Mathematical PhysicsMathematical 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. |
Was andere dazu sagen - Rezension schreiben
Es wurden keine Rezensionen gefunden.
Inhalt
Introduction | 2 |
Categories | 4 |
The Category of Groups | 17 |
Subgroups | 25 |
Normal Subgroups | 30 |
Homomorphisms | 33 |
Direct Products and Sums of Groups | 36 |
Relations | 40 |
Compactness | 166 |
The CompactOpen Topology | 173 |
Connectedness | 178 |
Example Dynamical Systems | 184 |
Homotopy | 189 |
Homology | 200 |
Homology Relation to Homotopy | 212 |
The Homology Functors | 215 |
The Category of Vector Spaces | 45 |
Subspaces | 54 |
Linear Mappings Direct Products and Sums | 59 |
From Real to Complex Vector Spaces and Back | 63 |
Duals | 66 |
Multilinear Mappings Tensor Products | 72 |
Example Minkowski Vector Space | 80 |
Example The Lorentz Group | 88 |
Functors | 91 |
The Category of Associative Algebras | 98 |
The Category of Lie Algebras | 105 |
Example The Algebra of Observables | 112 |
Example Fock Vector Space | 115 |
Representations General Theory | 121 |
Representations on Vector Spaces | 126 |
The Algebraic Categories Summary | 133 |
Subsets and Mappings | 135 |
Topological Spaces | 137 |
Continuous Mappings | 148 |
The Category of Topological Spaces | 155 |
Nets | 161 |
Uniform Spaces | 218 |
The Completion of a Uniform Space | 226 |
Topological Groups | 235 |
Topological Vector Spaces | 241 |
Categories Summary | 249 |
Measure Spaces | 250 |
Constructing Measure Spaces | 258 |
Measurable Functions | 260 |
Integrals | 263 |
Distributions | 271 |
Hilbert Spaces | 278 |
Bounded Operators | 286 |
The Spectrum of a Bounded Operator | 294 |
The Spectral Theorem Finitedimensional Case | 303 |
Continuous Functions of a Hermitian Operator | 307 |
Other Functions of a Hermitian Operator | 312 |
The Spectral Theorem | 320 |
Operators Not Necessarily Bounded | 325 |
SelfAdjoint Operators | 330 |
| 344 | |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
action addition applied associative algebra basis bounded operator called Cauchy chapter choose claim clearly closed collection commutes compact complex composition condition connected consider consisting construction contains continuous mapping converges corresponding coset cover define definition denote diagram direct sum distribution element entourage equivalence example Exercise exists fact figure Finally Find function functor give given Hence Hermitian operator Hilbert space homomorphism homotopy identity immediate integrable intersection isomorphism Lie algebra linear mapping loop measure space morphism neighborhood normal Note notion object observer obtain open sets particular physical positive Proof properties Prove real line real number regard relation representation representative satisfied sends sequence Similarly square-integrable step structure subgroup subset subspace Suppose theorem tion topological space topological vector space uniform space union unique vector space whence write zero
Verweise auf dieses Buch
Symmetries and Curvature Structure in General Relativity Graham S. Hall Keine Leseprobe verfügbar - 2004 |
Bibliografische Informationen
| Titel | Mathematical Physics Chicago Lectures in Physics |
| Autor/in | Robert Geroch |
| Ausgabe | illustriert |
| Verlag | University of Chicago Press, 1985 |
| ISBN | 0226288625, 9780226288628 |
| Länge | 351 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |