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The Dirac bracket is a generalization of the Poisson bracket developed by Paul Dirac to treat classical systems with second class constraints in Hamiltonian mechanics, and to thus allow them to undergo canonical quantization. It is an important part of Dirac's development of Hamiltonian mechanics to elegantly handle more general Lagrangians, when constraints and thus more apparent than dynamical variables are at hand.〔; Dover, ISBN 0486417131.〕 More abstractly, the two-form implied from the Dirac bracket is the restriction of the symplectic form to the constraint surface in phase space.〔See pages 48-58 of Ch. 2 in Henneaux, Marc and Teitelboim, Claudio, ''Quantization of Gauge Systems''. Princeton University Press, 1992. ISBN 0-691-08775-X〕 This article assumes familiarity with the standard Lagrangian and Hamiltonian formalisms, and their connection to canonical quantization. Details of Dirac's modified Hamiltonian formalism are also summarized to put the Dirac bracket in context. == Inadequacy of the standard Hamiltonian procedure == The standard development of Hamiltonian mechanics is inadequate in several specific situations: # When the Lagrangian is at most linear in the velocity of at least one coordinate; in which case, the definition of the canonical momentum leads to a ''constraint''. This is the most frequent reason to resort to Dirac brackets. For instance, the Lagrangian (density) for any fermion is of this form. # When there are gauge (or other unphysical) degrees of freedom which need to be fixed. # When there are any other constraints that one wishes to impose in phase space. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dirac bracket」の詳細全文を読む スポンサード リンク
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