Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Isham C. — Modern Differential Geometry for Physicists
Isham C. — Modern Differential Geometry for Physicists

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Modern Differential Geometry for Physicists

Автор: Isham C.

Аннотация:

These lecture notes are the content of an introductory course on modern, co-ordinate-free differential geometry which is taken by first-year theoretical physics PhD students, or by students attending the one-year MSc course, "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen bearing in mind the way in which differential geometry is applied to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields, nonlinear sigma models and other types of nonlinear field systems that feature in modern quantum field theory. This edition of the text contains an additional chapter that introduces some of the basic ideas of general topology needed in differential geometry. A number of small corrections and additions have also been made. The volume is divided into four parts. The first provides an introduction to general topology, the second covers introductory co-ordinate-free differential geometry, the third examines geometrical aspects of the theory of Lie groups and Lie group actions on manifolds, and the fourth provides an introduction to the theory of fibre bundles. In the introduction to differential geometry the author lays considerable stress on the basic ideas of "tangent space structure", which he develops from several different points of view - some geometrical, others more algebraic.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 306

Добавлена в каталог: 23.11.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$(x,y)_G$      233
$(\frac{\partial}{\partial{x^{\mu}}})_p$f      81
$Ad_g$      162
$Aut(\xi)$      226
$A^c$      11
$A_L$      160
$B^n(\mathcal{M})$      142
$B_F(\mathcal{M})$      218
$B_{\epsilon}(\overrightarrow{x})$      5
$C([a,b],\mathds{R})$      9
$C^{\infty}$      62
$dx^m$      125
$D\omega$      272
$f^{-1}(a)$      48
$F{\rightarrow}E{\rightarrow}^{\pi}{\mathcal{M}$      204
$GL^{+}(n,\mathds{R}$)      154
$g_p$      180
$h^*(k)$      127
$H^n_{DR}(\mathcal{M})$      143
$h_{*}(\upsilon)$      78
$h_{*}X$      105
$I_p$      250
$i_q$      94
$j_p$      94
$l^2 (X)$      9
$L^A$      159
$L^{*}(G)$      171
$l_g$      150
$L_{X^f}$      98
$L_{X^Y}$      116
$L_{X^{\omega}}$      130
$O_p$      180
$P_F$      233
$R_A$      162
$r_g$      150
$S^1$      65
$S^n$      68
$S^{\infty}$      229
$T\mathcal{M}$      74
$T^{*} \mathcal{M}$      123
$T^{*}_{p} \mathcal{M}$      123
$T^{r,s}_{p} \mathcal{M}$      133
$T_n$      5
$T_{p} \mathcal{M}$      74
$V^{*}$      121
$V_p P$      254
$X^a$      191
$x^{\mu}$      63
$x_n \rightarrow^{N(x)} x$      24
$X_p$      97
$X_p$(f)      99
$X_u$      98
$Z^n(\mathcal{M})$      142
$\alpha := \beta$      4
$\alpha\vdash\beta$      26
$\exists$      24
$\frac{\partial x^{\prime\nu}}{\partial x^{\mu}}$      101
$\gamma(E)$      248
$\lambda ^d$      171
$\mathbf{B}(\mathcal{M})$      223
$\mathbf{Z}$      16
$\mathcal{F}([a,b],\mathds{R})$      24
$\mathcal{G}$      224
$\mathcal{L}_{X^f}$      98
$\mathcal{M}(\xi)$      204
$\mathcal{M}_p$      192
$\mathcal{N}(X)$      34
$\mathcal{N}^{(2)} (x) \cong \mathcal{N}^{(1)} (x)$      26
$\mathcal{U}$F      219
$\mathds{C}$      4
$\mathds{C}P^n$      188
$\mathds{C}P^{\infty}$      229
$\mathds{C}^{\infty}(\mathcal{M})$      79
$\mathds{C}_{*}$      222
$\mathds{R} P^n$      188
$\mathds{R}$      5
$\mathds{r}^n$      5
$\mathds{r}_{+}$      110
$\mathfrak{n}$-form      135
$\mathfrak{n}$-form closed      142
$\mathfrak{n}$-form exact      142
$\mathfrak{n}$-form left-invariant      171
$\mathfrak{n}$-form right-invariant      171
$\mathfrak{n}$-form, exterior derivative of      137
$\mathfrak{n}$-form, exterior product of      135
$\omega_1 \wedge \omega_2$      135
$\omega_\eta$      219
$\omega_\mu$      126
$\overline{A}$      53
$\overrightarrow{a}\cdot\overrightarrow{b}$      5
$\overrightarrow{x}$      5
$\overrightarrow{x}_n \rightarrow\overrightarrow{x}$      5
$\preceq$      15
$\tau(x)$      34
$\tau(р_0,р)$      234
$\Upsilon$      95
$\upsilon$(f)      75
$\widetilde{s}$(x)      218
$\xi$[F]      233
$\{x|P(x)\}$      4
$\|u\|$      8
${A^n}(\mathcal{M})$      135
${D_p}\mathcal{M}$      80
${h^*}\omega$      127
${\alpha}^{\uparrow}$      263
${\bigoplus}^r$V      133
${\langle}L,\upsilon\rangle$      121
${\nabla}_{|\alpha|}$      269
${\upsilon}^{\mu}$      87
$|X|$      34
(E,$\pi,\mathcal{M}$)      202
a$\cup$b      146
A$\subset$B      5
A$\times$B      6
a$\vee$b      19
a$\wedge$b      18
Accumulation point      47
Adjoint map      162
Anti-homomorphism      152
Associated bundle      233
Associated bundle, automorphism group of      239
Associated bundle, local isomorphism between pair of      237
Associated bundle, map between pair of      237
Associated bundle, trivial      237
Bd(A)      12
Bianchi identity      274
Billiard-ball hairy      101
Boolean algebra      20 42
Boundary of a set      12
Boundary point      12 31
Bundle      202
Bundle $C^{\infty}$      204
Bundle base space      202
Bundle cross-section of      see "Cross-section"
Bundle etale      212
Bundle fibre      204
