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Dirac Equation and Fisher Information.

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Researchers derived Dirac's theory using a relativistic flow Lagrangian and a Lorentz invariant Fisher information term. This extends previous work on Schrödinger and Pauli theories, integrating quantum mechanics principles into fluid dynamics frameworks.

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Area of Science:

  • Theoretical Physics
  • Quantum Mechanics
  • Fluid Dynamics

Background:

  • Schrödinger's theory was previously derived using a potential flow Lagrangian with a Fisher information term.
  • Pauli's electron spin theory was extended using a Clebsch flow Lagrangian with non-zero vorticity.

Purpose of the Study:

  • To represent Dirac's relativistic theory using a flow Lagrangian framework.
  • To incorporate quantum mechanical requirements into a relativistic fluid dynamics model.

Main Methods:

  • Utilized a recent relativistic flow Lagrangian.
  • Incorporated a Lorentz invariant Fisher information term.

Main Results:

  • Successfully represented Dirac's theory within the relativistic flow Lagrangian framework.
  • Demonstrated the necessity of a Lorentz invariant Fisher information term for quantum mechanics.

Conclusions:

  • The study extends the Lagrangian-based derivation of quantum theories to include relativistic spin.
  • This approach unifies quantum mechanics and fluid dynamics at a relativistic level.