close
1.

図書
図書
1. Partial differential equations of mathematical physics and integral equations
Ronald B. Guenther and John W. Lee
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1988  xii, 544 p. ; 25 cm
所蔵情報: loading…
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. Rotating fields in general relativity
Jamal Nazrul Islam
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1985  vi, 122 p. ; 24 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface
Introduction / 1：
The Einstein equations for a rotating metric and some classes of solutions / 2：
The Kerr and Timimatsu-Sato solutions / 3：
Rotating neutral dust / 4：
rotating Einstein-Maxwell fields / 5：
Rotating charged dust / 6：
Appendix
References
Index
Preface
Introduction / 1：
The Einstein equations for a rotating metric and some classes of solutions / 2：
4.

図書
図書
4. Supermanifolds (: pbk.)
Bryce DeWitt
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1984  xiv, 316 p. ; 24 cm
シリーズ名: Cambridge monographs on mathematical physics
所蔵情報: loading…
目次情報: 続きを見る
Preface to the first edition
Preface to the second edition
Analysis over supernumbers / 1：
Supernumbers and superanalytic functions / 1.1：
Grassmann algebras
Supernumbers
c-numbers and a-numbers
Superanalytic functions of supernumbers
Integration of superanalytic functions of supernumbers
Real supernumbers. Differentiable functions of real c-numbers and their integrals / 1.2：
Complex conjugation
Functions, distributions and integrals over R[subscript c]
Fourier transforms over R[subscript c]
Functions and integrals over R[subscript a] / 1.3：
Basic definitions
Fourier transforms over R[subscript a]
Integrals over R[superscript n][subscript a]
Supervector spaces / 1.4：
Definition
Bases
Pure bases
Pure real bases
Standard bases
Linear transformations, supertranspositions and dual supervector spaces / 1.5：
Change of basis
Shifting indices. The supertranspose
Extensions of the supertransposition rules
Dual supervector spaces
Dual bases
Further index-shifting conventions
The supertrace and the superdeterminant / 1.6：
The supertrace
The superdeterminant
The superdeterminant in special cases
The superdeterminant in the general case
Integration over R[superscript m][subscript c] [times] R[superscript n][subscript a] / 1.7：
Notation
Integration
Homogeneous linear transformations of the a-number coordinates
Homogeneous linear transformations of all the coordinates
Nonlinear transformations
Gaussian integrals over R[superscript m][subscript c] [times] R[superscript n][subscript a]
Exercises
Comments on chapter 1
Supermanifolds / 2：
Definition and structure of supermanifolds / 2.1：
Topology of R[superscript m][subscript c] [times] R[superscript n][subscript a]. Differentiable mappings
Supermanifolds, charts and atlases
Scalar fields and supercurves
Diffeomorphisms and embeddings
Ordinary manifolds. Skeleton and body of a supermanifold
Projectively Hausdorff, compact, paracompact and orientable supermanifolds. Realizations of the body
Supervector structures on supermanifolds / 2.2：
Scalar fields as supervectors
Contravariant vector fields
Alternative presentation of contravariant vector fields
Components
Tangent spaces
Tangents to supercurves
Super Lie brackets, local frames and covariant vector fields / 2.3：
Supercommutators and antisupercommutators
A matter of notation
The super Lie bracket
Local frames
Super Lie brackets of local frame fields
Covariant vector fields
Differentials
Tensor fields / 2.4：
Tensors at a point
The supervector space T[superscript r] [subscript s](p)
Tensor products
Tensor and multitensor fields
Index-shifting conventions. Contractions
The unit tensor field
The Lie derivative / 2.5：
Explicit forms
Lie derivations as supervectors
The derivative mapping
Integral supercurves. Congruences
Dragging of tensor fields
Forms / 2.6：
The exterior product
Bases for forms
Derivations of forms
The exterior derivative
The inner product
Connections / 2.7：
The connection components
Multiple covariant derivatives. The torsion
The Riemann tensor field
The super Bianchi identity
Parallel transport. Supergeodesics
Distant parallelism
Riemannian supermanifolds / 2.8：
The metric tensor field
Canonical form of the metric tensor at a point
Canonical or orthosymplectic bases
Riemannian connections
The curvature tensor field
The Ricci tensor field
Flat Riemannian supermanifolds
Conformally related Riemannian supermanifolds. The Weyl tensor field
Conformally flat Riemannian supermanifolds
Killing vector fields
Conformal Killing vector fields
The global conformal group
Integration over supermanifolds / 2.9：
Integration over R[superscript m][subscript c] [times] R[superscript n][subscript a]. Measure functions
Locally finite atlases and partitions of unity
Integration over paracompact orientable supermanifolds
Integration over Riemannian supermanifolds
Integrals of total divergences
The compact case
An example
Comments on chapter 2
Super Lie groups. General theory / 3：
Definition and structure of super Lie groups / 3.1：
Canonical diffeomorphisms
Left- and right-invariant vector fields
Left- and right-invariant local frame fields
Left- and right-invariant congruences
One-parameter Abelian subgroups
The exponential mapping. Canonical coordinates
The super Lie algebra
The structure constants
The right and left auxiliary functions
Identities satisfied by the auxiliary functions
Construction of a super Lie group from its super Lie algebra
Realizations of super Lie groups / 3.2：
Orbits
Transitive realizations
Isotropy subgroups
Coset spaces
Killing flows
Properties of the coordinate components of the Q[subscript a]
A special canonical coordinate system
Coordinates for the coset spaces
Classification of transitive realizations
Matrix representations of super Lie groups
Contragredient representations
Inner automorphisms. The adjoint representation
Matrix representations of the super Lie algebra
Geometry of coset spaces / 3.3：
Invariant tensor fields
