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LEADER: 03234mam a2200361 a 4500
001 2820062
005 20221013020506.0
008 000428t20012001riu b 001 0 eng
010 $a 00033139
020 $a0821820567 (alk. paper)
035 $a(OCoLC)ocm44084035
035 $9ARU1259CU
035 $a(NNC)2820062
035 $a2820062
040 $aDLC$cDLC$dNNC$dOrLoB-B
041 1 $aeng$hger
050 00 $aQA649$b.B47 2001
082 00 $a516.3/6$221
100 1 $aBerndt, Rolf,$d1940-$0http://id.loc.gov/authorities/names/n98029558
240 10 $aEinführung in die symplektische Geometrie.$lEnglish$0http://id.loc.gov/authorities/names/n00011243
245 13 $aAn introduction to symplectic geometry /$cRolf Berndt ; translated by Michael Klucznik.
260 $aProvidence, R.I. :$bAmerican Mathematical Society,$c[2001], ©2001.
300 $axvi, 195 pages ;$c26 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aGraduate studies in mathematics,$x1065-7339 ;$vv. 26
504 $aIncludes bibliographical references (p. 185-187) and index.
505 00 $tSome Aspects of Theoretical Mechanics.$tThe Lagrange equations.$tHamilton's equations.$tThe Hamilton-Jacobi equation.$tA symplectic interpretation.$tHamilton's equations via the Poisson bracket.$tTowards quantization --$gCh. 1.$tSympletic Algebra.$tSymplectic vector spaces.$tSymplectic morphisms and symplectic groups.$tSubspaces of symplectic vector spaces.$tComplex structures of real symplectic spaces --$gCh. 2.$tSymplectic Manifolds.$tSymplectic manifolds and their morphisms.$tDarboux's theorem.$tThe cotangent bundle.$tKahler manifolds.$tCoadjoint oribits.$tComplex projective space.$tSymplectic invariants (a quick view) --$gCh. 3.$tHamiltonian Vector Fields and the Poisson Bracket.$tPreliminaries.$tHamiltonian systems.$tPoisson brackets.$tContact manifolds --$gCh. 4.$tThe Moment Map.$tDefinitions.$tConstructions and examples.$tReduction of phase spaces by the consideration of symmetry --$gCh. 5.$tQuantization.$tHomogeneous quadratic polynomials and sl[subscript 2].
505 80 $tPolynomials of degree 1 and the Heisenberg group.$tPolynomials of degree 2 and the Jacobi group.$tThe Groenewold-van Hove theorem.$tTowards the general case.$gApp. A.$tDifferentiable Manifolds and Vector Bundles.$tDifferentiable manifolds and their tangent spaces.$tVector bundles and their sections.$tThe tangent and the cotangent bundles.$tTensors and differential forms.$tConnections.$gApp. B.$tLie Groups and Lie Algebras.$tLie algebras and vector fields.$tLie groups and invariant vector fields.$tOne-parameter subgroups and the exponent map.$gApp. C.$tA Little Cohomology Theory.$tCohomology of groups.$tCohomology of Lie algebras.$tCohomology of manifolds.$gApp. D.$tRepresentations of Groups.$tLinear representations.$tContinuous and unitary representations.$tOn the construction of representations.
650 0 $aSymplectic manifolds.$0http://id.loc.gov/authorities/subjects/sh85131553
650 0 $aGeometry, Differential.$0http://id.loc.gov/authorities/subjects/sh85054146
830 0 $aGraduate studies in mathematics ;$vv. 26.$0http://id.loc.gov/authorities/names/n92111274
852 00 $bmat$hQA649$i.B47 2001