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A first class constraint is a dynamical quantity in a constrained Hamiltonian system whose Poisson bracket with all the other constraints vanishes on the constraint surface in phase space. To calculate the first class constraint, one assumes that there are no second class constraints, or that they have been calculated previously, and their Dirac brackets generated.
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References
- Anderson, James L.; Bergmann, Peter G. (1951). "Constraints in covariant field theories". Physical Review. Series 2. 83 (5): 1018–1025. Bibcode:1951PhRv...83.1018A. doi:10.1103/PhysRev.83.1018. MR 0044382.
- Dirac, Paul A.M. (1964). Lectures on quantum mechanics. Belfer Graduate School of Science Monographs Series. Vol. 2. New York: Belfer Graduate School of Science. ISBN 9780486417134. MR 2220894. 2001 reprint by Dover.
Footnotes
- ↑ Dirac 1964, p. 43.
- ↑ Dirac 1964, p. 8.
- ↑ Dirac 1964, p. 14.
- ↑ Anderson & Bergmann 1951, p. 1019.
- ↑ Dirac, Paul A.M. (1950). "Generalized Hamiltonian dynamics". Canadian Journal of Mathematics . 2: 129–148. doi: 10.4153/CJM-1950-012-1 . ISSN 0008-414X. MR 0043724. S2CID 119748805.
- ↑ Dirac, Paul A.M. (1958). "Generalized Hamiltonian dynamics". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 246 (1246): 326–332. Bibcode:1958RSPSA.246..326D. doi:10.1098/rspa.1958.0141. ISSN 0962-8444. JSTOR 100496. MR 0094205. S2CID 122175789.
- ↑ Dirac, Paul A.M. (1958). "The theory of gravitation in Hamiltonian form". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 246 (1246): 333–343. Bibcode:1958RSPSA.246..333D. doi:10.1098/rspa.1958.0142. ISSN 0962-8444. JSTOR 100497. MR 0094206. S2CID 122053391.
- ↑ Dirac 1964.