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Noncommutative Geometry

https://doi.org/10.4171/owr/2009/41
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In Search of Schrödinger's Cap: Pricing Derivatives with Quantum Probability
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Groupoid and Algebra of the Infinite Quantum Spin Chain
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The Standard Model and Dark Matter in a Unified Einstein-Dirac System with Discrete Extra Dimensions
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The Noncommutative Geometry of Configuration Spaces and the Problem of Reconciling General Relativity with Quantum Field Theory
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Geometric Flavours of Quantum Field Theory on a Cauchy Hypersurface. Part I: Gaussian Analysis and Other Mathematical Aspects
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Comparison of Levi-Civita Connections in Noncommutative Geometry
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Noncommutative geometry and fundamental interactions: the first ten years
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Harmonic Analysis of Fractal Processes viaC* ‐ Algebras
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Dixmier traces of operators on Banach and Hilbert spaces
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On interpolation properties of compact bilinear operators
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Second‐order trace formulas
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Curvature and Weitzenböck formula for spectral triples
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Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. Part I.
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Four‐Dimensional Gravity on a Covariant Noncommutative Space (II)
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Causal Fermion Systems and Octonions
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Dirac Operators on Configuration Spaces: Fermions with Half‐integer Spin, Real Structure, and Yang–Mills Quantum Field Theory
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The Noncommutative Geometry of Configuration Spaces and the Problem of Reconciling General Relativity With Quantum Field Theory
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Fractal and multifractal geometry: scaling symmetry and statistics
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Quantization of Scalar Fields in Curved Background and Quantum Algebras
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Noncommutative Riemann Integration and Novikov–Shubin Invariants for Open Manifolds
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Quantum maps and automorphisms
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On the Foundations of Noncommutative Geometry
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Algebraic Lessons from the Theory of Quantum Integrable Models
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Symmetries Wider Than Supersymmetry
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Noncommutative Geometry, Wodzciki residue-
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Mohamed El Naschie’s ∈ (∞) Cantorian space-time and its consequences in cosmology
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Regularization and Renormalization of Quantum Field Theories on Noncommutative Spaces
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Particle Physics on Noncommutative Space-Time
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Quantum Entropies in a Classical Context
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Coherent and Dissipative Transport in Aperiodic Solids: An Overview
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Geometric Properties of Transport in Quantum Hall Systems
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Non-commutative Extensions of Classical Theories in Physics
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Whither Quantum Theory?
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Methods from Multiscale Theory and Wavelets Applied to Nonlinear Dynamics
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Fractals in the Quantum Theory of Spacetime
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Chronological Calculus in Systems and Control Theory
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References
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Resonance Gyrons and Quantum Geometry
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The Geometry of Space-Time and Its Deformations from a Physical Perspective
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The Deformation Philosophy, Quantization and Noncommutative Space-Time Structures
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Jordan Structures and Non-Associative Geometry
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Noncommutative Geometry in the Framework of Differential Graded Categories
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Symmetries Wider than Supersymmetry
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Dirac Operators and Index Theory
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Differential Forms Canonically Associated to Even-Dimensional Compact Conformal Manifolds
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Standard Quantum Spheres
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Noncommutative Vieta Theorem and Symmetric Functions
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Positive Curvature, Macroscopic Dimension, Spectral Gaps and Higher Signatures
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On the Weak Homotopy Type of Étale Groupoids
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Two Approaches to Non-Commutative Geometry
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Chronological Calculus in Systems and Control Theory
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Quantum Space-Time Groups and Beyond
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Dirac Operators and Index Theory
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Exercises in Equivariant Cohomology
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Differential Geometry of Quantum States, Observables and Evolution
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A Residue Formula for Locally Compact Noncommutative Manifolds
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H. Weyl’s Deep Insights intotheMathematicalandPhysicalWorlds: His Important Contribution to the Philosophy of Space, Time and Matter
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Trotter–Kato Product Formulae in Dixmier Ideal
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On the Geometry of Some Braid Group Representations
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Set Theory and Quotients
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Higher Segal Spaces
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Spaces, Bundles and Characteristic Classes in Differential Geometry
