This advanced textbook caters to masters and graduate students immersed in relativistic quantum theory, specifically the quantization and renormalization of gauge fields. With a scarcity of resources on this subject, and no recent publications, this book fills a critical gap. It guides readers from foundational principles to the cutting edge of the field, equipping them with the knowledge to perform calculations involving higher-spin fields and develop groundbreaking theories.

Topics covered include:

Relativistic invariance, Lorentz group, (anti-) de Sitter space
Relativistic fields, gauge symmetries and algebras
Fermionic fields, Rarita-Schwinger construct, supersymmetries
Classical field equations, constraints, degrees of freedom counting
Causality, Velo-Zwanziger problem
Path-integral quantization of theories with constraints, Faddeev-Popov ghosts
Perturbation theory, Feynman rules
Renormalization, tree-level unitarity
Micro-causality, dispersion relations, sum rules
Connection with string theory, Vasiliev theories, higher-spin fields in AdS space
Each chapter features pedagogical examples suitable for exercises. Interactive notebooks in Wolfram Mathematica provide engaging illustrations of example calculations, complemented by FORM (computer algebra) codes for select calculations.