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Group Theory in Physics: From Lie Algebras to Grand Unification

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Description

Do you really want to understand why the laws of nature work the way they do… or are you content to use ready-made formulas without seeing the architecture behind them? If you’ve ever felt there’s a hard gap between abstract definitions and “physicist-style” computations, this book is the bridge you’ve been looking for: a rigorous, hands-on guide that turns theory into practical working tools—right up to the most ambitious ideas of unification. Florian Shtini builds this volume with a clear goal: to give advanced students and researchers a mathematically solid yet genuinely usable foundation for modern theoretical physics. The approach is that of a complete study companion: from the basics of continuous groups and their algebras, to the calculation techniques you actually need when moving from concepts to models and predictions. Inside this book you will learn… how to rigorously build the core tools (translation maps, invariant fields, the tangent space at the identity) to arrive at a truly “workable” definition of the algebra associated with a group; how to use structural objects such as the Killing form and the adjoint representation to navigate classification and recognize what kind of algebra you are dealing with; how to work systematically with physically central examples (especially the cases that recur in quantum field theory and fundamental interactions), gaining repeatable procedures rather than isolated recipes; how to master roots and weights to the point where you can read and exploit Dynkin diagrams as calculation tools, not just pictures to memorize; how to compute operational quantities (such as Casimirs, dimensions, and characters via standard formulas and recursions) to quickly validate results and check the consistency of models and representations; how to decompose tensor products and tackle branching rules with a “workbench” mindset: what to do, in what order, and how to avoid the most common mistakes when reducing to subgroups and lower-energy representations; how to connect mathematical structure to the key steps needed when exploring unification scenarios, where correct representation decompositions determine particle content and interaction selection. If you want to stop taking technical steps “on faith” and start rebuilding definitions and calculations from the ground up with confidence—up to the tools used in research—this book is one of the most direct investments you can make in your scientific independence. Bring it into your study path and make it your reference: every chapter adds a real brick to your ability to work with continuous structures and representations in theoretical physics.

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
20 February 2026
Listed Since
22 February 2026

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