Authors: Bhushan Poojary
In this paper, we extend the Dirac equation into a complex spacetime framework, generalizing relativistic quantum mechanics to incorporate imaginary dimensions of space and time. Building upon the analyticity conditions introduced in our previous work on the Schrödinger equation, we derive the complexified Dirac equation, ensuring consistency with relativistic covariance and spinor structure. The resulting formulation naturally splits into real and imaginary parts, offering novel geometric interpretations of spin, mass, and quantum fluctuations as manifestations of the imaginary curvature of spacetime. We explore the coupling of the complexified Dirac spinor to electromagnetic fields through the imaginary part of the spacetime metric, suggesting a unified geometric origin of spin and electromagnetism. Potential implications for zitterbewegung, neutrino oscillations, and extensions toward quantum gravity are discussed. This framework offers a promising pathway toward a unified understanding of quantum field theory, geometry, and fundamental forces within a complexified spacetime manifold.
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[v1] 2025-04-28 20:17:06
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