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Non-commutative Topology
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Spaces, Bundles, Homology/Cohomology and Characteristic Classes in Non-commutative Geometry
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Hochschild, Cyclic and Periodic Cyclic Homology
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Local Hochschild Homology of the Algebra of Hilbert–Schmidt Operators on Simplicial Spaces
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A survey of spectral models of gravity coupled to matter
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Commutants mod normed ideals
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Curvature in noncommutative geometry
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Differentials on an Algebra
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Hopf Algebras and Their Bicovariant Calculi
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Curvature, Cohomology and Sheaves
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Quantum Principal Bundles and Framings
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Vector Fields and Differential Operators
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Quantum Complex Structures
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Quantum Riemannian Structures
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Quantum Spacetime
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Notations and Preliminaries
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Applications
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Snyder-de Sitter Meets the Grosse-Wulkenhaar Model
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A Survey of Ron Douglas’s Contributions to the Index Theory of Toeplitz Operators
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Twisted Dirac Operator on Quantum SU(2) in Disc Coordinates
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Quantum Differentials and Function Spaces
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Pragmaticism as a Philosophy of Cognitive Mathematics
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Peirce on Mathematical Reasoning and Discovery
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Classical Systems in Quantum Mechanics
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Quantised Calculus for Perturbed Massive Dirac Operator on Noncommutative Euclidean Space
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A Noncommutative Geometric Approach to the Batalin–Vilkovisky Construction
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Operators, Algebras and Their Invariants for Aperiodic Tilings
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The Dixmier Trace and the Noncommutative Residue for Multipliers on Compact Manifolds
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Commentaries and Further Developments
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Deformed Joint Free Distributions of Semicircular Elements Induced by Multi Orthogonal Projections
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Symbolic Calculus for Singular Curve Operators
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Reality Without Realism
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All 4-Dimensional Smooth Schoenflies Balls Are Geometrically Simply-Connected
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Classical Differential Topology and Non-commutative Geometry
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Topological Quantum Field Theory and the Emergence of Physical Space–Time from Geometry. New Insights into the Interactions Between Geometry and Physics
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Introduction
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Locally Compact Quantum Metric Spaces and Spectral Triples
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Comparing Banach Spaces for Systems of Free Random Variables Followed by the Semicircular Law
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Pragmaticism as a Philosophy of Cognitive Mathematics
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Peirce on Mathematical Reasoning and Discovery
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Spectra and Type III Factors
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Applications to Solid State Systems
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Quantum and Stochastic Mathematical Physics
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A Guide to Penrose Tilings
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Analysis on Noncompact Manifolds and Index Theory: Fredholm Conditions and Pseudodifferential Operators
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Examples
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The Maurer–Cartan Form of Operator Pencils
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Riemannian Spin Manifolds
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Noncommutative Riemannian Spin Manifolds
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The Local Index Formula in Noncommutative Geometry
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Unitary Metric Colligations and Their Model Representations
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“Le complément supérieur”: On the Poetics of Mathematics
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Foliations and Operator Algebras
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Pythagorean and Platonic Conceptions in XXth Century Physics
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Measure of Non-compactness of Operators Interpolated by Limiting Real Methods
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Traces of Commutators of Integral Operators – the Aftermath
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q-Calculus and physics
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Elliptic Theory for Operators Associated with Diffeomorphisms of Smooth Manifolds
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Arithmetic Aspect of $$ C_r^*SL(2) $$
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Cyclic homology and pseudodifferential operators, a survey
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Noncommutative Gravity
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From Fractal Groups to Fractal Sets
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Regularisation of Secondary Characteristic Classes and Unusual Index Formulas for Operator-valued Symbols
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Fermionic Second Quantization and the Geometry of the Restricted Grassmannian
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Models for the Leaf Space of a Foliation
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Quantization of Singular Symplectic Quotients
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Homology of complete symbols and noncommutative geometry
