MARC Record from harvard_bibliographic_metadata

LEADER: 05496cam a2200325Ia 4500
001 012573796-3
005 20120719021335.0
008 100106s2010 njua b 001 0 eng d
020 $a9789814299732
020 $a9814299731
035 0 $aocn496951805
040 $aBTCTA$beng$cBTCTA$dYDXCP$dEUX$dBWX$dCDX$dDGU
050 4 $aQC20$b.L43 2010
082 4 $a530
245 00 $aLectures on advanced mathematical methods for physicists /$cSunil Mukhi, N. Mukunda.
260 $aNew Jersey :$bWorld Scientific,$c2010.
300 $aviii, 278 p. :$bill. ;$c24 cm.
500 $a"Hindustan Book Agency"
504 $aIncludes bibliographical references (p.[273]-274) and index.
505 0 $a1. Topology. 1.1. Preliminaries. 1.2. Topological spaces. 1.3. Metric spaces. 1.4. Basis for a topology. 1.5. Closure. 1.6. Connected and compact spaces. 1.7. Continuous functions. 1.8. Homeomorphism. 1.9. Separability -- 2. Homotopy. 2.1. Loops and homotopies. 2.2. The fundamental group. 2.3. Homotopy type and contractibility. 2.4. Higher homotopy groups -- 3. Differentiable manifolds I. 3.1. The definition of a manifold. 3.2. Differentiation of functions. 3.3. Orient ability. 3.4. Calculus on manifolds : vector and tensor fields. 3.5. Calculus on manifolds : differential forms. 3.6. Properties of differential forms. 3.7. More about vectors and forms -- 4. Differentiable manifolds II. 4.1. Riemannian geometry. 4.2. Frames. 4.3. Connections, curvature and torsion. 4.4. The volume form. 4.5. Isometry. 4.6. Integration of differential forms. 4.7. Stokes' theorem. 4.8. The Laplacian on forms --
505 0 $a5. Homology and cohomology. 5.1. Simplicial homology. 5.2. De Rham cohomology. 5.3. Harmonic forms and de Rham cohomology -- 6. Fibre bundles. 6.1. The concept of a fibre bundle. 6.2. Tangent and cotangent bundles. 6.3. Vector bundles and principal bundles -- 7. Review of groups and related structures. 7.1. Definition of a group. 7.2. Conjugate elements, equivalence classes. 7.3. Subgroups and cosets. 7.4. Invariant (normal) subgroups, the factor group. 7.5. Abelian groups, commutator subgroup. 7.6. Solvable, nilpotent, semisimple and simple groups. 7.7. Relationships among groups. 7.8. Ways to combine groups - direct and semidirect products. 7.9. Topological groups, Lie groups, compact Lie groups --
505 0 $a8. Review of group representations. 8.1. Definition of a representation. 8.2. Invariant subspaces, reducibility, decomposability. 8.3. Equivalence of representations, Schur's lemma. 8.4. Unitary and orthogonal representations. 8.5. Contragredient, adjoint and complex conjugate representations. 8.6. Direct products of group representations -- 9. Lie groups and Lie algebras. 9.1. Local coordinates in a Lie group. 9.2. Analysis of associativity. 9.3. One-parameter subgroups and canonical coordinates. 9.4. Integrability conditions and structure constants. 9.5. Definition of a (real) Lie algebra : Lie algebra of a given Lie group. 9.6. Local reconstruction of Lie group from Lie algebra. 9.7. Comments on the G[symbol])[symbol] relationship. 9.8. Various kinds of and operations with Lie algebras -- 10. Linear representations of Lie algebras --
505 0 $a11. Complexification and classification of Lie algebras. 11.1. Complexification of a real Lie algebra. 11.2. Solvability, Levi's theorem, and Cartan's analysis of complex (semi) simple Lie algebras. 11.3. The real compact simple Lie algebras -- 12. Geometry of roots for compact simple Lie algebras -- 13. Positive roots, simple roots, Dynkin diagrams. 13.1. Positive roots. 13.2. Simple roots and their properties. 13.3. Dynkin diagrams -- 14. Lie algebras and Dynkin diagrams for SO(2l), SO(2l+1), USp(2l), SU(l+1). 14.1. The SO(2l) family - D[symbol] of Cartan. 14.2. The SO(2l+1) family - B[symbol] of Cartan. 14.3. The USp(2l) family - C[symbol] of Cartan. 14.4. The SU(l+1) family - A[symbol] of Cartan. 14.5. Coincidences for low dimensions and connectedness -- 15. Complete classification of all CSLA simple root systems. 15.1. Series of lemmas. 15.2. The allowed graphs [symbol]. 15.3. The exceptional groups --
505 0 $a16. Representations of compact simple Lie algebras. 16.1. Weights and multiplicities. 16.2. Actions of E[symbol] and SU(2)[symbol] - the Weyl group. 16.3. Dominant weights, highest weight of a UIR. 16.4. Fundamental UIR's, survey of all UIR's. 16.5. Fundamental UIR's for A[symbol], B[symbol], C[symbol], D[symbol]. 16.6. The elementary UIR's. 16.7. Structure of states within a UIR -- 17. Spinor representations for real orthogonal groups. 17.1. The Dirac algebra in even dimensions. 17.2. Generators, weights and reducibility of U(S) - the spinor UIR's of D[symbol]. 17.3. Conjugation properties of spinor UIR's of D[symbol]. 17.4. Remarks on antisymmetric tensors under D[symbol] = SO(2l). 17.5. The spinor UIR's of B[symbol] = SO(2l+[symbol]). 17.6. Antisymmetric tensors under B[symbol] = SO(2l+1) --
505 0 $a18. Spinor representations for real pseudo orthogonal groups. 18.1. Definition of SO(q,p) and notational matters. 18.2. Spinor representations S([symbol]) of SO(p,q) for p + q [symbol] 2l. 18.3. Representations related to S([symbol]). 18.4. Behaviour of the irreducible spinor representations S[symbol]. 18.5. Spinor representations of SO(p,q) for p+q = 2l+1. 18.6. Dirac, Weyl and Majorana spinors for SO(p,q).
650 0 $aMathematical physics.
700 1 $aMukhi, Sunil
700 1 $aMukunda, N.
988 $a20100922
906 $0OCLC