberg, "Lee model and quantization of nonlinear field equations," Nucl. Phys. 4, 532 (1957). W. Heisenberg, "Quantum theory of fields and elementary particles," Rev. Mod. Phys. 29, 269 (1957).
2. W. Heisenberg, "Zur Quantentheorie nichtrenormierbarer Wellengleichungen," Z. Naturforsch. 9a, 292 (1954). W. Heisenberg, F. Kortel and H. Mitter, "Zur Quantentheorie nichtlinear Wellengleichungen III," Z. Naturforsch. 10a, 425 (1955). W. Heisenberg, "Erweiterungen des Hilbert-Raums in der Quantentheorie der Wellenfelder," Z. Phys., 144, 1 (1956). P. Askoli and W. Heisenberg, "Zur Quantentheorie nichtlinear Wellengleichungen IV: Elektrodynamik," Z. Naturforsch. 12a, 177 (1957). W. Heisenberg, "Lee model and quantization of nonlinear field equations," Nucl. Phys. 4, 532 (1957). W. Heisenberg, "Quantum theory of fields and elementary particles," Rev. Mod. Phys. 29, 269 (1957).
3. W. Heisenberg, "Zur Quantentheorie nichtrenormierbarer Wellengleichungen," Z. Naturforsch. 9a, 292 (1954). W. Heisenberg, F. Kortel and H. Mitter, "Zur Quantentheorie nichtlinear Wellengleichungen III," Z. Naturforsch. 10a, 425 (1955). W. Heisenberg, "Erweiterungen des Hilbert-Raums in der Quantentheorie der Wellenfelder," Z. Phys., 144, 1 (1956). P. Askoli and W. Heisenberg, "Zur Quantentheorie nichtlinear Wellengleichungen IV: Elektrodynamik," Z. Naturforsch. 12a, 177 (1957). W. Heisenberg, "Lee model and quantization of nonlinear field equations," Nucl. Phys. 4, 532 (1957). W. Heisenberg, "Quantum theory of fields and elementary particles," Rev. Mod. Phys. 29, 269 (1957).
4. W. Heisenberg, "Zur Quantentheorie nichtrenormierbarer Wellengleichungen," Z. Naturforsch. 9a, 292 (1954). W. Heisenberg, F. Kortel and H. Mitter, "Zur Quantentheorie nichtlinear Wellengleichungen III," Z. Naturforsch. 10a, 425 (1955). W. Heisenberg, "Erweiterungen des Hilbert-Raums in der Quantentheorie der Wellenfelder," Z. Phys., 144, 1 (1956). P. Askoli and W. Heisenberg, "Zur Quantentheorie nichtlinear Wellengleichungen IV: Elektrodynamik," Z. Naturforsch. 12a, 177 (1957). W. Heisenberg, "Lee model and quantization of nonlinear field equations," Nucl. Phys. 4, 532 (1957). W. Heisenberg, "Quantum theory of fields and elementary particles," Rev. Mod. Phys. 29, 269 (1957).
5. W. Heisenberg, "Zur Quantentheorie nichtrenormierbarer Wellengleichungen," Z. Naturforsch. 9a, 292 (1954). W. Heisenberg, F. Kortel and H. Mitter, "Zur Quantentheorie nichtlinear Wellengleichungen III," Z. Naturforsch. 10a, 425 (1955). W. Heisenberg, "Erweiterungen des Hilbert-Raums in der Quantentheorie der Wellenfelder," Z. Phys., 144, 1 (1956). P. Askoli and W. Heisenberg, "Zur Quantentheorie nichtlinear Wellengleichungen IV: Elektrodynamik," Z. Naturforsch. 12a, 177 (1957). W. Heisenberg, "Lee model and quantization of nonlinear field equations," Nucl. Phys. 4, 532 (1957). W. Heisenberg, "Quantum theory of fields and elementary particles," Rev. Mod. Phys. 29, 269 (1957).
6. W. Heisenberg, "Zur Quantentheorie nichtrenormierbarer Wellengleichungen," Z. Naturforsch. 9a, 292 (1954). W. Heisenberg, F. Kortel and H. Mitter, "Zur Quantentheorie nichtlinear Wellengleichungen III," Z. Naturforsch. 10a, 425 (1955). W. Heisenberg, "Erweiterungen des Hilbert-Raums in der Quantentheorie der Wellenfelder," Z. Phys., 144, 1 (1956). P. Askoli and W. Heisenberg, "Zur Quantentheorie nichtlinear Wellengleichungen IV: Elektrodynamik," Z. Naturforsch. 12a, 177 (1957). W. Heisenberg, "Lee model and quantization of nonlinear field equations," Nucl. Phys. 4, 532 (1957). W. Heisenberg, "Quantum theory of fields and elementary particles," Rev. Mod. Phys. 29, 269 (1957).
7. W. Heisenberg, Introduction to the Unified Field Theory of Elementary Particles (Max-Planck-Institut für Physik und Astrophysik, Interscience, New York, 1966).
8. c superconductivity," Phys. Rev. B 64, 024522 (2001).
9. V. Dzhunushaliev, "Nonperturbative quantization of the cylindrically symmetric strongly oscillating field," Phys. Lett. B498, 218(2001). V. Dzhunushaliev and D. Singleton, "Monopole-like configuration from quantized SU(3) gauge fields," hepth/0102081.
10. V. Dzhunushaliev, "Nonperturbative quantization of the cylindrically symmetric strongly oscillating field," Phys. Lett. B498, 218(2001). V. Dzhunushaliev and D. Singleton, "Monopole-like configuration from quantized SU(3) gauge fields," hepth/0102081.
11. D. F. Kurdgelaidze, "The foundations of nonassociative classical field theory," Acta Phys. Hung. 57, 79 (1985).
12. J. Lohmus, E. Paal, and L. Sorgsepp, Nonassociative Algebras In Physics (Hadronic Press, Palm Harbor, 1994).
13. A. I. Nesterov and L. V. Sabinin, "Nonassociative geometry: Towards discrete structure of spacetime," Phys. Rev. D 62, 081501 (2000).
14. R. Wulkenhaar, "The standard model within non-associative geometry," Phys. Lett. B 390, 119 (1997).
15. V. Dzhunushaliev, "Particle scattering in nonassociative quantum field theory," Theor. Math. Phys. 100, 1082 (1994). V. Dzhunushaliev and D. Singleton, "Quantization of classical singular solutions in Yang-Mills theory," Nuovo Cimento 117B, 137 (2002).
16. V. Dzhunushaliev, "Particle scattering in nonassociative quantum field theory," Theor. Math. Phys. 100, 1082 (1994). V. Dzhunushaliev and D. Singleton, "Quantization of classical singular solutions in Yang-Mills theory," Nuovo Cimento 117B, 137 (2002).
17. A. A. Abrikosov, L. P. Gorkov, I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Pergamon, Oxford, 1965).