Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 5th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 5–12, 2003. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-8-7/pbk). 189-202 (2004).
The construction of phase spaces in field theory is discussed. In particular, following a paper by G. J. Zuckerman
[In: Action principles and global geometry. Mathematical aspects of string theory, Proc. Conf., San Diego/Calif. 1986, Adv. Ser. Math. Phys. 1, 259–284 (1987; Zbl 0669.58014
)], the author reviews a Hamiltonian formulation of Lagrangian field theory – in terms of the variational bicomplex of a fixed trivial fiber bundle [for the definition of this bicomplex, see for example I. M. Anderson
, Introduction to the variational bicomplex. Mathematical aspects of classical field theory, Proc. AMS-IMS-SIAM Jt. Summer Res. Conf., Seattle/WA (USA) 1991, Contemp. Math. 132, 51–73 (1992; Zbl 0772.58013
); I. M. Anderson
and N. Kamran
, Acta Appl. Math. 41, 135–144 (1995; Zbl 0848.58043
)] – based on an extension to infinite dimensions of J.-M. Souriau’s symplectic approach to mechanics. The problem is how to build phase spaces in a covariant way, using directly the Lagrangian and not going through Dirac’s theory of constraints. A basic example is presented.