Differential equations for geometrical structures
Integrability of the differential equations
A special coordinate system
Condition for the existence of a group-invariant measure function
Condition for the existence of a group-invariant metric tensor field
Condition for the existence of a group-invariant connection
Solutions of the differential equations
Geometry of the group supermanifold
Identity of the left- and right-invariant connections
Parallelism at a distance in the group supermanifold
Integration over the group
A special class of super Lie groups
Comments on chapter 3
Super Lie groups. Examples / 4：
Construction of super Lie algebras and super Lie groups / 4.1：
Properties of the structure constants
Conventional super Lie groups, Z[subscript 2]-graded algebras
Unconventional super Lie groups
Structure of conventional super Lie Groups. The extending representation
Construction of a class of super Lie algebras
The classical super Lie groups / 4.2：
The group GL (m, n)
The group SL (m, n)
The group SL (m, m)/GL (1, 0)
The orthosymplectic group OSp (m, n)
The Kac notation
The group P(m)
The group Q(m)
The exceptional simple super Lie groups / 4.3：
The groups D(2, 1, [alpha])
The group F(4)
The structure of F(4)
Pseudorepresentation of F(4)
The group G(3)
The structure of G[subscript 2]
The structure of G(3)
Pseudorepresentation of G(3)
Super Lie groups of basic importance in physics / 4.4：
The super de Sitter group
The super Poincare group
The coset space: super Poincare group/SO(1, 3)
Killing flows and invariant connections
Riemannian geometry of the coset space
The super Lorentz group
The Cartan super Lie groups / 4.5：
The diffeomorphism group Diff(M)
The group SDiff(M, [mu])
The canonical transformation group Can(M, [omega])
The group of contact transformations
The case m = 0
The group W(n)
The groups S(n) and S(n)
The groups H(n) and H(n)
Comments on chapter 4
Selected applications of supermanifold theory / 5：
Superclassical dynamical systems / 5.1：
Configuration spaces
Supermanifolds as configuration spaces
Space of histories
The action functional and the dynamical equations
Infinitesimal disturbances and Green's functions
Reciprocity relations
The Peierls bracket
Peierls bracket identities
Super Hilbert spaces / 5.2：
Linear operators
Physical observables
Quantum systems / 5.3：
Transition to the quantum theory
The Schwinger variational principle
External sources
Chronologically ordered form of the operator dynamical equations
The Feynman functional integral
A simple Fermi system / 5.4：
Action functional and Green's functions
Eigenvectors of x
The energy
A pure basis
An alternative representation
The functional integral representation of [x", t"|x', t']
Evaluation of the functional integral
The average superclassical trajectory
Propagator for x[subscript av](t)
The Fermi oscillator / 5.5：
Mode functions and Hamiltonian
Basic supervectors
Eigenvectors of x[subscript 1] and x[subscript 2]. Choice of pure basis
Coherent states
The functional integral representation of [a"*, t"
Direct evaluation of the functional integral
The importance of endpoint contributions
The stationary trajectory as a matrix element
The Feynman propagator
The Bose oscillator / 5.6：
Energy eigenvectors
Hamilton-Jacobi theory
The amplitude [x', t'|x', t'] and its functional integral representation
The functional-integral representation of [a"*, t"
The stationary path between coherent states
Energy eigenfunctions
Bose-Fermi supersymmetry / 5.7：
The simplest model
New conserved quantities
The Bose-Fermi supersymmetry group
Eigenvectors of Q[subscript 1] and Q[subscript 2]
The supersymmetry group as a transformation group
Auxiliary variable
Nonlinear Bose-Fermi supersymmetry
The supersymmetry group
The energy spectrum
Spontaneously broken supersymmetry
Comments on chapter 5
Applications involving topology / 6：
Nontrivial configuration spaces / 6.1：
Standard canonical systems
Green's functions
Equivalence of Peierls and Poisson brackets
Quantization / 6.2：
Problems with the naive quantization rule
Operator-valued forms. The projection m-form
The position operator
Vector operators
The momentum operator
Restriction to a local chart
Lack of uniqueness of the momentum operator
Overlapping charts. Transformation of coordinates
The position representation
The momentum operator in the position representation
The Schrodinger equation
The position representation of the projection m-form
Curved configuration spaces / 6.3：
A special class of systems
Covariant variation
Covariant differentiation with respect to t
The dynamical equations
Covariant functional differentiation
The Feynman functional integral and its meaning / 6.4：
Formal computation of det G[superscript +][x]
The functional integral
Normalization
Ambiguity in the functional integral
Homotopy
Homotopy mesh
The total amplitude
Change of homotopy mesh
The role of homology
The universal covering space
The total amplitude revisited
The Hamiltonian operator: a nonlattice derivation / 6.5：
Integration over phase space
Evaluation of the chronologically ordered Hamiltonian
Approximate evaluation of the path integral / 6.6：
Brief review of Hamilton-Jacobi theory
The Van Vleck-Morette determinant
Jacobi fields and the Green's function for the trajectory x[subscript c]
Determinantal relations
The loop expansion
The WKB approximation
The heat kernel expansion
Role of the two-loop term in the independent verification of (6.5.25)
New variables
Computation of the two-loop term
Supersymmetry and the Euler-Poincare characteristic / 6.7：
Inclusion of a-type dynamical variables
Green's functions and Peierls brackets
Energy and supersymmetry group
Basis supervectors
Differential representation of operators
The Euler-Poincare characteristic
Functional integral for the coherent-state transition amplitude
The Chern-Gauss-Bonnet formula
Comments on chapter 6
References
Index
Preface to the first edition
Preface to the second edition
Analysis over supernumbers / 1：
5.

