Trails in Modern Theoretical and Mathematical Physics

This book celebrates the life and work of the late Giovanni Morchio (19442021). It features scientific and anecdotal contributions written by his former colleagues, co-authors, and students, as well as senior scientists who were active witnesses to the dramatic advances in physics and in mathematics that took place during his 50-year-long career.

The volume begins with a biographical introduction, detailing Giovanni Morchio's life and his role as a physicist, mathematician, teacher, and scientist. The core of the book covers a vast spectrum of ideas, reflecting Dr Morchio's scientific interests. Each chapter develops a specific topic of modern research, ranging from quantum mechanics and quantum field theory to additional themes such as the connection between general relativity and Newtonian gravitation. Every contribution provides a historical retrospective, a survey of advances, an outlook of future perspectives and challenges, and an updated bibliography. The last part collects the authors' recollections of their professional and personal interactions with Dr Morchio, in recognition of his deep achievements, his exceptional pedagogical qualities, and his praiseworthy social and pro bono commitment.

Authored by physicists of international calibre covering a broad range of subjects, the book will be a valuable reference for researchers and students of theoretical and mathematical physics.

Valuable reviews in modern problems in mathematical physics A shared tribute in the mathematical physics and theoretical physics communities Valuable reviews in modern problems in theoretical physics

Autorentext

Andrea Cintio was trained as a theoretical and mathematical physicist and is currently a post-doctoral researcher at the Institute for Chemical-Physical Processes (IPCF) of the Italian Research Council (CNR). His research interests concern multi-physics modelling of materials in electromagnetic fields. His present activity is focussed on numerical methods for the study of emergent properties of neural circuits in the network dynamics of high-level behaviours.
Alessandro Michelangeli is an Alexander von Humboldt Senior Researcher at the Institute for Applied Mathematics and at the Hausdorff Center for Mathematics, Bonn, an associated member of the Trieste Institute for Theoretical Quantum Technologies, Trieste, and professor of mathematics and natural sciences at the Prince Mohammad Bin Fahd University, Al-Khobar. He previously held positions at the LMU Munich and the SISSA Trieste.

His research is at the interface of analysis, mathematical physics, and theoretical physics. He is primarily involved in functional analysis, operator theory, and non-linear partial differential equations. His main focus is on mathematical methods for quantum mechanics and their applications to models and problems of relevance for solid state physics and theoretical physics. He is also committed to applying operator-theoretic methods for the rigorous understanding of certain popular numerical algorithms, as well as in foundational questions in theoretical physics.

Inhalt

A. Introduction: "Giovanni Morchio and his role as a Physicist, Mathematician, Teacher ,Scientist".- B. Scientific Part.- Euclidean Quantum Field Theory: A Modern Mathematical Retrospective.- Deformed Cannonical Commutation Relations and Weak Eigenstates of Number-Like Operators.- Grassmannian and Chiral Anomaly.- Local Gauge Fields Recovered from GaugeInvariant Local Observables.- Relativistic Newtonian Gravitation.- Retrospective on Constructive Quantum Field Theory from the 1970s to Nowadays.- Asymptotic Abelianness and Braided Tensor C*-Categories.- Spectral Stochastic Processes in Quantum Mechanics.- Infrared Problem and Spontaneous Breaking of the Lorenz Group in QED.- Determinants, Manifolds with Boundary, and Dirac Operators. Symmetry Breaking in Classical and Quantum Systems.- C. Tribute and IN MEMORIAM Part.