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Valter Moretti

    Teoria Spettrale e Meccanica Quantistica
    Spectral Theory and Quantum Mechanics
    Fundamental Mathematical Structures of Quantum Theory
    Analytical Mechanics
    • 2023

      Analytical Mechanics

      Classical, Lagrangian and Hamiltonian Mechanics, Stability Theory, Special Relativity

      • 860 pages
      • 31 hours of reading

      Focused on classical Mathematical Physics, this textbook introduces key concepts such as Classical Mechanics, Lagrangian and Hamiltonian formulations, and significant theorems like Lyapunov stability and Poincaré recurrence. It rigorously explores Special Relativity through an axiomatic approach, emphasizing the logical-mathematical structure of the theories. The text highlights critical themes like Galilean and Poincaré symmetries, the interplay between symmetries and constants of motion, and the global description of Dynamics. Designed for flexibility, it caters to diverse curricula and student needs.

      Analytical Mechanics
    • 2019

      Fundamental Mathematical Structures of Quantum Theory

      Spectral Theory, Foundational Issues, Symmetries, Algebraic Formulation

      • 352 pages
      • 13 hours of reading

      Focusing on advanced mathematical structures in quantum theory, this textbook offers a thorough exploration of the connections between logic, lattice theory, and probability. Designed for MSc students, it covers essential topics such as von Neumann algebras and the algebraic formulation relevant to quantum mechanics. The text also delves into hidden-variable interpretations, discussing significant results like Gleason's and the Kochen-Specker theorems, and examines concepts of realism and non-contextuality in relation to the Bell inequality.

      Fundamental Mathematical Structures of Quantum Theory
    • 2018

      Spectral Theory and Quantum Mechanics

      Mathematical Foundations of Quantum Theories, Symmetries and Introduction to the Algebraic Formulation

      • 950 pages
      • 34 hours of reading

      Focusing on the mathematical foundations of quantum theories, this book serves as an introductory text on linear functional analysis, particularly emphasizing Hilbert spaces. It delves into spectral theory elements crucial for physics, while also examining physical phenomenology. The latter sections shift towards the formal and logical aspects of the theory, providing a comprehensive understanding of how mathematical principles underpin quantum mechanics.

      Spectral Theory and Quantum Mechanics