Geometry of Time-Spaces: Non-Commutative Algebraic Geometry, Applied to Quantum Theory by Laudal Olav Arnfinn – A Compre

Introduction

Dive into a groundbreaking exploration where abstract algebra meets the fabric of reality. Geometry of Time-Spaces: Non-Commutative Algebraic Geometry, Applied to Quantum Theory by Laudal Olav Arnfinn is not just a book—it is a bold reimagining of the mathematical foundations of modern physics. Published by World Scientific Publishing Company, this hardcover volume offers Indian students, researchers, and mathematicians a rare opportunity to engage with cutting-edge non-commutative geometry and its direct application to quantum theory. If you are ready to move beyond conventional textbooks and into the frontiers of mathematical physics, this monograph is your gateway.

Book Overview

This monograph presents a unified framework where non-commutative algebraic geometry becomes the lens through which time, space, and quantum phenomena are redefined. Laudal Olav Arnfinn introduces a novel definition of time, where mathematical velocities form a compact set, naturally leading to special and general relativity. From this foundation, a general quantum theory emerges, seamlessly integrating with classical results. The book uses a “toy” model that surprisingly contains the classical gauge groups u(1), su(2), and su(3), along with theories of spin and quarks. It is a rigorous, self-contained work for those who seek to understand the deep algebraic structures underlying physical laws.

Key Highlights

• Pioneering non-commutative deformation theory applied to physics
• New definition of time leading to compact velocity sets and relativity
• Canonical Dirac derivation from non-commutative phase spaces
• Explicit toy model reproducing gauge groups u(1), su(2), su(3)
• Bridges pure algebra with quantum mechanics and particle physics
• Hardcover edition from World Scientific, ideal for long-term reference

Inside the Book

Readers will journey through chapters that build from non-commutative deformation theory and moduli theory of associative algebra representations, to a new theory of phase spaces. The Dirac derivation is presented as a natural consequence of the algebraic structure. Later sections apply these tools to model time, relativity, and quantum systems, culminating in the emergence of gauge symmetries. The mathematical exposition is detailed yet accessible to those with a solid background in algebra and geometry.

Key Topics

• Non-commutative algebraic geometry fundamentals
• Moduli spaces of representations
• Non-commutative phase spaces and Dirac derivations
• Mathematical definition of time and relativistic consequences
• Quantum theory from algebraic principles
• Gauge groups u(1), su(2), su(3) from toy models
• Spin, quarks, and standard model connections

Reader Benefits

• Gain a fresh perspective on time as a mathematical construct
• Understand how non-commutative geometry naturally yields quantum mechanics
• See explicit algebraic derivations of gauge symmetries
• Equip yourself with advanced tools for research in mathematical physics
• Own a durable hardcover reference for your academic library

Learning Outcomes

• Master the basics of non-commutative deformation theory
• Apply moduli theory to physical problems
• Derive relativistic kinematics from algebraic velocity compactness
• Construct quantum theories using algebraic methods
• Identify gauge structures within algebraic models

Who Should Read

This book is ideal for graduate students and researchers in mathematics, theoretical physics, and quantum foundations. It suits those with prior knowledge of algebra, algebraic geometry, or quantum mechanics who wish to explore alternative mathematical formulations. Indian students preparing for advanced research or doctoral work in mathematical physics will find it particularly enriching. It is also valuable for faculty members seeking fresh material for specialized courses on non-commutative geometry.

About the Author

Laudal Olav Arnfinn is a distinguished mathematician known for his deep contributions to algebraic geometry and deformation theory. His work has consistently pushed the boundaries of how algebra can model physical reality. This monograph represents decades of his original research, presented with clarity and rigor.

About the Publisher

World Scientific Publishing Company is a leading academic publisher headquartered in Singapore, renowned for high-quality scientific and mathematical literature. With a global reputation for publishing works by Nobel laureates and field-leading researchers, World Scientific ensures that this monograph meets the highest scholarly standards.

Conclusion

Geometry of Time-Spaces is not merely a book—it is an intellectual adventure. For Indian readers passionate about the deepest questions of time, space, and quantum reality, this hardcover volume offers a rare synthesis of algebra and physics. Whether you are a student aiming to understand gauge theories from first principles or a researcher seeking novel mathematical tools, this monograph will inspire and challenge you. Add it to your collection and step into the future of theoretical physics.