close
1.

図書
図書
1. Topology and geometry for physicists (: pbk)
Charles Nash, Siddhartha Sen
出版情報: London ; Tokyo : Academic Press, 1983  x, 311 p. ; 24 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface
Basic Notions of Topology and the Value of Topological Reasoning
Differential Geometry
Manifolds and Differential Forms
The Fundamental Group
The Homology Groups
The Higher Homotopy Groups
Cohomology and De Rham Cohomology
Fibre Bundles and Further Differential Geometry
Morse Theory
Defects, Textures, and Homotopy Theory
Yang-Mills Theories
Instantons and Monopoles
Subject Index
Preface
Basic Notions of Topology and the Value of Topological Reasoning
Differential Geometry
2.

図書
図書
2. Symplectic techniques in physics
Victor Guillemin, Shlomo Sternberg
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1984  xi, 468 p. ; 24 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface
Introduction / I：
Gaussian optics / 1：
Hamilton's method in Gaussian optics / 2：
Fermat's principle / 3：
From Gaussian optics to linear optics / 4：
Geometrical optics, Hamilton's method, and the theory of geometrical aberrations / 5：
Fermat's principle and Hamilton's principle / 6：
Interference and diffraction / 7：
Gaussian integrals / 8：
Examples in Fresnel optics / 9：
The phase factor / 10：
Fresnel's formula / 11：
Fresnel optics and quantum mechanics / 12：
Holography / 13：
Poisson brackets / 14：
The Heisenberg group and representation / 15：
The Groenwald-van Hove theorem / 16：
Other quantizations / 17：
Polarization of light / 18：
The coadjoint orbit of a semidirect product / 19：
Electromagnetism and the determination of symplectic structures / 20：
Epilogue: Why symplectic geometry?
The geometry of the moment map / II：
Normal forms / 21：
The Darboux-Weinstein theorem / 22：
Kaehler manifolds / 23：
Left-invariant forms and Lie algebra cohomology / 24：
Symplectic group actions / 25：
The moment map and some of its properties / 26：
Group actions and foliations / 27：
Collective motion / 28：
Cotangent bundles and the moment map for semidirect products / 29：
More Euler-Poisson equations / 30：
The choice of a collective Hamiltonian / 31：
Convexity properties of toral group actions / 32：
The lemma of stationary phase / 33：
Geometric quantization / 34：
Motion in a Yang-Mills field and the principle of general covariance / III：
The equations of motion of a classical particle in a Yang-Mills field / 35：
Curvature / 36：
The energy-momentum tensor and the current / 37：
The principle of general covariance / 38：
Isotropic and coisotropic embeddings / 39：
Symplectic induction / 40：
Symplectic slices and moment reconstruction / 41：
An alternative approach to the equations of motion / 42：
The moment map and kinetic theory / 43：
Complete integrability / IV：
Fibrations by tori / 44：
Collective complete integrability / 45：
Collective action variables / 46：
The Kostant-Symes lemma and some of its variants / 47：
Systems of Calogero type / 48：
Solitons and coadjoint structures / 49：
The algebra of formal pseudodifferential operators / 50：
The higher-order calculus of variations in one variable / 51：
Contractions of symplectic homogeneous spaces / V：
The Whitehead lemmas / 52：
The Hochschild-Serre spectral sequence / 53：
Galilean and Poincare elementary particles / 54：
Coppersmith's theory / 55：
References
Index
Preface
Introduction / I：
Gaussian optics / 1：
3.

図書
図書
3. Differential geometry for physicists : Stony Brook lectures
Andrzej Trautman
出版情報: Napoli : Bibliopolis, c1984  145 p. ; 23 cm
シリーズ名: Monographs and textbooks in physical science ; 2
所蔵情報: loading…
4.

