Mathematical Frameworks for Analyzing Quantum Field Theory

Abstract

Quantum Field Theory (QFT) provides a foundational framework for understanding particle physics and interactions at a fundamental level. This article presents a comprehensive overview of mathematical frameworks utilized in the analysis and formulation of QFT. Emphasis is placed on the integration of differential geometry, algebraic structures, and functional analysis within the context of QFT. The paper discusses the role of various mathematical tools such as Lie groups, tensor calculus, and gauge theory in the development and application of QFT models. Through detailed examples and theoretical exposition, this work aims to bridge the gap between abstract mathematical concepts and their practical implementation in theoretical physics.