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1.

図書

図書
edited by L. Accardi ... [et al.]
出版情報: Singapore : World Scientific, c2001  xiii, 480 p.; 26 cm
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2.

図書

図書
L. Accardi, C.C. Heyde (editors)
出版情報: New York ; Tokyo : Springer, c1998  xi, 356 p. ; 24 cm
シリーズ名: Lecture notes in statistics ; 128
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3.

図書

図書
managing editor, L. Accardi ; editorial board, A. Frigerio ... [et al.]
出版情報: Singapore : World Scientific, c1991-  v. ; 23 cm
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4.

図書

図書
L. Accardi, W. von Waldenfels, (eds.)
出版情報: Berlin ; New York : Springer-Verlag, c1990  vi, 413 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1442
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5.

図書

図書
L. Accardi, W. von Waldenfels (eds.)
出版情報: Berlin ; Tokyo : Springer-Verlag, c1989  vi, 355 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1396
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6.

図書

図書
L. Accardi, W. von Waldenfels, [editors]
出版情報: Berlin ; Tokyo : Springer-Verlag, c1988  vi, 373 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1303
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7.

図書

図書
edited by L. Accardi and W. von Waldenfels
出版情報: Berlin ; New York : Springer-Verlag, c1985  vi, 534 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1136
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8.

図書

図書
edited by L. Accardi, A. Frigerio and V. Gorini
出版情報: Berlin ; New York : Springer-Verlag, 1984  vi, 411 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1055
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9.

図書

図書
ルイジ・アカルディ著 ; 松岡隆志訳
出版情報: 東京 : 牧野書店 , 東京 : 星雲社 (発売), 2015.7  xviii, 388p ; 21cm
シリーズ名: 数理情報科学シリーズ ; 28
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目次情報: 続きを見る
第0章 : 議論の核心
第1章 : 科学と量子論:その基盤における問題
第2章 : 量子論の疑わしきパラドックス
第3章 : 不確定性原理:新しい物理学の核心
第4章 : 数学モデル、物理的実在、そして完全性
第5章 : 量子パラドックスの解法:初期の試み
第6章 : 他の解の可能性:量子確率論
第7章 : 異なる解の初めての比較
第8章 : 相対論と量子論:その間で主張される矛盾
第9章 : カメレオン、適応系、反応する統計:その非古典的な姿
第0章 : 議論の核心
第1章 : 科学と量子論:その基盤における問題
第2章 : 量子論の疑わしきパラドックス
10.

図書

図書
Luigi Accardi, Yun Gang Lu, Igor Volovich
出版情報: Berlin : Springer, c2002  xx, 473 p. ; 24 cm
シリーズ名: Physics and astronomy online library
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目次情報: 続きを見る
Statement of the Problem and Simplest Models / Part I:
Notations and Statement of the Problem / 1:
The Schrödinger Equation / 1.1:
White Noise Approximation for a Free Particle: The Basic Formula / 1.2:
The Interaction Representation: Propagators / 1.3:
The Heisenberg Equation / 1.4:
Dynamical Systems and Their Perturbations / 1.5:
Asymptotic Behaviour of Dynamical Systems: The Stochastic Limit / 1.6:
Slow and Fast Degrees of Freedom / 1.7:
Emergence of White Noise Hamiltonian Equations from the Stochastic Limit / 1.8:
From Interaction to Heisenberg Evolutions: Conditions on the State / 1.10:
From Interaction to Heisenberg Evolutions: Conditions on the Observable / 1.11:
Forward and Backward Langevin Equations / 1.12:
The Open System Approach to Dissipation and Irreversibility: Master Equation / 1.13:
Classical Processes Driving Quantum Phenomena / 1.14:
The Basic Steps ofthe Stochastic Limit / 1.15:
Connection with the Central Limit Theorems / 1.16:
Classical Systems / 1.17:
The Backward Transport Coefficient and the Arrow of Time / 1.18:
The Master and Fokker-Planck Equations: Projection Techniques / 1.19:
The Master Equation in Open Systems: an Heuristic Derivation / 1.20:
The Semiclassical Approximation for the Master Equation / 1.21:
Beyond the Master Equation / 1.22:
Other Rescalings when the Time Correlations Are not Integrable / 1.23:
Connections with the Classical Homogeneization Problem / 1.25:
Algebraic Formulation of the Stochastic Limit / 1.26:
Notes / 1.27:
Quantum Fields / 2:
Creation and Annihilation Operators / 2.1:
Gaussianity / 2.2:
Types of Gaussian States: Gauge-Invariant, Squeezed, Fock and Anti-Fock / 2.3:
Free Evolutions of Quantum Fields / 2.4:
States Invariant Under Free Evolutions / 2.5:
Existence of Squeezed Stationary Fields / 2.6:
Positivity of the Covariance / 2.7:
Dynamical Systems in Equilibrium: the KMS Condition / 2.8:
Equilibrium States: the KMS Condition / 2.9:
q-Gaussian Equilibrium States / 2.10:
Boson Gaussianity / 2.11:
Boson Fock Fields / 2.12:
Free Hamiltonians for Boson Fock Fields / 2.13:
White Noises / 2.14:
Boson Fock White Noises and Classical White Noises / 2.15:
Boson Fock White Noises and Classical Wiener Processes / 2.16:
Boson Thermal Statistics and Thermal White Noises / 2.17:
Canonical Representation of the Boson Thermal States / 2.18:
Spectral Representation of Quantum White Noise / 2.19:
Locality of Quantum Fields and Ultralocality of Quantum White Noises / 2.20:
Those Kinds of Fields We Call Noises / 3:
Convergence of Fields in the Sense of Correlators / 3.1:
Generalized White Noises as the Stochastic Limit ofGaussian Fields / 3.2:
Existence of Fock, Temperature and Squeezed White Noises / 3.3:
Convergence of the Field Operator to a Classical White Noise / 3.4:
Beyond the Master Equation: The Master Field / 3.5:
Discrete Spectrum Embedded in theContinuum / 3.6:
The Stochastic Limit of a Classical Gaussian Random Field / 3.7:
Semiclassical Versus Semiquantum Approximation / 3.8:
An Historical Example: The Damped Harmonic Oscillator / 3.9:
Emergence of the White Noise: A Traditional Derivation / 3.10:
Heuristic Origins of Quantum White Noise / 3.11:
Relativistic Quantum White Noises / 3.12:
Space-Time Rescalings: Multidimensional White Noises / 3.13:
The Chronological Stochastic Limit / 3.14:
Open Systems / 3.15:
The Nonrelativistic QED Hamiltonian / 4.1:
The Dipole Approximation / 4.2:
The Rotating-Wave Approximation / 4.3:
Composite Systems / 4.4:
Assumptions on the Environment (Field, Gas, Reservoir, etc.) / 4.5:
Assumptions on the System Hamiltonian / 4.6:
The Free Hamiltonian / 4.7:
Multiplicative (Dipole-Type) Interactions: Canonical Form / 4.8:
Approximations of the Multiplicative Hamiltonian / 4.9:
Rotating-Wave Approximation Hamiltonians / 4.9.1:
No Rotating-Wave Approximation Hamiltonians with Cutoff / 4.9.2:
Neither Dipole nor Rotating-Wave Approximation Hamiltonians Without Cutoff / 4.9.3:
The Generalized Rotating-WaveApproximation / 4.10:
The Stochastic Limit of the Multiplicative Interaction / 4.11:
The Normal Form of the White Noise Hamiltonian Equation / 4.12:
Invariance of the Ito Correction Term Under Free System Evolution / 4.13:
The Stochastic Golden Rule: Langevin and Master Equations / 4.14:
Classical Stochastic Processes Underlying Quantum Processes / 4.15:
The Fluctuation-Dissipation Relation / 4.16:
Vacuum Transition Amplitudes / 4.17:
How to Avoid Decoherence / 4.18:
The Energy Shell Scalar Product: Linewidths / 4.20:
Dispersion Relations and the Ito Correction Term / 4.21:
Multiplicative Coupling with the Rotating Wave Approximation: ArbitraryGaussianState / 4.22:
Multiplicative Coupling with RWA: Gauge Invariant State1 / 4.24:
RedShifts and Blue Shifts / 4.25:
The Free Evolution of the Master Field / 4.26:
Algebras Invariant Under the Flow / 4.27:
Spin-Boson Systems / 4.28:
Dropping the Rotating-Wave Approximation / 5.1:
The Master Field / 5.2:
The White Noise Hamiltonian Equation / 5.3:
The Operator Transport Coefficient: no Rotating-Wave Approximation, Arbitrary Gaussian Reference State / 5.4:
Different Roles of the Positive and Negative Bohr Frequencies / 5.5:
No Rotating-Wave Approximation with Cutoff: Gauge Invariant States / 5.6:
No Rotating-Wave Approximation with Cutoff: Squeezing States / 5.7:
The Stochastic Golden Rule for Dipole Type Interactions and Gauge-Invariant States / 5.8:
The Stochastic GoldenRule / 5.9:
The Langevin Equation / 5.10:
Subalgebras Invariant Under the Generator / 5.11:
The Langevin Equation: Generic Systems / 5.12:
The Stochastic Golden Rule Versus Standard Perturbation Theory / 5.13:
Spin-Boson Hamiltonian / 5.14:
The Damping and Oscillating Regimes: Fock Case / 5.15:
The Damping and the Oscillating Regimes: Nonzero Temperature / 5.16:
No Rotating-Wave Approximation Without Cutoff / 5.17:
The Drift Term for Gauge-Invariant States / 5.18:
The Stochastic Limit of the Generalized Spin-Boson Hamiltonian / 5.19:
Convergence to Equilibrium: Connections with Quantum Measurement / 5.21:
Control of Coherence / 5.23:
Dynamics of Spin Systems / 5.24:
Nonstationary White Noises / 5.25:
Measurements and Filtering Theory / 5.26:
Input-Output Channels / 6.1:
The Filtering Problem in Classical Probability / 6.2:
Field Measurements / 6.3:
Properties of the Input and Output Processes / 6.4:
The Filtering Problem in Quantum Theory / 6.5:
Filtering of a Quantum System Over a Classical Process / 6.6:
Nondemolition Processes / 6.7:
Standard Scheme to Construct Examples of Nondemolition Measurements / 6.8:
Discrete Time Nondemolition Processes / 6.9:
Idea of the Proof and Causal Normal Order / 6.10:
Term-by-Term Convergence of the Series / 7.1:
Vacuum Transition Amplitude: The Fourth-Order Term / 7.2:
Vacuum Transition Amplitude: Non-Time-ConsecutiveDiagrams / 7.3:
The Causal ?-Function and the Time-Consecutive Principle / 7.4:
Theory of Distributions on the Standard Simplex / 7.5:
The Second-Order Term of the Limit Vacuum Amplitude / 7.6:
The Fourth-Order Term of the Limit Vacuum Amplitude / 7.7:
Higher-Order Terms of the Vacuum-Vacuum Amplitude / 7.8:
Proof of the Normal Form of the White Noise Hamiltonian Equation / 7.9:
The Unitarity Condition for the Limit Equation / 7.10:
Normal Form ofthe Thermal White Noise Equation: Boson Case / 7.11:
From White Noise Calculus to Stochastic Calculus / 7.12:
Chronological Product Approach to the Stochastic Limit / 8:
Chronological Products / 8.1:
The Limit of the nth Term, Time-Ordered Product Approach: Vacuum Expectation / 8.2:
The Stochastic Limit, Time-Ordered Product Approach: General Case / 8.4:
Functional Integral Approach to the Stochastic Limit / 9:
Statement of the Problem / 9.1:
The StochasticLimit of the Free Massive Scalar Field / 9.2:
The StochasticLimit of the Free Massless Scalar Field / 9.3:
Polynomial Interactions / 9.4:
The StochasticLimit of the Electromagnetic Field / 9.5:
Low-Density Limit: The Basic Idea / 10:
The Low-Density Limit: Fock Case, NoSystem / 10.1:
The Low-Density Limit: Fock Case, Arbitrary System Operator / 10.2:
Comparison of the Distribution and the Stochastic Approach / 10.3:
LDL General, Fock Case, No System Operator, ? = 0 / 10.4:
Six Basic Principles of the Stochastic Limit / 11:
Polynomial Interactions with Cutoff / 11.1:
Assumptions on the Dynamics: Standard Models / 11.2:
Polynomial Interactions: Canonical Forms, FockCase / 11.3:
Polynomial Interactions: Canonical Forms, Gauge-Invariant Case / 11.4:
The Stochastic Universality Class Principle / 11.5:
The Case of Many Independent Fields / 11.6:
The Block Principle: Fock Case / 11.7:
The Stochastic Resonance Principle / 11.8:
The Orthogonalization Principle / 11.9:
The Stochastic Bosonization Principle / 11.10:
The Time-Consecutive Principle / 11.11:
Strongly Nonlinear Regimes / Part II:
Particles Interacting with a Boson Field / 12:
A Single Particle Interacting with a Boson Field / 12.1:
Dynamical q-Deformation: Emergence of the Entangled Commutation Relations / 12.2:
The Two-Point and Four-Point Correlators / 12.3:
The Stochastic Limit of the N-Point Correlator / 12.4:
The q-Deformed Module Wick Theorem / 12.5:
The Wick Theorem for the QED Module / 12.6:
The Limit White Noise Hamiltonian Equation / 12.7:
Free Independence of the Increments of the Master Field / 12.8:
Boltzmannian White Noise Hamiltonian Equations: Normal Form / 12.9:
Unitarity Conditions / 12.10:
Matrix Elements of the Solution / 12.11:
Normal Form of the QED Module Hamiltonian Equation / 12.12:
Unitarity ofthe Solution: Direct Proof / 12.13:
Matrix Elements of the Limit Evolution Operator / 12.14:
Nonexponential Decays / 12.15:
Equilibrium States / 12.16:
The Master Field321 / 12.17:
Proof of the Result for the Two-and Four-Point Correlators / 12.18:
The Vanishing ofthe Crossing Diagrams / 12.19:
The Hot Free Algebra / 12.20:
Interaction of the QEM Field with a Nonfree Particle / 12.21:
The Limit Two-Point Function / 12.22:
The Limit Four-Point Function / 12.23:
The Limit Hilbert Module / 12.24:
The Limit Stochastic Process / 12.25:
The Stochastic Differential Equation / 12.26:
The Anderson Model / 12.27:
Non relativistic Fermions in External Potential: The Anderson Model / 13.1:
The Limit of the Connected Correlators / 13.2:
The Four-Point Function / 13.3:
The Limit of the Connected Transition Amplitude / 13.4:
Proof of(13.4.3) / 13.5:
Solution of the Nonlinear Equation(13.4.2) / 13.6:
Field-Field Interactions / 13.7:
Interacting Commutation Relations / 14.1:
The Tri-linear Hamiltonian with Momentum Conservation / 14.2:
Proof of Theorem 14.2.1 / 14.3:
Example: Four Internal Lines / 14.4:
The Stochastic Limit for Green Functions / 14.5:
Second Quantized Representation of the Nonrelativistic QED Hamiltonian / 14.6:
Interacting Commutation Relations and QED Module Algebra / 14.7:
Decay and the Universality Class of the QED Hamiltonian / 14.8:
Photon Splitting Cascades and New Statistics / 14.9:
Estimates and Proofs / Part III:
Analytical Theory of Feynman Diagrams / 15:
The Connected Component Theorem / 15.1:
The Factorization Theorem / 15.2:
The Caseof Many Independent Fields / 15.3:
The Fermi Block Theorem / 15.4:
Non-Time-Consecutive Terms: The First Vanishing Theorem / 15.5:
Non-Time Consecutive Terms: The Second Vanishing Theorem / 15.6:
The Type-I Term Theorem / 15.7:
The Double Integral Lemma / 15.8:
The Multiple-Simplex Theorem / 15.9:
The Multiple Integral Lemma / 15.10:
The Second Multiple-Simplex Theorem / 15.11:
Some Combinatorial Facts and the Block Normal Ordering Theorem / 15.12:
Term-by-Term Convergence / 16:
The Universality Class Principle and Effective Interaction Hamiltonians / 16.1:
Block and Orthogonalization Principles / 16.2:
References / 16.3:
Index
Statement of the Problem and Simplest Models / Part I:
Notations and Statement of the Problem / 1:
The Schrödinger Equation / 1.1:
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