図書
図書
4. Geometrical methods of mathematical physics (: pbk)
Bernard F. Schutz
出版情報: Cambridge ; New York : Cambridge University Press, 1980  xii, 250 p. ; 24 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface
Some basic mathematics / 1：
The space R[superscript n] and its topology / 1.1：
Mappings / 1.2：
Real analysis / 1.3：
Group theory / 1.4：
Linear algebra / 1.5：
The algebra of square matrices / 1.6：
Bibliography / 1.7：
Differentiable manifolds and tensors / 2：
Definition of a manifold / 2.1：
The sphere as a manifold / 2.2：
Other examples of manifolds / 2.3：
Global considerations / 2.4：
Curves / 2.5：
Functions on M / 2.6：
Vectors and vector fields / 2.7：
Basis vectors and basis vector fields / 2.8：
Fiber bundles / 2.9：
Examples of fiber bundles / 2.10：
A deeper look at fiber bundles / 2.11：
Vector fields and integral curves / 2.12：
Exponentiation of the operator d/d[lambda] / 2.13：
Lie brackets and noncoordinate bases / 2.14：
When is a basis a coordinate basis? / 2.15：
One-forms / 2.16：
Examples of one-forms / 2.17：
The Dirac delta function / 2.18：
The gradient and the pictorial representation of a one-form / 2.19：
Basis one-forms and components of one-forms / 2.20：
Index notation / 2.21：
Tensors and tensor fields / 2.22：
Examples of tensors / 2.23：
Components of tensors and the outer product / 2.24：
Contraction / 2.25：
Basis transformations / 2.26：
Tensor operations on components / 2.27：
Functions and scalars / 2.28：
The metric tensor on a vector space / 2.29：
The metric tensor field on a manifold / 2.30：
Special relativity / 2.31：
Lie derivatives and Lie groups / 2.32：
Introduction: how a vector field maps a manifold into itself / 3.1：
Lie dragging a function / 3.2：
Lie dragging a vector field / 3.3：
Lie derivatives / 3.4：
Lie derivative of a one-form / 3.5：
Submanifolds / 3.6：
Frobenius' theorem (vector field version) / 3.7：
Proof of Frobenius' theorem / 3.8：
An example: the generators of S[superscript 2] / 3.9：
Invariance / 3.10：
Killing vector fields / 3.11：
Killing vectors and conserved quantities in particle dynamics / 3.12：
Axial symmetry / 3.13：
Abstract Lie groups / 3.14：
Examples of Lie groups / 3.15：
Lie algebras and their groups / 3.16：
Realizations and representations / 3.17：
Spherical symmetry, spherical harmonics and representations of the rotation group / 3.18：
Differential forms / 3.19：
The algebra and integral calculus of forms / A：
Definition of volume -- the geometrical role of differential forms / 4.1：
Notation and definitions for antisy mmetric tensors / 4.2：
Manipulating differential forms / 4.3：
Restriction of forms / 4.5：
Fields of forms / 4.6：
Handedness and orientability / 4.7：
Volumes and integration on oriented manifolds / 4.8：
N-vectors, duals, and the symbol [epsilon][subscript ij...k] / 4.9：
Tensor densities / 4.10：
Generalized Kronecker deltas / 4.11：
Determinants and [epsilon][subscript ij...k] / 4.12：
Metric volume elements / 4.13：
The differential calculus of forms and its applications / B：
The exterior derivative / 4.14：
Notation for derivatives / 4.15：
Familiar examples of exterior differentiation / 4.16：
Integrability conditions for partial differential equations / 4.17：
Exact forms / 4.18：
Proof of the local exactness of closed forms / 4.19：
Lie derivatives of forms / 4.20：
Lie derivatives and exterior derivatives commute / 4.21：
Stokes' theorem / 4.22：
Gauss' theorem and the definition of divergence / 4.23：
A glance at cohomology theory / 4.24：
Differential forms and differential equations / 4.25：
Frobenius' theorem (differential forms version) / 4.26：
Proof of the equivalence of the two versions of Frobenius' theorem / 4.27：
Conservation laws / 4.28：
Vector spherical harmonics / 4.29：
Applications in physics / 4.30：
Thermodynamics
Simple systems / 5.1：
Maxwell and other mathematical identities / 5.2：
Composite thermodynamic systems: Caratheodory's theorem / 5.3：
Hamiltonian mechanics
Hamiltonian vector fields / 5.4：
Canonical transformations / 5.5：
Map between vectors and one-forms provided by [characters not reproducible] / 5.6：
Poisson bracket / 5.7：
Many-particle systems: symplectic forms / 5.8：
Linear dynamical systems: the symplectic inner product and conserved quantities / 5.9：
Fiber bundle structure of the Hamiltonian equations / 5.10：
Electromagnetism / C：
Rewriting Maxwell's equations using differential forms / 5.11：
Charge and topology / 5.12：
The vector potential / 5.13：
Plane waves: a simple example / 5.14：
Dynamics of a perfect fluid / D：
Role of Lie derivatives / 5.15：
The comoving time-derivative / 5.16：
Equation of motion / 5.17：
Conservation of vorticity / 5.18：
Cosmology / E：
The cosmological principle / 5.19：
Lie algebra of maximal symmetry / 5.20：
The metric of a spherically symmetric three-space / 5.21：
Construction of the six Killing vectors / 5.22：
Open, closed, and flat universes / 5.23：
Connections for Riemannian manifolds and gauge theories / 5.24：
Introduction / 6.1：
Parallelism on curved surfaces / 6.2：
The covariant derivative / 6.3：
Components: covariant derivatives of the basis / 6.4：
Torsion / 6.5：
Geodesics / 6.6：
Normal coordinates / 6.7：
Riemann tensor / 6.8：
Geometric interpretation of the Riemann tensor / 6.9：
Flat spaces / 6.10：
Compatibility of the connection with volume-measure or the metric / 6.11：
Metric connections / 6.12：
The affine connection and the equivalence principle / 6.13：
Connections and gauge theories: the example of electromagnetism / 6.14：
Solutions and hints for selected exercises / 6.15：
Notation
Index
Appendix
Preface
Some basic mathematics / 1：
The space R[superscript n] and its topology / 1.1：
5.