図書
図書
5. Random media
George Papanicolaou, editor
出版情報: New York ; Tokyo : Springer-Verlag, c1987  xi, 321 p. ; 25 cm
シリーズ名: The IMA volumes in mathematics and its applications ; v. 7
所蔵情報: loading…
6.

図書
図書
6. Symmetries of Maxwell's equations
W.I. Fushchich and A.G. Nikitin ; translated by John R. Schulenberger
出版情報: Dordrecht [Netherlands] ; Tokyo : D. Reidel, c1987  xiv, 214 p. ; 25 cm
シリーズ名: Mathematics and its applications ; Soviet series
所蔵情報: loading…
7.

図書
図書
7. 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：
8.

図書
図書
8. Quantum mechanics of atoms and molecules (: New York ; : Wien)
Walter Thirring ; translated by Evans M. Harrell
出版情報: New York : Springer, c1981  viii, 300 p. ; 25 cm
シリーズ名: A course in mathematical physics / Walter Thirring ; 3
所蔵情報: loading…
9.

図書
図書
9. Mathematical physics
Robert Carroll
出版情報: Amsterdam ; Tokyo : North-Holland, 1988  x, 399 p. ; 25 cm
シリーズ名: North-Holland mathematics studies ; 152
Notas de matemática ; 121
所蔵情報: loading…
10.

