What if the mathematical symmetries underlying modern physics allowed far more possibilities than the Standard Model admits? In Beyond the Standard Model, Nathalie Debergh and Jean‑Pierre Petit take readers on a rigorous yet accessible journey through the deep algebraic structures that shape contemporary theoretical physics — and explore what happens when we dare to follow those structures beyond conventional boundaries.
Drawing from the elegance of Lie groups, Lie algebras, and representation theory, the authors reveal how the geometry of symmetry has guided physics for more than a century. From the rotation group SO(3) to the Lorentz and Poincaré groups, the book shows how particles can be understood not merely as objects, but as representations of spacetime symmetries — a perspective that naturally raises profound questions about mass, spin, and the very nature of matter.
The narrative then moves to the heart of relativistic quantum mechanics: the Dirac equation. Through clear explanations and carefully chosen examples, the authors revisit negative‑energy solutions, discrete symmetries, and the conceptual puzzles that have shaped quantum theory. Their analysis opens the door to a bold question: Could negative mass be physically meaningful?
In its third part, the book introduces readers to the powerful and often overlooked framework of geometric algebra. This modern mathematical language unifies reflections, rotations, spacetime structure, and even complex mass transformations in a way that feels both natural and illuminating. Step by step, the authors show how geometric algebra reshapes familiar concepts and suggests new avenues for theoretical exploration.
Finally, the book ventures into quantum field theory, examining how negative‑mass solutions might fit into a coherent and predictive framework. These “perspectives” are not speculative fantasies but carefully reasoned extensions grounded in symmetry, algebra, and the logic of field theory.
Accessible, ambitious, and intellectually stimulating, Beyond the Standard Model is ideal for readers who enjoy deep theoretical insights presented with clarity and pedagogical care. Whether you are a physicist, a mathematician, or simply a curious mind, this book invites you to rethink what is possible — and to explore the hidden structures that may lie beyond the Standard Model.