図書
図書
5. Mathematical topics between classical and quantum mechanics
N.P. Landsman
出版情報: New York : Springer, c1998  xix, 529 p. ; 24 cm
シリーズ名: Springer monographs in mathematics
所蔵情報: loading…
6.

図書
図書
6. Clifford algebras and spinor structures : a special volume dedicated to the memory of Albert Crumeyrolle, 1919-1992
edited by Rafał Abłamowicz and Pertti Lounesto
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1995  xx, 421 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 321
所蔵情報: loading…
7.

図書
図書
7. Ordinary and stochastic differential geometry as a tool for mathematical physics
by Yuri E. Gliklikh
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1996  xvi, 189 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 374
所蔵情報: loading…
8.

図書
図書
8. Methods of noncommutative analysis : theory and applications
Vladimir E. Nazaikinskii, Victor E. Shatalov, Boris Yu. Sternin
出版情報: Berlin ; New York : Walter de Gruyter, 1996  x, 373 p. ; 25 cm
シリーズ名: De Gruyter studies in mathematics ; 22
所蔵情報: loading…
9.

図書
図書
9. Algebraic foundations of non-commutative differential geometry and quantum groups
Ludwig Pittner
出版情報: New York ; Berlin : Springer, c1996  xii, 469 p. ; 24 cm
シリーズ名: Lecture notes in physics ; . New series m, Monographs ; m39
所蔵情報: loading…
10.

図書
図書
10. Geometric quantization
by Nicholas Woodhouse
出版情報: Oxford : Clarendon Press, 1980  xi, 316 p. ; 24 cm
所蔵情報: loading…
目次情報: 続きを見る
Symplectic Geometry / 1：
Lagrangian and Hamiltonian Mechanics / 2：
Symmetry / 3：
Hamilton-Jacobi Theory / 4：
Complex Polarizations / 5：
Elementary Relativistic Systems / 6：
Classical Fields / 7：
Prequantization / 8：
Quantization / 9：
The Metaplectic Correction / 10：
Symplectic Geometry / 1：
Lagrangian and Hamiltonian Mechanics / 2：
Symmetry / 3：
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