図書
図書
10. A collection of problems on the equations of mathematical physics (: gw ; : us)
edited by V.S. Vladimirov ; translated from the Russian by Eugene Yankovsky
出版情報: Moscow : Mir Publishers , Berlin ; Tokyo : Springer, 1986  288 p. ; 24 cm
所蔵情報: loading…
11.

図書
図書
11. Analysis and mathematical physics
Hans Triebel
出版情報: Dordrecht ; Tokyo : D. Reidel, c1986  xxviii, 456 p. ; 23 cm
シリーズ名: Mathematics and its applications ; . East European series
所蔵情報: loading…
12.

図書
図書
12. 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：
13.

図書
図書
13. Mathematical analysis of physical systems
[edited by] Ronald E. Mickens
出版情報: New York : Van Nostrand Reinhold Co., c1985  x, 357 p. ; 24 cm
所蔵情報: loading…
14.

図書
図書
14. Functional analysis. Rev. and enl. ed
Michael Reed, Barry Simon
出版情報: New York ; Tokyo : Academic Press, c1980  xv, 400 p. ; 24 cm
シリーズ名: Methods of modern mathematical physics / Michael Reed, Barry Simon ; 1
所蔵情報: loading…
目次情報: 続きを見る
Preliminaries
Hilbert Spaces
Banach Spaces
Topological Spaces
Locally Convex Spaces
Bounded Operators
The Spectral Theorem
Unbounded Operators
The Fourier Transform
Supplementary Material
List of Symbols
Index
Preliminaries
Hilbert Spaces
Banach Spaces
15.

図書
図書
15. Finsler geometry, relativity and guage theories
by G.S. Asanov
出版情報: Dordrecht ; Boston : D. Reidel , Hingham, Mass. : Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, c1985  x, 370 p. ; 25 cm
シリーズ名: Fundamental theories of physics
所蔵情報: loading…
16.

図書
図書
16. Analysis, manifolds and physics. Rev. ed (pt. 1, Basics ; pt. 2, 92 applications)
by Yvonne Choquet-Bruhat, Cécile DeWitt-Morette, with Margaret Dillard-Bleick
出版情報: Amsterdam ; Tokyo : North-Holland, 1982-1989  2 v. ; 25 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface
Review of fundamental notions of analysis / Chapters: I：
Differential calculus on Banach spaces / II：
Differentiable manifolds, finite dimensional case / III：
Integration on manifolds / IV：
Riemannian manifolds Kahlerian manifolds / V：
bis. Connections on a principle fibre bundle
Distributions / VI：
Differentiable manifolds, infinite dimensional case / VII：
References
Symbols
Index
Preface
Review of fundamental notions of analysis / Chapters: I：
Differential calculus on Banach spaces / II：
17.

図書
図書
17. Nonstandard methods in stochastic analysis and mathematical physics (: pbk)
Sergio Albeverio ... [et al.]
出版情報: Orlando ; Tokyo : Academic Press, 1986  xi, 514 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; 122
所蔵情報: loading…
18.

図書
図書
18. Random processes for classical equations of mathematical physics
by S.M. Ermakov, V.V. Nekrutkin, and A.S. Sipin
出版情報: Dordrecht : Boston : Kluwer Academic, c1989  xx, 281 p. ; 25 cm
シリーズ名: Mathematics and its applications ; . Soviet series ; v. 34
所蔵情報: loading…
19.

図書
図書
19. Supersymmetries and infinite-dimensional algebras (: pbk)
J.F. Cornwell
出版情報: London ; Tokyo : Academic Press, c1989  xxii, 628 p. ; 24 cm
シリーズ名: Techniques of physics ; 10 . Group theory in physics ; v. 3
所蔵情報: loading…
目次情報: 続きを見る
Lie Superalgebras, Lie Supergroups, and Their Applications: Introduction to Superalgebras and Supermatrices
General Properties of Lie Superalgebras
Superspace and Lie Supergroups
The Poincar*aae Superalgebras and Supergroups
Poincar*aae Supersymmetric Fields
Simple Lie Superalgebras
Infinite-Dimensional Lie Algebras and Superalgebras and their Applications: The Structure of Kac-Moody Algebras
Representations of Kac-Moody Algebras
The Virasoro Algebra and Superalgebras
Algebraic Aspects of the Theory of Strings and Superstrings
Proofs of Certain Theorems on Su / Appendices：
Lie Superalgebras, Lie Supergroups, and Their Applications: Introduction to Superalgebras and Supermatrices
General Properties of Lie Superalgebras
Superspace and Lie Supergroups
20.

