Relativistic Quantum Mechanics Reference

Use this chapter when the derivation is known but a sign, factor, matrix convention or normalization needs checking. Each lookup states its scope and points to the corresponding derivation. The tables work as complete convention packages; selecting individual lines from incompatible packages can change a calculation.

Choose a lookup by the quantity being compared

Question	Reference	First check
How does a mostly-plus source translate?	Metric Signatures	Translate the operator, phase and adjoint together
How do inverse energies become lengths or cross sections?	Natural Units	Restore $\hbar,c$ and the electromagnetic rationalization
Which gamma matrices and adjoint are in use?	Gamma-Matrix Conventions	Basis, index placement, $\gamma^5$ and tensor definitions
Which momentum does a negative-frequency spinor label?	Spinor Conventions	Mode phase, future label, norm and energy projector
What is the parity or C sign of a bilinear?	Dirac Bilinear Table	Definition and commuting versus fermionic statistics
Which kernel has the required source and boundary condition?	Propagator Table	Delta-source factor before pole prescription
Where do the factors of $2E$ and $2\pi$ go?	Relativistic Normalization	State overlap, measure and coefficient as a set
Which generator describes the retained sector?	Common Relativistic Hamiltonians	State space, rest energy, domain and approximation
What does this repeated letter mean here?	Symbol Index	Scalar, matrix, operator or distribution
Which source should I study next?	Reading List	Entry capability and a concrete exit calculation

Start with Metric and Units for the shared spacetime and unit definitions.

Translate a disagreement as a complete package

For a formula copied from another source, compare these groups in order:

1. Spacetime and units: metric signature, orientation, upper/lower indices, Fourier phase and explicit constants.
2. Coupling: signed charge, potential components, covariant derivative and gauge phase.
3. Spinors: basis, adjoint, chirality, tensor definition, momentum label and normalization.
4. States and kernels: completeness measure, external-leg factors, source equation and boundary prescription.
5. Physical model: prescribed or dynamical source, retained energy sector, statistics, domain and approximation.

For example, a minus sign between two scalar Green functions can come from opposite differential operators. A factor of $i$ can distinguish a unit-source inverse from a time-ordered correlator. A factor of $\sqrt{2E}$ can come from a state normalization. Determine which object is being compared before treating the discrepancy as a physics error.

Use Symmetry Conventions for complete P/T/C operations: a matrix without its argument transformation, complex conjugation and statistics is not the full symmetry rule.

Connect the table to a calculation

The Scattering and Propagators chapter derives the source, amplitude and phase-space formulas. The Notebooks chapter supplies executable checks of boosts, spinors, wave packets, spectra, scattering and kernels. Follow the linked derivation when a table does not cover your assumptions.

For a shorter reminder across the broader site, consult the Relativistic QM Formula Cards or Hamiltonian Cards. The general symbol index and QFT bridge bibliography serve wider navigation tasks.

References

• Bjorken, James D., and Sidney D. Drell. Relativistic Quantum Mechanics. McGraw–Hill, 1964. Wave equations, currents and covariant matrix elements.
• Dreiner, Herbi K., Howard E. Haber, and Stephen P. Martin. “Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry.” Physics Reports 494, 1–196 (2010). doi:10.1016/j.physrep.2010.05.002. Spinor convention comparisons.
• Weinberg, Steven. The Quantum Theory of Fields, Volume I: Foundations. Cambridge University Press, 1995. doi:10.1017/CBO9781139644167. State normalization and representation conventions.