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The first-order Lorentz-covariant equation for spinor fields, predicting spin- structure and antiparticle solutions.
wp-physics-dirac_equationnlab-physics-dirac_equationtong-qftpdg-rppEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Dirac gamma matrices represent a spacetime Clifford algebra.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
wp-physics-dirac_equationnlab-physics-dirac_equationwp-clifford_algebranlab-clifford_algebraThis is an authored directed relation from the source endpoint to the target endpoint.
Gamma matrices realize the Clifford algebra in the Dirac operator.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
wp-gamma_matricesnlab-clifford_algebratong-qftwp-physics-dirac_equationnlab-physics-dirac_equationpdg-rppThis is an authored directed relation from the source endpoint to the target endpoint.
The Dirac equation is the relativistic spinor wave equation.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
wp-physics-dirac_equationnlab-physics-dirac_equationwp-physics-relativistic_quantum_mechanicsnlab-physics-quantum_mechanicsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The Darwin contact term appears at order in the low-energy Foldy–Wouthuysen expansion of Dirac dynamics in an electric field.
The target is recovered from the source either in a stated mathematical or asymptotic limit, or through a quantitatively controlled approximation with identified small parameters or omitted terms. The edge label and detail must state which case applies and its regime of validity.
wp-physics-darwin_termnist-hydrogenThis is an authored directed relation from the source endpoint to the target endpoint.
The Dirac–Coulomb Hamiltonian uses Dirac one-electron dynamics for each electron.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
wp-physics-relativistic_atomic_structurenist-atomic-spectroscopywp-physics-dirac_equationnlab-physics-dirac_equationThis is an authored directed relation from the source endpoint to the target endpoint.
The Pauli Hamiltonian is obtained by a low-energy expansion of the Dirac theory in electromagnetic fields.
The target retains the degrees of freedom and interactions relevant below a stated scale or within a stated regime, while higher-energy or unresolved degrees of freedom from the source are integrated out, coarse-grained, or encoded in effective couplings.
wp-physics-pauli_equationwp-physics-dirac_equationnlab-physics-dirac_equationThis is an authored directed relation from the source endpoint to the target endpoint.
The positron supplied empirical support for the antiparticle sector implied by relativistic electron theory.
The source theory, law, entity, prediction, or structural claim is directly tested, supported, constrained, or established by the target experiment or observation. Experimental support is not final logical proof; the edge detail states exactly what was measured.
wp-physics-positronaps-positronThis is an authored directed relation from the source endpoint to the target endpoint.
Spin–orbit coupling appears at order in the low-energy expansion of Dirac dynamics, with many-electron and nuclear corrections treated separately.
The target is recovered from the source either in a stated mathematical or asymptotic limit, or through a quantitatively controlled approximation with identified small parameters or omitted terms. The edge label and detail must state which case applies and its regime of validity.
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