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Quantized reduction as a tensor product
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Analysis of geometric operators on open manifolds: A groupoid approach
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On Some New Type of Infinite Dimensional Laplacians
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The small Hankel operator in several complex variables
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Spectral Geometry: An Introduction and Background Material for this Volume
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Rapport sur la K-théorie (1956–1997)
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Noncommutative Geometry and Quantum Hall Effect
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Operator Algebras and Conformal Field Theory
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The Local Index Formula in Noncommutative Geometry
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The tangent space in sub-Riemannian geometry
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Manifolds
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The Algebraic Quantum Formalism
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On the Foundational Assumptions of Modern Physics
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The Sound of Fractal Strings and the Riemann Hypothesis
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Elements of Noncommutative Algebra
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Poincaré-Birkhoff-Witt Basis
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Quantizations of Kac-Moody Algebras
inferred← citeshttps://doi.org/10.1007/978-3-319-22704-7_4openalex-snapshot
Algebra of Skew-Primitive Elements
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Multilinear Operations
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Braided Hopf Algebras
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Binary Structures
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Algebra of Primitive Nonassociative Polynomials
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Introduction
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The Noncommutative Supersymmetric Standard Model
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Noncommutative Geometry and the Physics of the LHC Era
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Wave Equations with Non-commutative Space and Time
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New Results on Old Spectral Triples for Fractals
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Bulk and Boundary Invariants for Complex Topological Insulators
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Commutator Inequalities via Schur Products
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Lectures on Matrix Field Theory
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Introductory Remarks
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The Noncommutative Moyal-Weyl Spaces R θ d
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The Fuzzy Sphere
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The Multitrace Approach
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Music of Quantum Circles
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Matter, Mind, and Time
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Electron Dynamics: Concrete Physical Models
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Non-commutative Brillouin Torus
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Where We Stand Today
inferred← citeshttps://doi.org/10.1007/978-3-319-64813-2_9openalex-snapshot
Quanta of Space-Time and Axiomatization of Physics
inferred← citeshttps://doi.org/10.1007/978-3-319-65427-0_10openalex-snapshot
Weighted Direct Product of Spectral Triples
inferred← citeshttps://doi.org/10.1007/978-3-319-65427-0_3openalex-snapshot
Principal Fiber Bundles in Non-commutative Geometry
inferred← citeshttps://doi.org/10.1007/978-3-319-65810-0_1openalex-snapshot
Introduction
inferred← citeshttps://doi.org/10.1007/978-3-319-65810-0_2openalex-snapshot
The Exponential Transform
inferred← citeshttps://doi.org/10.1007/978-3-319-65810-0_3openalex-snapshot
Hilbert Space Factorization
inferred← citeshttps://doi.org/10.1007/978-3-319-65810-0_4openalex-snapshot
Exponential Orthogonal Polynomials
inferred← citeshttps://doi.org/10.1007/978-3-319-65810-0_6openalex-snapshot
Mother Bodies
inferred← citeshttps://doi.org/10.1007/978-3-319-65810-0_7openalex-snapshot
Examples
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Comparison with Classical Function Spaces
inferred← citeshttps://doi.org/10.1007/978-3-319-67205-2_10openalex-snapshot
Creation of Matter in a Noncommutative Universe
inferred← citeshttps://doi.org/10.1007/978-3-319-70157-8_1openalex-snapshot
Higher Categorical Aspects of Hall Algebras
inferred← citeshttps://doi.org/10.1007/978-3-319-70658-0_116-2openalex-snapshot
Space and Time in the Foundations of Mathematics, or Some Challenges in the Interactions with Other Sciences
inferred← citeshttps://doi.org/10.1007/978-3-319-72299-3_9openalex-snapshot
Spectral Triples on O N
inferred← citeshttps://doi.org/10.1007/978-3-319-76596-9_7openalex-snapshot
Theoretical Properties of Materials Formed as Wire Network Graphs from Triply Periodic CMC Surfaces, Especially the Gyroid
inferred← citeshttps://doi.org/10.1007/978-3-319-76732-1openalex-snapshot
Coherent States and Their Applications - A Contemporary Panorama
inferred← citeshttps://doi.org/10.1007/978-3-319-94758-7_1openalex-snapshot
Thermostructure
inferred← citeshttps://doi.org/10.1007/978-3-319-94788-4openalex-snapshot
Spectral Action in Noncommutative Geometry
inferred← citeshttps://doi.org/10.1007/978-3-319-94788-4_1openalex-snapshot
The Dwelling of the Spectral Action
inferred← citeshttps://doi.org/10.1007/978-3-322-90191-0_8openalex-snapshot
Mannigfaltigkeiten
inferred← citeshttps://doi.org/10.1007/978-3-540-27855-9_14openalex-snapshot
Bivariant K- and Cyclic Theories
inferred← citeshttps://doi.org/10.1007/978-3-540-27855-9_15openalex-snapshot
The Baum–Connes and the Farrell–Jones Conjectures in K- and L-Theory
inferred← citeshttps://doi.org/10.1007/978-3-540-27855-9_4openalex-snapshot
Bott Periodicity in Topological, Algebraic and Hermitian K-Theory
inferred← citeshttps://doi.org/10.1007/978-3-540-32665-6_6openalex-snapshot
Aspects of Nonlocality in Quantum Mechanics
inferred← citeshttps://doi.org/10.1007/978-3-540-70997-8_9openalex-snapshot
Lattices, packings and tilings in the plane
inferred← citeshttps://doi.org/10.1007/978-3-540-74956-1_27openalex-snapshot
Erratum
inferred← citeshttps://doi.org/10.1007/978-3-540-89793-4_6openalex-snapshot
Noncommutative Spaces
inferred← citeshttps://doi.org/10.1007/978-3-540-95891-8_8openalex-snapshot
Randomness and Determination, from Physics and Computing towards Biology
inferred← citeshttps://doi.org/10.1007/978-3-642-02261-6_23openalex-snapshot
A Duality for Algebras of Lattice-Valued Modal Logic
showing the first 200 of 2012
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