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
The canonical formalism when the Lagrangian has time-derivatives which are higher than second order, alluded to in text, is due to M. Ostrogradskii, Mem. Act. St.Petersburg, VI4, 385 (1850).
The result that the surface term at the final time-slice in the variation of the action gives the canonical one-form is, in essence, an old result going back to nineteenth century work on analytical mechanics. In the context of quantum field theory, it is also the basis of Schwinger’s quantum action principle. For some modern references, see V. Guillemin and S. Sternberg, Symplectic Techniques in Physics, Cambridge University Press (1990); J. Schwinger, Phys. Rev. 82, 914 (1951); C. Črnkovic and E. Witten, in Three Hundred Years of Gravitation, S.W. Hawking and W. Israel (eds.), Cambridge University Press (1987); G.J. Zuckerman, in Mathematical Aspects of String Theory, S.T. Yau (ed.), World Scientific (1987).
Casimir effect and Hawking radiation were briefly mentioned in text. Casimir effect is covered in detail in K.A. Milton, The Casimir Effect, World Scientific Pub. Co. (2001).
Hawking radiation and many related effects are discussed in V.P. Frolov and I.D. Novikov, Black Hole Physics: Basic Concepts and New Developments, Kluwer Academic Publishers (1998).
The original spin-statistics theorem is due to Pauli, with later more general approaches due to many others. In the context of relativistic quantum field theory, a good general reference is R.F. Streater and A.S. Wightman, PCT, Spin and Statistics and All That, W.A. Benjamin, Inc. (1964).
For the topological approach to spin-statistics for point particles, see R.P. Feynman, “The Reason for Antiparticles” in Elementary Particles and the Laws of Physics, Oxford University Press (1987); R.D. Tscheuschner, Int. J. Theor. Phys. 28, 1269 (1989); A.P. Balachandran et al, Mod. Phys. Lett. A5, 1574 (1990). This is related to earlier work on spin-statistics for solitons by a number of people, some of which can be traced from the last reference quoted.
A nice discussion of the spin-statistics theorem in the framework of path integrals is K. Fujikawa, Int. J. Mod. Phys. A16, 4025 (2001).
For the canonical procedure on symmetrization of energy-momentum tensor, see F. Belinfante, Physica 6, 887 (1939); ibid. 7, 305 (1940). The symmetric energy-momentum tensor via variation of the metric is discussed in many books on relativity, for example, S. Weinberg, Gravitation and Cosmology, Wiley Text Books (1972); L. Landau and E.M. Lifshitz, Classical Theory of Fields, Butterworth-Heinemann, 4th edition (1980).
The classical conformal invariance of Maxwell equations goes back to E. Cunningham, Proc. Lond. Math. Soc. 8, 77 (1910); H. Bateman, Proc. Lond. Math. Soc. 8, 223 (1910).
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
(2005). Canonical Quantization. In: Quantum Field Theory. Graduate Texts in Contemporary Physics. Springer, New York, NY. https://doi.org/10.1007/0-387-25098-0_3
Download citation
DOI: https://doi.org/10.1007/0-387-25098-0_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-21386-6
Online ISBN: 978-0-387-25098-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)