図書
図書
20. Spin geometry
H. Blaine Lawson, Jr. and Marie-Louise Michelsohn
出版情報: Princeton, N.J. : Princeton University Press, 1989  xii, 427 p. ; 25 cm
シリーズ名: Princeton mathematical series ; 38
所蔵情報: loading…
21.

図書
図書
21. Mathematical foundations of classical statistical mechanics : continuous systems
D.Ya. Petrina, V.I. Gerasimenko, and P.V. Malyshev ; translated from the Russian by P.V. Malyshev and D.V. Malyshev
出版情報: New York ; Tokyo : Gordon and Breach Science Publishers, c1989  xvii, 338 p. ; 24 cm
シリーズ名: Advanced studies in contemporary mathematics ; v. 6
所蔵情報: loading…
目次情報: 続きを見る
Problem for the BBGKY Hierarchy
Equilibrium States
Canonical Ensemble
Grand Canonical Ensemble
Thermodynamic Limit for Non-equilibrium Systems
Stationary Solutions of the BBGKY Hierarchy of Equations / Appendix 1：
Existence of the Hamiltonian Dynamics of Infinitely Many Particles / Appendix 2：
References
Index
Problem for the BBGKY Hierarchy
Equilibrium States
Canonical Ensemble
22.

図書
図書
22. The penrose transform : its interaction with representation theory
Robert J. Baston and Michael G. Eastwood
出版情報: Oxford : Clarendon Press , New York ; Tokyo : Oxfrod University Press, 1989  xv, 213 p. ; 24 cm
シリーズ名: Oxford mathematical monographs
所蔵情報: loading…
目次情報: 続きを見る
Introduction / 1：
Lie Algebras and Flag Manifolds / 2：
Homogeneous Vector Bundles on G/P / 3：
The Weyl Group, its Actions, and Hasse Diagrams / 4：
The Bott-Borel-Weil Theorem / 5：
Realizations of G/P / 6：
The Penrose Transform / 7：
The Bernstein-Gelfand-Gelfand Resolution / 8：
The Penrose Transformation in Practice / 9：
Constructing Unitary Representations / 10：
Module Structures on Cohomology / 11：
Conclusion and Outlook / 12：
Introduction / 1：
Lie Algebras and Flag Manifolds / 2：
Homogeneous Vector Bundles on G/P / 3：
23.

図書
図書
23. Bäcklund transformations and their applications
C. Rogers and W.F. Shadwick
出版情報: New York : Academic Press, 1982  xiii, 334 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 161
所蔵情報: loading…
24.

図書
図書
24. Lecture notes on particle systems and percolation
Richard Durrett
出版情報: Pacific Grove, Calif. : Wadsworth & Brooks/Cole, c1988  viii, 335 p. ; 25 cm
シリーズ名: The Wadsworth & Brooks/Cole statistics/probability series
所蔵情報: loading…
25.

図書
図書
25. Direct methods (: Basel ; : Boston)
Aleksandr A. Samarskii, Evgenii S. Nikolaev ; translated from the Russian by Stephen G. Nash
出版情報: Basel [Switzerland] ; Boston : Birkhäuser, 1989  xxxv, 242 p. ; 24 cm
シリーズ名: Numerical methods for grid equations / Aleksandr A. Samarskii, Evgenii S. Nikolaev ; translated from the Russian by Stephen G. Nash ; v. 1
所蔵情報: loading…
26.

図書
図書
26. Iterative methods (: Basel ; : Boston)
Aleksandr A. Samarskii, Evgenii S. Nikolaev ; translated from the Russian by Stephen G. Nash
出版情報: Basel [Switzerland] ; Boston : Birkhäuser, 1989  xv, 502 p. ; 24 cm
シリーズ名: Numerical methods for grid equations / Aleksandr A. Samarskii, Evgenii S. Nikolaev ; translated from the Russian by Stephen G. Nash ; v. 2
所蔵情報: loading…
27.

