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Geroch R. — Mathematical physics
Geroch R. — Mathematical physics



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Название: Mathematical physics

Автор: Geroch R.

Аннотация:

Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the "whys" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle physics, and astrophysics.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 356

Добавлена в каталог: 18.11.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Lie algebra, quotient algebra      105
Lie algebra, real      104
Lie algebra, representation of      127
Lie algebra, subalgebra of      105
Lie algebra, universal enveloping algebra      106
Limit point      161
linear combination      46
Linear mapping      45
Linear mapping, continuous      244
Linear mapping, image of      58
Linear mapping, kernel of      58
Linearly independent      47
Locally compact      171
Locally simply connected      198
Loop      189
Loop space      189
Loop, zero loop      189
Mapping, continuous      147
Mapping, continuous linear      244
Mapping, image of      134
Mapping, inverse image of      134
Mapping, linear      45
Mapping, uniformly continuous      222
Maximal element      41
Measurable, function      259
Measurable, set      249
Measure of a set      249
Measure space      249
Measure space, disjoint union      257
Measure space, integral      264
Measure space, product      258
Measure space, sum      257
Measure, convergence in      269
Measure, Lebesque      253
Measure, space      249
Measure, subspace      257
Metric space      137
Momentum operator      333
Monomorphism      4
Morphism      3
Morphism, epi-      4
Morphism, identity      3
Morphism, iso-      7
Morphism, mono-      4
Multilinear mapping      71
n-cycle      206
n-cycle, boundary of      204
n-cycle, homologous      207
n-simplex      199
Neighborhood      138
Net      161
Net, accumulation point of      163
Net, Cauchy      225
Net, convergence of      161
Net, limit point of      161
Norm of operator      286
Norm of vector      277
Normal subgroup      29
Normal subgroup, generated      29
Object      3
Object, morphisfism of      3
Object, sub-      7
Open set      136
Operator      325
Operator, adjoint of      289 329
Operator, bounded      285
Operator, closed      340
Operator, configuration      332
Operator, domain of      325
Operator, eigenvalue      293
Operator, eigenvector      293
Operator, equality of      325
Operator, extension of      325
Operator, hermitian      290
Operator, inverse      295
Operator, invertible      295
Operator, momentum      333
Operator, projection      290
Operator, regular value      295
Operator, self-adjoint      330
Operator, spectral family of      319
Operator, spectrum of      295 339
Operator, unitary      292
Ordered by inclusion      40
Ordered, partially      40
Ordered, totally      40
Orthogonal vectors      281
Orthonormal basis      283
Partial ordering      40
Permutation group      17
Plane, punctured      188
Plane, topological      138
Product of measure spaces      258
Product, cartesian      10
Product, direct      18
Product, inner      277
Product, tensor      72
Projection operator      290
Punctured plane      188
Quotient, algebra      102 105
Quotient, group      30
Quotient, topology      152
Quotient, vector space      54
Real associative algebra      97
Real associative algebra, category of      98
Real Lie algebra      104
Real Lie algebra, category of      105
Real line      137
Real vector space      44
Real vector space, category of      45
Reals, additive group of      16
Reals, measure space of      253
Reals, topological group of      235
Reals, uniform space of      218
Region of integration      266
Regular value, of, operator      295
Relation      39
Relation, equivalence      39
Reparameterization      191
Representation      120 125
Representation of a group      125
Representation of a Lie algebra      125
Representation of associative algebra      125
Representation of object      120
Representation on vector space      125
Representation, direct product of      121
Representation, direct sum of      121
Representation, faithful      124
Representation, irreducible      128
Representation, sub-      122
Representation, tensor product of      126
Right coset      26
Self-adjoint operator      330
Semigroup      103
SEQUENCE      160
Sequence, Cauchy      225
Set, Cantor      255
Set, Cartesian product of      10
Set, category of      4
Set, disjoint union of      11
Set, empty      134
simplex      199
Simply connected      194
Space, Hilbert      277
Space, loop      189
Space, measure      249
Space, metric      137
Space, topological      136
Space, uniform      217
Space, vector      44
span      47
Spectral family      319
Spectrum of bounded operator      295
Spectrum of self-adjoint operator      339
square-integrable      279
Step function      260
Step function, integrable      262
Step function, integral of      262
Subalgebra of associative algebra      101
Subalgebra of Lie algebra      105
Subalgebra, Casimir      109
Subalgebra, generated      101 105
Subobject      7
Subobject, invariant      122
Subrepresentation      122
Subset      134
Subspace of Hilbert space      280
Subspace of vector space      53
Subspace, generated      53 281
Subspace, topological      151
Subspace, uniform      227
Subspaces, complementary      54
Sum of distributions      272
Sum of measures      257
Sum of vectors      44
Sum, direct      8
Superset      134
Support of distribution      274
Support of function      270
Tensor product of representations      126
Tensor product of vector spaces      72
Topological group      234
Topological group of reals      235
Topological group, category of      236
Topological group, category of complete      237
Topological group, complete      237
Topological group, completion of      237
Topological group, continuous homomorphism of      236
Topological plane      138
Topological space      136
Topological space, category of      154
Topological space, category of Hausdorff      154
Topological space, cohomology group      216
Topological space, connected      177
Topological space, connected component of      180
Topological space, contractible      198
Topological space, dense subset of      326
Topological space, direct product      155
Topological space, direct sum      157
Topological space, hausdorff      144
Topological space, homology group      208
Topological space, homotopy group      194
Topological space, isomorphism of      154
Topological space, locally compact      171
Topological space, locally simply connected      198
Topological space, net      161
Topological space, sequence      160
Topological space, simply connected      194
Topological space, subspace      151
Topological space, totally disconnected      181
Topological vector space      240
Topological vector space, category of      244
Topological vector space, category of complete      244
Topological vector space, complete      244
Topological vector space, completion of      244
Topological vector space, complex      242
Topological vector space, continuous, linear mapping      244
Topological vector space, real      240
topology      136
Topology, coarser      142
Topology, compact-open      172
Topology, discrete      136
Topology, finer      142
Topology, generated      143
Topology, indiscrete      136
Topology, induced      150 151
Topology, quotient      152
Totally disconnected      181
Totally ordered      40
Uniform space      217
Uniform space of reals      218
Uniform space, category of      223
Uniform space, category of complete      227
Uniform space, complete      226
Uniform space, completion of      227
Uniform space, entourage      217
Uniform space, subspace      227
Uniform space, uniformly continuous mapping      222
Uniformity      218
Uniformly continuous mapping      222
Union, disjoint      11
Unit, of associative algebra      103
Unitary operator      292
Universal enveloping algebra      106
Upper semicontinuous      314
Vector      44
Vector space      44
Vector space, basis      47
Vector space, category of complex      45
Vector space, category of real      45
Vector space, category of topological      244
Vector space, complementary subspace      54
Vector space, complete topological      244
Vector space, completion of topological      244
Vector space, complex      44
Vector space, coset      54
Vector space, dimension of      51
Vector space, direct product of      59
Vector space, direct sum of      59
Vector space, dual of      65
Vector space, free      45
Vector space, infinite-dimensional      51
Vector space, linear mapping of      45
Vector space, multilinear mapping of      71
Vector space, quotient space      54
Vector space, real      44
Vector space, representation of      125
Vector space, subspace      53
Vector space, tensor product of      72
Vector space, topological      240
Vectors, linear combination of      46
Vectors, linearly independent      47
Vectors, span      47
Zero loop      189
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