A tensor form of the Dirac equation
N. G. Marchuk
TL;DR
This paper demonstrates that the Dirac equation for an electron can be reformulated as a tensor equation, expressing it entirely in tensor form.
Contribution
It introduces a tensor formulation of the Dirac equation, providing a new mathematical perspective on quantum mechanics.
Findings
Dirac equation can be expressed as a tensor equation
Tensor formulation preserves all tensor properties in the equation
Provides a new framework for analyzing quantum equations
Abstract
We prove the following theorem: the Dirac equation for an electron (invented by P.A.M.Dirac in 1928) can be written as a tensor equation. An equation is called a tensor equation if all values in it are tensors and all operations in it take tensors to tensors.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Quantum and Classical Electrodynamics · Noncommutative and Quantum Gravity Theories