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Madelung Structure of the Dirac Equation
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Madelung Structure of the Dirac Equation
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We consider the Dirac equations in polar form proving that they can equivalently be re-configured into a system of equations consisting of derivatives of the velocity density plus the Hamilton-Jacobi equation, giving the momentum in terms of relativistic quantum potentials (i.e. displaying first-order derivatives of the two degrees of freedom of the spinor field): this system is said to have Madelung structure. Conservation laws, second-order equations and multi-valuedness are also discussed.
Forward citations
Cited by 2 Pith papers
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The Schrodinger Equation as a Gauge Theory
The Schrödinger equation is locally equivalent to a gauge theory with one-form fields in 2+1D and two-form fields in 3+1D, with BF and Chern-Simons terms organizing electromagnetic couplings, anyons, Berry phases, and...
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The Schrodinger Equation as a Gauge Theory
Schrödinger equation is locally equivalent to a non-relativistic gauge theory via one-form or two-form gauge fields on the probability current, with global topology from phase winding quantization.
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