図書
図書
27. Geometric phases in physics (: hdc ; : pbk)
[edited by] Alfred Shapere, Frank Wilczek
出版情報: Singapore : World Scientific, [1989]  xiv, 509 p. ; 26 cm
シリーズ名: Advanced series in mathematical physics / editors-in-charge, D.H. Phong, S.-T. Yan ; v. 5
所蔵情報: loading…
28.

図書
図書
28. Functional integration and semiclassical expansions
F. Langouche, D. Roekaerts, and E. Tirapegui
出版情報: Dordrecht, Holland ; Boston : D. Reidel Pub. Co. , Hingham, MA : Sold and distributed in the U.S.A. and Canada by Kluwer Boston, c1982  xii, 313 p. ; 24 cm
シリーズ名: Mathematics and its applications ; v. 10
所蔵情報: loading…
29.

図書
図書
29. Topics in physical geometry
Robert Hermann
出版情報: Brookline, Mass. : Math Sci Press, c1988  xv, 595 p. ; 24 cm
シリーズ名: Interdisciplinary mathematics ; v. 24
所蔵情報: loading…
30.

図書
図書
30. Spinor and twistor methods in space-time geometry (pbk)
Roger Penrose, Wolfgang Rindler
出版情報: Cambridge [Cambridgeshire] : Cambridge University Press, 1986  ix, 501 p. ; 24 cm
シリーズ名: Cambridge monographs on mathematical physics ; . Spinors and space-time ; Vol. 2
所蔵情報: loading…
目次情報: 続きを見る
Preface
Summary of volume 1
Twistors / 6：
Null congruences / 7：
Classification of curvature tensors / 8：
Conformal infinity / 9：
Appendix
References
Subject and author index
Index of symbols
Preface
Summary of volume 1
Twistors / 6：
31.

図書
図書
31. Two-spinor calculus and relativistic fields (: pbk)
Roger Penrose, Wolfgang Rindler
出版情報: Cambridge [Cambridgeshire] : Cambridge University Press, 1984  x, 458 p. ; 24 cm
シリーズ名: Cambridge monographs on mathematical physics ; . Spinors and space-time ; v. 1
所蔵情報: loading…
目次情報: 続きを見る
Preface
The geometry of world-vectors and spin-vectors / 1：
Abstract indices and spinor algebra / 2：
Spinors and world-tensors / 3：
Differentiation and curvature / 4：
Fields in space-time / 5：
Appendix
References
Subject and author index
Index of symbols
Preface
The geometry of world-vectors and spin-vectors / 1：
Abstract indices and spinor algebra / 2：
32.

図書
図書
32. Hermann Weyl, 1885-1985 : centenary lectures (: gw ; : us)
delivered by C.N. Yang, R. Penrose, A. Borel at the ETH Zürich ; edited by K. Chandrasekharan
出版情報: Berlin ; Tokyo : Published for the Eidgenössische Technische Hochschule Zürich [by] Springer-Verlag, c1986  119 p. ; 24 cm
所蔵情報: loading…
33.

図書
図書
33. Hamiltonian methods in the theory of solitons (: us ; : gw)
L.D. Faddeev, L.A. Takhtajan ; translated from the Russian by A.G. Reyman
出版情報: Berlin ; Tokyo : Springer-Verlag, c1987  ix, 592 p. ; 24 cm
シリーズ名: Springer series in Soviet mathematics
所蔵情報: loading…
34.

図書
図書
34. Differential geometry, gauge theories, and gravity (: pbk)
M. Göckeler, T. Schücker
出版情報: Cambridge ; New York : Cambridge University Press, 1989  xii, 230 p. ; 23 cm
シリーズ名: Cambridge monographs on mathematical physics
所蔵情報: loading…
目次情報: 続きを見る
Preface
Exterior algebra / 1：
Differential forms on open subsets of Rn / 2：
Metric structures / 3：
Gauge theories / 4：
Einstein-Cartan theory / 5：
The Lie derivative / 6：
Manifolds / 7：
Lie groups / 8：
Fibre bundles / 9：
Monopoles, instantons, and related fibre bundles / 10：
Spin / 11：
An algebraic approach to anomalies / 12：
Anomalies from graphs / 13：
References
Bibliography
Notation
Index
Preface
Exterior algebra / 1：
Differential forms on open subsets of Rn / 2：
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