Telegraph Equations and Complementary Dirac Equation from Brownian Movement

Show more

References

[1] G. N. Ord, “Classical Analog of Quantum Phase,” International Journal of Theoretical Physics, Vol. 31, No. 7, 1992, pp. 1177-1195. doi:10.1007/BF00673919

[2] D. G. C. McKeon and G. N. Ord, “Time Reversal in Stochastic Processes and the Dirac Equation,” Physical Review Letters, Vol. 69, No. 1, 1992, pp. 3-4.

[3] G. N. Ord, “A Reformulation of the Feynman Chessboard Model,” Journal of Statistical Physics, Vol. 66, No. 1-2, 1992, pp. 647-659. doi:10.1007/BF01060086

[4] G. N. Ord, “Quantum Interference from Charge Conservation,” Physics Letters A, Vol. 173, No. 4-5, 1993, pp. 343-346. doi:10.1016/0375-9601(93)90247-W

[5] G. N. Ord, “Schr?dinger’s Equation and Discrete Random Walks in a Potential Field,” Annals of Physics, Vol. 250, No. 1, 1996, pp. 63-68. doi:10.1006/aphy.1996.0088

[6] G. N. Ord, “The Schrodinger and Dirac Free Particle Equations without Quantum Mechanics,” Annals of Phy- sics, Vol. 250. No. 1, 1996, pp. 51-62.
doi:10.1006/aphy.1996.0087

[7] G. N. Ord and A. S. Deakin, “Random Walks, Continuum Limits, and Schr?dinger’s Equation,” Physical Review A, Vol. 54, No. 5, 1996, 3772-3778.
doi:10.1103/PhysRevA.54.3772

[8] M. Kac and Mt. Rocky, “A Stochastic Model Related to the Telegrapher’s Equation,” Rocky Mountain Journal of Mathematics, Vol. 4, No. 3, 1974, pp. 494-510.

[9] M. Kac, B. Gaveau, T. Jacobson and L. Schulman, “Relativistic Extension of the Analogy between Quantum Mechanics and Brownian Motion,” Physical Review Letters, 53, No. 5, 1984, pp. 419-422.

[10] D. G. C. McKeon and G. N. Ord, “Time Reversal and a Stochastic Model of the Dirac Equation in an Electromagnetic Field,” Canadian Journal of Physics, Vol. 82, No. 1, 2004, pp. 19-27.

[11] J. Dunkel, P. Talkner and P. Hanggi, “Relativistic Diffusion Processes and Random Walk Models,” Physical Review D, Vol. 75, No. 4, 2007, Article ID: 043001.
doi:10.1103/PhysRevD.75.043001

[12] E. M. Rabei, A.-W. Ajlouni and B. Humam, “Quantization of Brownian Motion,” International Journal of Theoretical Physics, Vol. 45, No. 9, 2006, 1613-1623.
doi:10.1007/s10773-005-9001-3

[13] B. S. Rajput, “Telegraph Equations and Complementary Dirac Equation from Classical Approach,” Acta Ciencia Indica, Vol. 36, No. 1, 2010, pp. 81-88.

[14] B. S. Rajput, “Quantum Equations from Brownian Motion,” Canadian Journal of Physics, Vol. 89, No. 2, 2011, pp. 185-191. doi:10.1139/P10-111

[15] B. S. Rajput, “Quantum Equations from Classical Approach,” Indian Journal of Physics, Vol. 85, No. 12, 2010, pp. 1817-1828. doi:10.1007/s12648-011-0195-3

[16] J. Y. Bang and M. S. Berger, “Possible Equilibria of Interacting Dark Energy Models,” Physical Review D, Vol. 74, No. 12, 2006, Article ID: 125012.
doi:10.1103/PhysRevD.74.125012

[17] Ed. Seidewitz, “Foundations of a Spacetime Path Formalism for Relativistic Quantum Mechanics,” Journal of Mathematical Physics, Vol. 47, No. 11, 2006, Article ID: 112302.