Relativistic wave equations with fractional derivatives and pseudodifferential operators

Journal of Applied Mathematics

Volumn 2, Issue 4, 2002, Pages 163-197

  Závada, Petr ^a  

^a NONE

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EID: 1842674323     PISSN: 1110757X     EISSN: None     Source Type: Journal    
DOI: 10.1155/S1110757X02110102     Document Type: Article

References (21)

1. D. G. Barci, C. G. Bollini, L. E. Oxman, and M. C. Rocca, Lorentz-invariant pseudo-differential wave equations, Internat. J. Theoret. Phys. 37 (1998), no. 12, 3015-3030.
2. N. Fleury and M. Rausch de Traubenberg, Linearization of polynomials, J. Math. Phys. 33 (1992), no. 10, 3356-3366.
3. N. Fleury and M. Rausch de Traubenberg, Finite-dimensional representations of Clifford algebras of polynomials, Adv. Appl. Clifford Algebras 4 (1994), no. 2, 123-130.
4. L. L. Foldy, Synthesis of covariant particle equations, Phys. Rev. (2) 102 (1956), 568-581.
5. W. I. Fushchich and A. G. Nikitin, Symmetries of Equations of Quantum Mechanics, Allerton Press, New York, 1994.
6. M. S. Joshi, Introduction to pseudo-differential operators, lecture notes, http://arxiv.org/abs/Math.AP/9906155, June 1999.
7. R. Kerner, $Z_3$-grading and the cubic root of the Dirac equation, Classical Quantum Gravity 9 (1992), 137-146.
8. C. Lämmerzahl, The pseudodifferential operator square root of the Klein-Gordon equation, J. Math. Phys. 34 (1993), no. 9, 3918-3932.
9. J. Patera and H. Zassenhaus, The Pauli matrices in $n$ dimensions and finest gradings of simple Lie algebras of type $A_{n-1}$, J. Math. Phys. 29 (1988), no. 3, 665-673.
10. M. S. Plyushchay and M. Rausch de Traubenberg, Cubic root of Klein-Gordon equation, Phys. Lett. B 477 (2000), no. 1-3, 276-284.
11. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Vol. 1, Gordon & Breach Science Publishers, New York, 1986.
12. A. Ramakrishnan, $L$-Matrix Theory or the Grammar of Dirac Matrices, Tata McGraw-Hill Publishing, New Delhi, 1972.
13. A. Raspini, Dirac equation with fractional derivatives of order 2/3, Fizika B 9 (2000), no. 2, 49-54.
14. M. Rausch de Traubenberg, Clifford algebras, supersymmetry and $Z_N$ symmetries: application in field theory, Habilitation thesis, Université Louis Pasteur, Laboratoire de Physique Théorique, France, February 1998, http://arxiv.org/abs/hep-th/9802141.
15. J. R. Smith, Second quantization of the square root Klein-Gordon operator, microscopic causality, propagators, and interactions, Tech. Report UCD-IIRPA-93-13, Phys. Dept., Univ. of California, Davis, 1993, preprint.
16. J. Sucher, Relativistic invariance and the square-root Klein-Gordon equation, J. Mathematical Phys. 4 (1963), no. 1, 17-23.
17. J. Szwed, The "square root" of the Dirac equation within supersymmetry, Phys. Lett. B 181 (1986), no. 3-4, 305-307.
18. F. Trèves, Introduction to Pseudodinferential and Fourier Integral Operators. Vol. 1, Plenum Press, New York, 1980.
19. F. Trèves, Introduction to Pseudodinferential and Fourier Integral Operators. Vol. 2, Plenum Press, New York, 1980.
20. M. W. Wong, An Introduction to Pseudo-Differential Operators, 2nd ed., World Scientific Publishing, New Jersey, 1999.
21. P. Závada, Operator of fractional derivative in the complex plane, Comm. Math. Phys. 192 (1998), no. 2, 261-285.