I have been awarded Ph. D. from Cochin University of Science and Technology (CUSAT), Cochin, Kerala under the guidance of Dr. R. S. Chakravarti (Ph. D. from Wasington University, USA).
My thesis entitled 'Geometric Algebra and Einstein's Electron:Deterministic Field Theories' studies the work of two physicists whose theories Einstein might have approved of: Toyoki Koga (1912-2010) and Mendel Sachs (1927-2012).
In the description of electron spin obtained through the conventional Copenhagen interpretation of quantum mechanics, the concrete picture of rotation was replaced by an abstract mathematical representation; visualization or visualisability was entirely lost. The work described in this thesis takes a step towards restoring this.
We use the geometric version of Clifford Algebra introduced by Hestenes, in which there are no matrices or complex numbers. Studying the analogue in Geometric Algebra of Koga’s solution to the Dirac equation, which represents a deterministic, localised field, we find that the Dirac field for a free electron is a sum of three terms:
1. A solution to the Klein-Gordon equation;
2. A rotating (spinning) field with two possible angular velocities, clockwise
and anticlockwise, for which we estimate the magnitude;
3. A term standing for shuddering motion along the spin axis.
The second field was guessed by Koga whereas the other two are probably introduced for the first time here.This theory also enables us to put a bound on the size of the electron field. It is found that the electron field is anisotropic; it has an axis of symmetry and the electron spins about this axis which has a fixed direction for a free electron.