Marsden, Jerrold E. (1982) Spaces of solutions of relativistic field theory with constraints. In: Differential geometric methods in mathematical physics, Clausthal 1980 : proceedings of an international conference held at the Technical University of Clausthal, FRG, July 23-25, 1980. Lecture Notes in Mathematics (905). Springer-Verlag , New York, pp. 29-43. ISBN 0387111972 http://resolver.caltech.edu/CaltechAUTHORS:20100825-105142237
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In this paper I shall explain how the reduction results of Marsden and Weinstein  can be used to study the space of solutions of relativistic field theories. Two of the main examples that will be discussed are the Einstein equations and the Yang-Mills equations. The basic paper on spaces of solutions is that of Segal . That paper deals with unconstrained systems and is primarily motivated by semilinear wave equations. We are mainly concerned here with systems with constraints in the sense of Dirac. Roughly speaking, these are systems whose four dimensional Euler-Lagrange equations are not all hyperbolic but rather split into hyperbolic evolution equations and elliptic constraint equations.
|Item Type:||Book Section|
|Additional Information:||© 1982, Springer-Verlag. Dedicated to Professor Bleuler on the occasion of his retirement. Research partially supported by the National Science Foundation.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||14 Sep 2010 18:03|
|Last Modified:||26 Dec 2012 12:21|
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