Relativistic quantum mechanics

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In physics, relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to those comparable to the speed of light c, and can accommodate massless particles. The theory has application in high energy physics,[1] particle physics and accelerator physics,[2] as well as atomic physics, chemistry[3] and condensed matter physics.[4][5] Non-relativistic quantum mechanics refers to the mathematical formulation of quantum mechanics applied in the context of Galilean relativity, more specifically quantizing the equations of classical mechanics by replacing dynamical variables by operators. Relativistic quantum mechanics (RQM) is quantum mechanics applied with special relativity. Although the earlier formulations, like the Schrödinger picture and Heisenberg picture were originally formulated in a non-relativistic background, a few of them (e.g. the Dirac or path-integral formalism) also work with special relativity.

Key features common to all RQMs include: the prediction of antimatter, spin magnetic moments of elementary spin 1⁄2 fermions, fine structure, and quantum dynamics of charged particles in electromagnetic fields.[6] The key result is the Dirac equation, from which these predictions emerge automatically. By contrast, in non-relativistic quantum mechanics, terms have to be introduced artificially into the Hamiltonian operator to achieve agreement with experimental observations.

The most successful (and most widely used) RQM is relativistic quantum field theory (QFT), in which elementary particles are interpreted as field quanta. A unique consequence of QFT that has been tested against other RQMs is the failure of conservation of particle number, for example in matter creation and annihilation.[7]

Paul Dirac's work between 1927 and 1933 shaped the synthesis of special relativity and quantum mechanics.[8] His work was instrumental, as he formulated the Dirac equation and also originated quantum electrodynamics, both of which were successful in combining the two theories.[9]

In this article, the equations are written in familiar 3D vector calculus notation and use hats for operators (not necessarily in the literature), and where space and time components can be collected, tensor index notation is shown also (frequently used in the literature), in addition the Einstein summation convention is used. SI units are used here; Gaussian units and natural units are common alternatives. All equations are in the position representation; for the momentum representation the equations have to be Fourier transformed – see position and momentum space.

  1. ^ Perkins, D.H. (2000). Introduction to High Energy Physics. Cambridge University Press. ISBN 978-0-521-62196-0.
  2. ^ Martin, B.R.; Shaw, G. (2008-12-03). Particle Physics. Manchester Physics Series (3rd ed.). John Wiley & Sons. p. 3. ISBN 978-0-470-03294-7.
  3. ^ Reiher, M.; Wolf, A. (2009). Relativistic Quantum Chemistry. John Wiley & Sons. ISBN 978-3-527-62749-3.
  4. ^ Strange, P. (1998). Relativistic Quantum Mechanics: With Applications in Condensed Matter and Atomic Physics. Cambridge University Press. ISBN 978-0-521-56583-7.
  5. ^ Mohn, P. (2003). Magnetism in the Solid State: An Introduction. Springer Series in Solid-State Sciences Series. Vol. 134. Springer. p. 6. ISBN 978-3-540-43183-1.
  6. ^ Martin, B.R.; Shaw, G. (2008-12-03). Particle Physics. Manchester Physics Series (3rd ed.). John Wiley & Sons. pp. 5–6. ISBN 978-0-470-03294-7.
  7. ^ Messiah, A. (1981). Quantum Mechanics. Vol. 2. North-Holland Publishing Company. p. 875. ISBN 978-0-7204-0045-8.
  8. ^ Schweber, Silvan S. (1994). QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga. Princeton, N.J: Princeton University Press. p. 573. ISBN 978-0-691-21328-6.
  9. ^ Bhaumik, Mani L. (2022). "How Dirac's Seminal Contributions Pave the Way for Comprehending Nature's Deeper Designs". Quanta. 8 (1): 88–100. arXiv:2209.03937. doi:10.12743/quanta.v8i1.96. S2CID 212835814.