Indefinite Inner Product Spaces by J Bognar
By definition, an indefinite inner product space is a real or complex vector space together with a symmetric (in the complex case: hermi- tian) bilinear form prescribed on it so that the corresponding quadratic form assumes both positive and negative values. The most important special case arises when a Hilbert space is considered as an orthogonal direct sum of two subspaces, one equipped with the original inner prod- uct, and the other with -1 times the original inner product. The subject first appeared thirty years ago in a paper of Dirac [1] on quantum field theory (d. also Pauli [lJ). Soon afterwards, Pontrja- gin [1] gave the first mathematical treatment of an indefinite inner prod- uct space. Pontrjagin was unaware of the investigations of Dirac and Pauli; on the other hand, he was inspired by a work of Sobolev [lJ, unpublished up to 1960, concerning a problem of mechanics. The attempts of Dirac and Pauli to apply the concept and elemen- tary properties of indefinite inner product spaces to field theory have been renewed by several authors. At present it is not easy to judge which of their results will contribute to the final form of this part of physics. The following list of references should serve as a guide to the extensive literature: Bleuler [1], Gupta [lJ, Kallen and Pauli [lJ, Heisen- berg [lJ-[4J, Bogoljubov, Medvedev and Polivanov [lJ, K.L.Nagy [lJ-[3], Berezin [lJ, Arons, Han and Sudarshan [1], Lee and Wick [1J.-
Methodes d'algebre abstraite en geometrie algebrique
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Invariant Subspaces
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Calculus of Fractions and Homotopy Theory
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Theorie der Limitierungsverfahren
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Compact Convex Sets and Boundary Integrals
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On the Problem of Plateau
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Integrability Theorems for Trigonometric Transforms
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Stochastic Differential Equations
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Some Properties of Differentiable Varieties and Transformations
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Commutation Properties of Hilbert Space Operators and Related Topics
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Discrete Subgroups of Lie Groups
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Neuere Untersuchungen über eindeutige analytische Funktionen
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Modular Lie Algebras
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Varieties of Groups
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Differential Geometry of Foliations
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Partial Differential Equations of Elliptic Type
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Algebren
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Recent Synthetic Differential Geometry
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Coding Theorems of Information Theory
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Bounded Integral Operators on L 2 Spaces
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Involutions on Manifolds
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Probability Measures on Locally Compact Groups
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The Burnside Problem and Identities in Groups
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Vollständige Systeme modaler und intuitionistischer Logik
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Riemann Surfaces and Generalized Theta Functions
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The Divisor Class Group of a Krull Domain
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Fourier Series with Respect to General Orthogonal Systems
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Cohomology Theory of Topological Transformation Groups
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Integration in Hilbert Space
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Angeordnete Strukturen
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Topology on Spaces of Holomorphic Mappings
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Ergodic Properties of Algebraic Fields
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Asymptotic Behavior and Stability Problems in Ordinary Differential Equations
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Complete Normed Algebras
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Theorie der Funktionen mehrerer komplexer Veranderlichen
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Manifolds all of whose Geodesics are Closed
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Potential Theory on Locally Compact Abelian Groups
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The Stone-Cech Compactification
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Ideaux de fonctions différentiables
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Topos anneles et schemas relatifs
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Capacites et processus stochastiques
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Sous-ensembles analytiques d'une variete banachique complexe
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Series de Fourier absolument convergentes
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Finiteness Conditions and Generalized Soluble Groups
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Idealtheorie
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Mathematische Grundlagenforschung Intuitionismus Beweistheorie
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Combinatorial Functors
| SKU | Unavailable |
| ISBN 13 | 9783642655692 |
| ISBN 10 | 3642655696 |
| Title | Indefinite Inner Product Spaces |
| Author | J Bognar |
| Series | Ergebnisse Der Mathematik Und Ihrer Grenzgebiete 2 Folge |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer |
| Year published | 2011-11-11 |
| Number of pages | 226 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |