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This monograph presents recent developments in thermal field theory. Ideas from thermal theory are combined with concepts from group theory using Lie algebras, allowing for applications not only to quantum field theory but also to quantum optics and statistical mechanics. This includes geometrical and topological aspects of spatially confined systems with applications to the Casimir effect, superconductivity, and effective models in particle physics. Finally, some developments in open systems are considered. The book provides a unified picture of the fundamental ideas and their applications and is important to the field, since it combines several diverse ideas that lead to a better understanding of different areas of physics.