Hamiltonian, Lagrangian and Physical Laws

DOI: 10.4236/oalib.1105536, PP. 1-11

Keywords: The Correspondence Principle, Constraints on Quantum Theories, the Variational Principle, First Order Quantum Equations, Second Order Quantum Equations

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Abstract:

The significance of the correspondence between the classical limit of quantum theories and the laws of classical physics is explained. It is proved that this correspondence yields constraints on acceptable quantum theories. The variational principle is taken as the basis of the analysis. The discussion shows that the first order Dirac equation abides by these constraints, whereas second order quantum equations fail to do that.

References

[1]	Landau, L.D. and Lifshitz, E.M. (1960) Mechanics. Pergamon, Oxford.
[2]	Goldstein, H., Poole, C. and Safko, J. (2002) Classical Mechanics. 3rd Edition, Addison Wesley, San Francisco, CA.
[3]	Landau, L.D. and Lifshitz, E.M. (2005) The Classical Theory of Fields. Elsevier, Amsterdam.
[4]	Dirac, P.A.M. (1958) The Principles of Quantum Mechanics. Oxford University Press, Lon-don.
[5]	Schiff, L.I. (1955) Quantum Mechanics. McGraw-Hill, New York.
[6]	https://en.wikipedia.org/wiki/Correspondence_principle
[7]	Weinberg, S. (1995) The Quantum Theory of Fields, Vol. I. Cambridge University Press, Cambridge.
[8]	Rohrlich, F. (2007) Classical Charged Particle. 3rd Edition, World Scientific, Singapore. https://doi.org/10.1142/6220
[9]	Bjorken, J.D. and Drell, S.D. (1965) Relativistic Quantum Fields. McGraw-Hill, New York. https://doi.org/10.1063/1.3047288
[10]	Merzbacher, E. (1970) Quantum Mechanics. John Wiley, New York.
[11]	Peskin, M.E. and Schroeder, D.V. (1995) An Introduction to Quantum Field Theory. Addison-Wesley, Reading, MA.
[12]	Tanabashi, M., et al. (2018) Particle Data Group. Physical Review D, 98, Article ID: 030001.
[13]	Halzen, F. and Martin, A.D. (1984) Quarks and Leptons, an Introductory Course in Modern Particle Physics. John Wiley, New York.
[14]	Bjorken, J.D. and Drell, S.D. (1964) Relativistic Quantum Mechanics. McGraw-Hill, New York.
[15]	Weinberg, S. (1995) The Quantum Theory of Fields, Vol. II. Cambridge University Press, Cambridge.
[16]	Berestetskii, V.B., Lifshitz, E.M. and Pitaevskii, L.P. (1982) Quantum Electrodynamics. Pergamon, Oxford.
[17]	Pauli, W. and Weisskopf, V. (1934) The Quantization of the Scalar Relativistic Wave Equation. Helvetica Physica Acta, 7, 709-731. English Translation: Miller, A.I. (1994) Early Quantum Electrodynamics, University Press, Cambridge, 188-205.
[18]	Jackson, J. D. (1975). Classical Electrodynamics. John Wiley, New York.
[19]	Dirac, P.A.M. (1928) The Quantum Theory of the Electron. Proceedings of the Royal Society of London A, 117, 610.
[20]	Darwin, C.G. (1928) The Wave Equations of the Electron. Proceedings of the Royal Society of London A, 118, 654.
[21]	Abazov, V.M., et al. (2012) D0 Collaboration. Physics Letters B, 718, 451-459.
[22]	Aad, G., et al. (2012) ATLAS Collaboration. Physics Letters B, 712, 289-462.
[23]	Dirac, P.A.M. (1978) The Mathematical Foundations of Quantum Theory. In: Marlow, A.R., Ed., Mathematical Foundations of Quantum Theory, Academic Press, New York. https://doi.org/10.1016/B978-0-12-473250-6.50005-4

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