Bundle fibre over x      202
Bundle G      220
Bundle isomorphism between a pair of      215
Bundle local isomorphism between a pair of      215
Bundle locally trivial      216
Bundle M-map      215
Bundle map      214
Bundle map, composition of pair of      215
Bundle normal      210
Bundle normal, of an embedding      249
Bundle of tensors      236
Bundle product      204
Bundle projection map of      202
Bundle pull-back      217
Bundle restriction to subset of base space      213
Bundle sub      213
Bundle total space      202
Bundle trivial      216
Bundle universal      219 228 232
Canonical      110
Cartan structural equation      272
Cartan — Maurer equation      173
Cartan — Maurer form      173 257
Cartesian product      6 36 64
Characteristic class      219 231
Closed set      13 31 35
Closure      53
Collection of subsets coarser than      26
Commutation relations affine      111
Compact space      47
Connection affine sum of pair of      256
Connection local representative of      256
Connection principal bundle in      254
Coordinate chart      61
Coordinate chart, atlas of      62
Coordinate chart, domain of      61
Coordinate functions      63
coordinates      63
Cotangent bundle      123
Cotangent space      123
Cotangent vector      123
Covariant derivative      269 270
Covering space      210
Cross-section      200 207 241
Cross-section, associated bundle of      246
Cross-section, local representative of      247
Cross-section, principal bundle of      230
Cross-section, product bundle of      207
Cross-section, pull-back of      218
Cross-section, tangent bundle of      98
Curvature two-form      272
Curve, definition of      73
Curve, horizontal lift of      263
Curve, tangent pair of      73
d(x,y)      6
deRham complex      141 171
DeRham's theorem      217
Derivation at a point      80
Derivation of the ring $C^{\infty}(\mathcal{M})$      99
Derivation, components of      84
df      131
Diff($\mathcal{M}$)      70
Diffeomorphism, definition of      70
Diffeomorphism, group of      70 224 229
Diffeomorphism, one-parameter group of      111
Differentiable manifold      62
Differentiable manifold, complex      63
Differentiable manifold, infinite-dimensional      63
Differential structure      62
Directed set      46
Directional derivative      75
Dual vector space      121
Dual vector space, dual basis of      121
Dual vector space, dual map between pair of      121
E($\xi$)      204
Eilenberg — MacLane space      228
Equivalence exact sequence      255
exp A      165
Exponential map      165
Ext(A)      12
Exterior derivative covariant      272
Exterior derivative, function of      131
Exterior of a set      12
Exterior point      12 31
f:A$\rightarrow$B      6
Filter base      29 47 50
Filter base, convergence with respect to      30
Filter, definition of      29
Filter, subbase      31
Filter, ultra      45
Finer than      26
First countable space      see "Topology first
Function $C^r$      69
Function continuous      49
Function diagonal      95
Function differentiable      70
Function distance      5
Function equivariant      178
Function inverse set      48
Function smooth      70
Function, homotopic pair of      145 218
Function, local representative of      69
G-product      232
Gauge group      16 224 229 231 258
Gauge orbit      16
Gauge transformation      224 226 239 258
GL(n,$\mathds{C}$)      153
GL(n,$\mathds{R}$)      152
Gribov effect      231
Group action      52
Group action, orbit of      52
Group Lorentz      157
Group, action on a set      175
Group, action on a set, free      179
Group, action on a set, kernel of      179
Group, action on a set, orbit of      180
Group, action on a set, orbit space of      182
Group, action on a set, stability group of      180
Group, action on a set, transitive      179
Group, adjoint representation of      168
Group, cohomology      201 217 219 229 232 242
Group, general linear, complex      284
Group, general linear, real      152
Group, holonomy      267
Group, homotopy      228 229 242 246
Group, left translation of      150
Group, orthogonal      155
Group, orthogonal special      157
Group, partial      113
Group, right translation of      150
Group, special linear      154
Group, special unitary      157
Group, spin      225
Group, topological      151
Group, unitary      157
Hausdorff space      see "Topology Hausdorff"
Heyting algebra      42
Homeomorphism      51
Homotopic functions      see "Function homotopic
Hopf bundle      222
hor($\tau$)      255
Horizontal subspace      268
Instanton      201 222 226 243
Int(A)      12
Integral curve      see "Vector field integral
Interior of a set      12
Interior point      12 31
Intuitionistic logic      42
Isotropy group      see "Group action stability
Jacobi identity      103
Jacobian matrix      88
K($\pi$,n)      228
Kaluza — Klein theory      201
Klein bottle      205
L(G)      158
Lattice a topology as an example      40
Lattice anti-atomic      45
Lattice atomic      44
Lattice complete      19 41
Lattice distributive      19 41
Lattice example of closed linear subspaces of a Hilbert space      22
Lattice structure on space of topologies      43
Lattice, definition of      19
Lattice, null element in      19
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте