Unifying Classical and Quantum Physics How classical and quantum physics can pass smoothly back and forth

This book presents a comprehensive exploration of affine quantization and its implications for quantum mechanics, quantum field theory, and even quantum gravity. Canonical quantization has been a cornerstone of quantum mechanics, but it struggles with certain fundamental problems, such as the quantization of a particle in a box. A new approach, affine quantization, offers a more robust framework, addressing challenges that canonical methods cannot resolve.

Drawing on the results of our collaboration, we develop a self-contained and rigorous exposition, complete with detailed proofs. Our goal is to provide a valuable reference for graduate students, mathematicians, and physicists seeking deeper insights into unresolved issues of the Standard Model—particularly the Higgs sector—and quantum gravity. From the triviality problem in scalar field theories to the role of quantization in addressing singularities, this book connects fundamental mathematical concepts with pressing questions in modern physics.

By presenting both theoretical developments and numerical results, we offer readers a structured approach to exploring novel quantization methods and their impact on contemporary physics.

Introduction.- Triviality of four dimensional ? 4 theory on the lattice.- The Higgs boson.- Initial singularity problem.- Quantization procedures.- Real scalar field theory.- Path integral Monte Carlo.- Complex scalar field theory.- Conclusions.

Riccardo Fantoni was born in Livorno, Italy, on August 30, 1970. He earned his physics degree cum laude from the University of Pisa in 1995 before pursuing graduate studies at the University of Illinois at Urbana-Champaign, where he obtained a Master’s in Physics in 1997. He later earned a Ph.D. in Physics from the University of Trieste in 2004.

Dr. Fantoni has held research and teaching positions at prestigious institutions, including the University "Ca’ Foscari" of Venice (2005–2008) and the National Institute for Theoretical Physics at Stellenbosch University (2009–2012). In 2018, he became a full professor of mathematics in the Italian secondary school system, and in 2019, he obtained the Italian national habilitation as an associate professor in theoretical physics of condensed matter.

His research focuses on developing analytical and computational methods for condensed and soft matter physics.