Abstract
It was shown by Pauli that expectation values in relati- vistic quantum mechanics for spin-1/2 particles are independent of the representation chosen for the Dirac matrices. In this paper we extend and generalize the works of Eddington, Sauter, Riesz, and Teitler to show that these expectation values may be calculated without choosing any representation for the Dirac matrices. This is done by replacing the column spinor wave function by a square matrix to obtain an equation which is similar but not identical to the Dirac equation.. This new equation, invented by Sauter, provides a framework in which only the algebraic properties of the matrix operators and wave functions are needed for all calculations in relativistic quantum mechanics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. Dirac, Roy. Soc. Proc. 117, 610 (1928).
W. Pauli, Ann. Inst. Henri Poincaré 6, 109 (1936).
F. Sauter, Z. Physik 63, 803 (1930).
F. Sauter, Z. Physik 64, 295 (1930).
F. Sauter, Z. Physik 97, 777 (1935).
A. Eddington, Fundamental Theory (Cambridge University Press, Cambridge, 1946), p. 143.
M. Riesz, Comptes Rendus du Dixième Congrès des Mathematiques des Pays Scandanaves, (Copenhagen, 1946), p. 123.
M. Riesz, Comptes Rendus du Douzième Congrès des Mathematiques des Pays Scandanaves, (Lund, 1953), p. 241.
S. Teitler, Nuovo Cimento SUPPL. 3, 1 (1965).
S. Teitler, Nuovo Cimento Suppl. 3, 15 (1965).
S. Teitler, J. Math. Phys. 6, 1976 (1965).
S. Teitler, J. Math. Phys. 7, 1730 (1965).
S. Teitler, J. Math. Phys. 7, 1739 (1966).
K. Greider, Phys. Rev. Lett. 44, 1718 (1980).
K. Greider, Found.Phys. 14, 467 (1984).
K. Greider, Found. Phys. 15, 693 (1985).
P. Holland, J. Phys. A, 16, 2363 (1983).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 D. Reidel Publishing Company
About this chapter
Cite this chapter
Ross, M.F. (1986). Representation-Free Calculations in Relativistic Quantum Mechanics. In: Chisholm, J.S.R., Common, A.K. (eds) Clifford Algebras and Their Applications in Mathematical Physics. NATO ASI Series, vol 183. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4728-3_28
Download citation
DOI: https://doi.org/10.1007/978-94-009-4728-3_28
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8602-8
Online ISBN: 978-94-009-4728-3
eBook Packages: Springer Book Archive