zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On phase spaces and the variational bicomplex (after G. Zuckerman). (English) Zbl 1065.37046
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.
37K05Hamiltonian structures, symmetries, variational principles, conservation laws
70S05Lagrangian formalism and Hamiltonian formalism
53D05Symplectic manifolds, general
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies