The Foldy-Wouthuysen transformation

Abstract

The Foldy-Wouthuysen transformation of the Dirac Hamiltonian is generally taught as simply a mathematical trick that allows one to obtain a two-component theory in the low-energy limit. It is not often emphasized that the transformed representation is the only one in which one can take a meaningful *classical limit*, in terms of particles and antiparticles. We briefly review the history and physics of this transformation.

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Cited by in corpus (49)

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• General properties of the Foldy-Wouthuysen transformation and applicability of the corrected original Foldy-Wouthuysen method
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• Classical Limit of Relativistic Quantum Mechanical Equations in the Foldy-Wouthuysen Representation
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• Spinning Particles on Spacelike Hypersurfaces and their Rest-Frame Description
• Exact form of the exponential Foldy-Wouthuysen transformation operator for an arbitrary-spin particle
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• Chiral kinetic theory from the on-shell effective theory: derivation of collision terms
• High-precision description and new properties of a spin-1 particle in a magnetic field
• Hamilton Operator and the Semiclassical Limit for Scalar Particles in an Electromagnetic Field
• Relativistic quantum-mechanical description of twisted paraxial electron and photon beams
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• Connection Between Wave Functions in the Dirac and Foldy-Wouthuysen Representations
• Calculations of the dominant long-range, spin-independent contributions to the interaction energy between two nonrelativistic Dirac fermions from double-boson exchange of spin-0 and spin-1 bosons with spin-dependent couplings
• New symmetry properties of pointlike scalar and Dirac particles
• The Exact Foldy-Wouthuysen Transformation for a Dirac Theory with the complete set of CPT-Lorentz violating terms
• Physical Signatures of Fermion-Coupled Axion Dark Matter
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• Relativistic Unruh-DeWitt detectors with quantized center of mass
• Impact of relativity on particle localizability and ground state entanglement
• Paraxial wave function and Gouy phase for a relativistic electron in a uniform magnetic field
• Observable Zitterbewegung in Curved Spacetimes
• Polarization of spin-1 particles without an anomalous magnetic moment in a uniform magnetic field
• The angular momentum of electron radiation in a uniform magnetic field
• Validation of the Eriksen Method of the Exact Foldy-Wouthuysen Representation
• Exact quantum-mechanical equations for particle beams
• From soft Dirac monopoles to the Dirac equation
• Relativistic Bohmian trajectories and Klein-Gordon currents for spin-0 particles
• Effective electric and magnetic polarizabilities of pointlike spin-1/2 particles
• Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian
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• Emergence of the wavefunction of a non-relativistic quantum particle from QFT
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