Wave Function as Geometric Entity

ABSTRACT

A spacial approach to the geometrization the theory of the electron has been proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any manifold. A solution of this equation is obtained in terms of geometric treatment. New experiments concerning the geometric nature wave function of electrons are proposed.

A spacial approach to the geometrization the theory of the electron has been proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any manifold. A solution of this equation is obtained in terms of geometric treatment. New experiments concerning the geometric nature wave function of electrons are proposed.

Cite this paper

B. Lev, "Wave Function as Geometric Entity,"*Journal of Modern Physics*, Vol. 3 No. 8, 2012, pp. 709-713. doi: 10.4236/jmp.2012.38096.

B. Lev, "Wave Function as Geometric Entity,"

References

[1] W. A. Fock, “Geometrizierung der Dirachschen Theorie des Elektrons,” Zeitschrift fur Physik, Vol. 57, 1929, p. 261.

[2] V. A. Zhelnorovich, “Theory of Spinors and Application in Mechanics and Physics,” Nauka, Moskow, 1982.

[3] E. Cartan, “Lecons Sur ia Theorie des Spineurs,” Actu- alites Scientifiques et Industries, Paris, 1938.

[4] G. Frobenius, “Uber Lineare Substitution and Bilinear Formen,” Grelle, Vol. 84, 1878, pp. 1-63.

[5] G. Kasanova, “Vector Algebra,” Presses Universitaires de France, 1976.

[6] B. J. Hiley and R. E. Callaghan, “The Cli?ord Algebra approach to Quantum Mechanics A: The Schrodinger and Pauli Particles,” University of London, London, 2010.

[7] C. Doran and A. N. Lasenby, “Geometric Algebra for Physicist,” Cambridge University Press, Cambridge, 2003.

[8] E. Conte, “An Example of Wave Packet Reduction Using Biquaternions,” Physics Essays, Vol. 6, No. 4, 1994, pp. 532-535.

[9] E. Conte, “Wave Function Collapse in Biquaternion Quantum Mechanics,” Physics Essays, Vol. 7, No. 4, 1994, pp. 14-20. doi:10.4006/1.3029160

[10] E. Conte, “On the Logical Origins of Quantum Mechanics Demonstrated By Using Clifford Algebra: A Proof that Quantum Interference Arises in a Clifford Algebraic Formulation of Quantum Mechanics,” Electronic Journal of Theoretical Physics, Vol. 8, No. 25, 2011, pp. 109-126.

[11] A. Khrennikov, “Linear Representations of Probabilistic Transformations Induced by Context Transitions,” Jour- nal of Physics A: Mathematical and General, Vol. 34, No. 47, 2001, pp. 9965-9981. doi:10.1088/0305-4470/34/47/304

[12] M. Cini, “Particle Interference without Waves,” Electronic Journal of Theoretical Physics, Vol. 3, No. 13, 2006, pp. 1-10.

[13] B. I. Lev, “Algebraic Approach to the Geometrization of the Interaction,” Modern Physics Letters, Vol. 3, No. 10, 1988, p. 1025.

[14] J. M. Benn and R. W. Tucker, “The Differential Approach to Spinors and their Symmetries,” Nuovo Cimento A, Vol. 88, 1985, p. 273.

[15] A. G. Klein, “Schr?dinger Inviolate: Neutron Optical Searches for Violations of Quantum Mechanics,” Physics B, Vol. 151, 1988, p. 44.

[1] W. A. Fock, “Geometrizierung der Dirachschen Theorie des Elektrons,” Zeitschrift fur Physik, Vol. 57, 1929, p. 261.

[2] V. A. Zhelnorovich, “Theory of Spinors and Application in Mechanics and Physics,” Nauka, Moskow, 1982.

[3] E. Cartan, “Lecons Sur ia Theorie des Spineurs,” Actu- alites Scientifiques et Industries, Paris, 1938.

[4] G. Frobenius, “Uber Lineare Substitution and Bilinear Formen,” Grelle, Vol. 84, 1878, pp. 1-63.

[5] G. Kasanova, “Vector Algebra,” Presses Universitaires de France, 1976.

[6] B. J. Hiley and R. E. Callaghan, “The Cli?ord Algebra approach to Quantum Mechanics A: The Schrodinger and Pauli Particles,” University of London, London, 2010.

[7] C. Doran and A. N. Lasenby, “Geometric Algebra for Physicist,” Cambridge University Press, Cambridge, 2003.

[8] E. Conte, “An Example of Wave Packet Reduction Using Biquaternions,” Physics Essays, Vol. 6, No. 4, 1994, pp. 532-535.

[9] E. Conte, “Wave Function Collapse in Biquaternion Quantum Mechanics,” Physics Essays, Vol. 7, No. 4, 1994, pp. 14-20. doi:10.4006/1.3029160

[10] E. Conte, “On the Logical Origins of Quantum Mechanics Demonstrated By Using Clifford Algebra: A Proof that Quantum Interference Arises in a Clifford Algebraic Formulation of Quantum Mechanics,” Electronic Journal of Theoretical Physics, Vol. 8, No. 25, 2011, pp. 109-126.

[11] A. Khrennikov, “Linear Representations of Probabilistic Transformations Induced by Context Transitions,” Jour- nal of Physics A: Mathematical and General, Vol. 34, No. 47, 2001, pp. 9965-9981. doi:10.1088/0305-4470/34/47/304

[12] M. Cini, “Particle Interference without Waves,” Electronic Journal of Theoretical Physics, Vol. 3, No. 13, 2006, pp. 1-10.

[13] B. I. Lev, “Algebraic Approach to the Geometrization of the Interaction,” Modern Physics Letters, Vol. 3, No. 10, 1988, p. 1025.

[14] J. M. Benn and R. W. Tucker, “The Differential Approach to Spinors and their Symmetries,” Nuovo Cimento A, Vol. 88, 1985, p. 273.

[15] A. G. Klein, “Schr?dinger Inviolate: Neutron Optical Searches for Violations of Quantum Mechanics,” Physics B, Vol. 151, 1988, p. 44.