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- W1519040981 abstract "We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different structures on it; rotational, Lorentz, and Poincare groups; special relativity. The main body of the manuscript includes manifolds, tensor fields, differential forms, integration, Riemannian and Lorentzian metrics, connection on vector and frame fiber bundles, affine geometry, Lie groups, transformation groups, homotopy and fundamental group, coverings, principal and associated fiber bundles, connections on fiber bundles, Killing vector fields, geodesics and extremals, symplectic and Poisson manifolds, Clifford algebras, principle of least action, canonical formalism for constrained systems. Applications of differential geometry in quantum theory (adiabatic theorem, Berry phase, Aharonov-Bohm effect), general relativity and geometric theory of defects are described. We give introduction to general relativity and its Hamiltonian formulation; describe scalar, spinor, electromagnetic and Yang-Mills fields. Riemannian and Lorentzian surfaces with one Killing vector field are discussed in detail, and their global structure is described using conformal block method. We also classified all global vacuum solutions of the Einstein equations, which have the form of warped product metrics of two surfaces. The manuscript is not a textbook, and intended for efficient reader." @default.
- W1519040981 created "2016-06-24" @default.
- W1519040981 creator A5022253469 @default.
- W1519040981 date "2013-10-30" @default.
- W1519040981 modified "2023-10-14" @default.
- W1519040981 title "Geometrical methods in mathematical physics" @default.
- W1519040981 cites W135102837 @default.
- W1519040981 cites W147901058 @default.
- W1519040981 cites W1479864490 @default.
- W1519040981 cites W1485237738 @default.
- W1519040981 cites W1502238698 @default.
- W1519040981 cites W1503627717 @default.
- W1519040981 cites W1504171473 @default.
- W1519040981 cites W1507850137 @default.
- W1519040981 cites W1512669534 @default.
- W1519040981 cites W1520319125 @default.
- W1519040981 cites W1530671168 @default.
- W1519040981 cites W1531504342 @default.
- W1519040981 cites W1533708179 @default.
- W1519040981 cites W1533846756 @default.
- W1519040981 cites W1552284467 @default.
- W1519040981 cites W1557699146 @default.
- W1519040981 cites W1560640234 @default.
- W1519040981 cites W1572433104 @default.
- W1519040981 cites W1573443250 @default.
- W1519040981 cites W1573927207 @default.
- W1519040981 cites W1574748035 @default.
- W1519040981 cites W1575763248 @default.
- W1519040981 cites W1580334901 @default.
- W1519040981 cites W1586369843 @default.
- W1519040981 cites W1611138248 @default.
- W1519040981 cites W1622494512 @default.
- W1519040981 cites W1642629289 @default.
- W1519040981 cites W1652399295 @default.
- W1519040981 cites W165787586 @default.
- W1519040981 cites W1668733367 @default.
- W1519040981 cites W1678846034 @default.
- W1519040981 cites W1800127362 @default.
- W1519040981 cites W1853767801 @default.
- W1519040981 cites W1882908034 @default.
- W1519040981 cites W1937221913 @default.
- W1519040981 cites W1963826009 @default.
- W1519040981 cites W1966021391 @default.
- W1519040981 cites W1966205023 @default.
- W1519040981 cites W1969239776 @default.
- W1519040981 cites W1969993883 @default.
- W1519040981 cites W1970592709 @default.
- W1519040981 cites W1971778372 @default.
- W1519040981 cites W1972098605 @default.
- W1519040981 cites W1972611398 @default.
- W1519040981 cites W1973527254 @default.
- W1519040981 cites W1974672421 @default.
- W1519040981 cites W1974883060 @default.
- W1519040981 cites W1975742755 @default.
- W1519040981 cites W1977702809 @default.
- W1519040981 cites W1978261718 @default.
- W1519040981 cites W1981457060 @default.
- W1519040981 cites W1982418259 @default.
- W1519040981 cites W1982967959 @default.
- W1519040981 cites W1983894121 @default.
- W1519040981 cites W1985105826 @default.
- W1519040981 cites W1985642220 @default.
- W1519040981 cites W1985824899 @default.
- W1519040981 cites W1986458951 @default.
- W1519040981 cites W1987202415 @default.
- W1519040981 cites W1989845559 @default.
- W1519040981 cites W1993502123 @default.
- W1519040981 cites W1997016186 @default.
- W1519040981 cites W1997126380 @default.
- W1519040981 cites W1997756830 @default.
- W1519040981 cites W1998866932 @default.
- W1519040981 cites W2000109703 @default.
- W1519040981 cites W2000468000 @default.
- W1519040981 cites W2003792694 @default.
- W1519040981 cites W2005196146 @default.
- W1519040981 cites W2005905916 @default.
- W1519040981 cites W2005935750 @default.
- W1519040981 cites W2008028604 @default.
- W1519040981 cites W2008791564 @default.
- W1519040981 cites W2009113252 @default.
- W1519040981 cites W2009930506 @default.
- W1519040981 cites W201268085 @default.
- W1519040981 cites W2014019764 @default.
- W1519040981 cites W2016294505 @default.
- W1519040981 cites W2020000507 @default.
- W1519040981 cites W2020489222 @default.
- W1519040981 cites W2021037765 @default.
- W1519040981 cites W2021870751 @default.
- W1519040981 cites W2025148421 @default.
- W1519040981 cites W2027106837 @default.
- W1519040981 cites W2027710569 @default.
- W1519040981 cites W2027940825 @default.
- W1519040981 cites W2028402761 @default.
- W1519040981 cites W2028948400 @default.
- W1519040981 cites W2031828766 @default.
- W1519040981 cites W2033328945 @default.
- W1519040981 cites W2033896893 @default.
- W1519040981 cites W2034066066 @default.
- W1519040981 cites W2036676626 @default.
- W1519040981 cites W2038947716 @default.