2001
DOI: 10.1088/0305-4470/34/28/304
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Algebraic solution for the vector potential in the Dirac equation

Abstract: The Dirac equation for an electron in an external electromagnetic field can be regarded as a singular set of linear equations for the vector potential. Radford's method of algebraically solving for the vector potential is reviewed, with attention to the additional constraints arising from non-maximality of the rank. The extension of the method to general spacetimes is illustrated by examples in diverse dimensions with both c-and a-number wavefunctions.

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Cited by 15 publications
(22 citation statements)
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“…In [18] two equivalent algebraic expressions for the 4-potential in terms of the Dirac solution are derived. At this point, we reproduce these expressions, using the notation adopted in this work.…”
Section: Definition 3 a Dirac Solutionmentioning
confidence: 99%
“…In [18] two equivalent algebraic expressions for the 4-potential in terms of the Dirac solution are derived. At this point, we reproduce these expressions, using the notation adopted in this work.…”
Section: Definition 3 a Dirac Solutionmentioning
confidence: 99%
“…where the complex 4 × 4 spinor-vector matrix M is a function only of the components of the Dirac spinor. Assuming the vector potential A is real, M is invertible, and an explicit expression for A in terms of the spinors can be obtained [4]. Substituting the inverted Dirac equation into the equations of motion for the gauge field results in a self-coupled system, where the charged fermion field interacts with itself in an internally consistent way.…”
Section: Introductionmentioning
confidence: 99%
“…Exploring algebraic solutions for the U(1) electromagnetic potential appearing in the Dirac equation, Refs. [16,17] showed the prototypical inversion theorem for the real vector potential. The SU(2) case was scrutinized in Ref.…”
Section: Introductionmentioning
confidence: 99%
“…For type-6 spinors, J and K are the only bilinears that are not null and, then, they do correspond to a dipole structure. The bilinear covariants also satisfy [12]: [16,18]:…”
Section: Introductionmentioning
confidence: 99%