E-grāmata: Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models

I. Measurements and Numbers.-
1. Mathematics and Reality.-
2.
Measurements and Natural Numbers.-
3. Measurements and Rational Numbers.-
4.
Real Numbers: Infinite Exactness of Measurements.-
5. On the Boundary of the
Real Continuum.-
6. Finite Exactness and m-adic Numbers.-
7. Rings of m-adic
Numbers.-
8. Ultrametric Spaces.-
9. Ultrametric Social Space.-
10. Non-Real
Models of Space.- II. Fundamentals.-
1. Einstein-Podolsky-Rosen Paradox.-
2.
Foundations of Quantum Mechanics.-
3. Foundations of Probability Theory.-
4.
Statistical Interpretation of Quantum mechanics.-
5. Quantum Probabilities;
Two Slit Experiment.-
6. Bells Inequality and the Death of Reality.-
7.
Individual Realists Interpretation and Hidden Variables.-
8. Orthodox
Copenhagen Interpretation.-
9. Einstein-Podolsky-Rosen Paradox and
Interpretations of Quantum Mechanics.- III. Non-Archimedean Analysis.-
1.
Exponential Function.-
2. Normed and Locally Convex Spaces.-
3. Locally
Constant Functions.-
4. Kaplanskys Theorem.-
5. Differentiate Functions.-
6.
Analytic Functions.-
7. Complex Non-Archimedean Numbers.-
8. Mahler Basis.-
9. Measures on the Ring of p-adic Integers.-
10. Volkenborn Integral (Uniform
Distribution).-
11. The Monna-Springer Integration Theory.- IV. The
Ultrametric Hilbert Space Description of Quantum Measurements with a Finite
Exactness.-
1. Critique of Interpretations of Quantum Mechanics.-
2.
Preparation Procedures and State Spaces.-
3. Ultrametric (m-adic) Hilbert
Space.-
4. m-adic (Ultrametric) Axiomatic of Quantum Measurements.-
5.
Heisenberg Uncertainty and Inexactness Relations.-
6. Energy Representation
for the Harmonic Oscillator.-
7. Einstein-Podolsky-Rosen Paradox and Infinite
Exactness of Measurements.-
8. Fuzzy Reality.-
9. Quantum-Classical
Heisenberg InexactnessRelation for the Harmonic Oscillator and Free
Particle.- V. Non-Kolmogorov Probability Theory.-
1. Frequency Probability
Theory.-
2. Measure and Probability.-
3. Densities.-
4. Integration
Technique.-
5. Non-Kolmogorov Axiomatics.-
6. Products of Probabilities.-
7.
Proportional and Classical Definitions of Probability.-
8. p-adic Asymptotic
of Bernoulli Probabilities.-
9. More Complicated p-adic Asymptotics.-
10.
p-adic Bernoulli Theorem.-
11. Non-symmetrical Bernoulli Distributions.-
12.
The Central Limit Theorem.- VI. Non-Kolmogorov Probability and Quantum
Physics.-
1. Dirac, Feynman, Wigner and Negative Probabilities.-
2. p-adic
Stochastic Point of View of Bells Inequality.-
3. An Example of p-adic
Negative Probability Behaviour.-
4. p-adic Stochastic Hidden Variable Model
with Violations of Bells Inequality.-
5. Quadri Variate Joint Probability
Distribution.-
6. Non-Kolmogorov Statistical Theory.-
7. Physical
Interpretation of Negative Probabilities in Prugoveckis Empirical Theory of
Measurement.-
8. Experiments to Find p-adic Stochastics in the Two Slit
Experiment.- VII. Position and Momentum Representations.-
1. Groups of
Unitary Isometric Operators in a p-adic Hilbert Space.-
2. p-adic Valued
Gaussian Integration and Spaces of Square Integrable Functions.-
3. A
Representation of the Translation Group.-
4. Gaussian Representations for the
Position and Momentum Operators.-
5. Unitary Isometric One Parameter Groups
Corresponding to the Position and Momentum Operators.-
6. Operator Calculus.-
7. Exactness of a Measurement of Positions and Momenta.-
8. Spectrum of
p-adic Position Operator.-
9. L2-space with respect to p-adic Lebesgue
distributions.-
10. Fourier Transform of L2-maps and Momentum
Representation.-
11. Schrödinger Equation.- VIII. p-adicDynamical Systems
with Applications to Biology and Social Sciences.-
1. Roots of Unity.-
2.
Dynamical Systems in Non-Archimedean Fields.-
3. Dynamical Systems in the
Field of Complex p-adic Numbers.-
4. Dynamical Systems in the Fields of
p-adic Numbers.-
5. Computer Calculations for Fuzzy Cycles.-
6. The Human
Subconscious as a p-adic Dynamical System.-
7. Ultrametric on the
Genealogical Tree.-
8. Social Dynamics.-
9. Human History as a p-adic
Dynamical System.-
10. God as p-adic Dynamical System.-
11. Struggle of
Civilizations.-
12. Economical and Social Effectiveness.- Open Problems.-
1.
Newtons Method (Hensel Lemma).-
2. Non-Real Reality.-
5. Quantum Mechanics
of Vladimirov and Volovich.