Schroedinger equation, spin and topology

The presence of imaginary unit i at a fundamental level in the Schroedinger wave equation has led to the mysterious interpretation of quantum theory. New interpretation of the Schroedinger wave equation transforming it to two coupled wave equations that can be written in real spinor form is proposed...

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Bibliographic Details
Published in:Quantum Studies : Mathematics and Foundations 2023-05, Vol.10 (2), p.293-305
Main Author: Tiwari, S. C.
Format: Article
Language:English
Subjects:
Angular momentum
Commutators
Electrodynamics
History and Philosophical Foundations of Physics
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Mathematics and Statistics
Particle spin
Quantum Physics
Quantum theory
Regular Paper
Schrodinger equation
Theoretical
Topology
Wave equations
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Summary:The presence of imaginary unit i at a fundamental level in the Schroedinger wave equation has led to the mysterious interpretation of quantum theory. New interpretation of the Schroedinger wave equation transforming it to two coupled wave equations that can be written in real spinor form is proposed. Spin angular momentum for free particle is derived based on this formalism. The proposition that spin is an emergent property in stochastic electrodynamics is critically examined in this context. It is shown that the geometric phase for Z 2 vortex gives a new insight on the nature of spin: pure gauge field of geometric origin carries spin-half that has topological origin. The geometric interpretation of Pauli algebra such that the commutators signify 2D directed area introduces topological aspect in the Pauli algebra. It is argued that topological origin of spin implies that it is the spin that gives the particle nature to the electron. A possible line of approach suggested for addressing fundamental questions in quantum theory is to incorporate topological aspect for spin in the stochastic approach. Possible alternative paradigm for unification is also suggested.
ISSN:2196-5609
2196-5617
DOI:10.1007/s40509-023-00295-3