categoriesphysics

Categoriesphysics is an interdisciplinary approach that uses category theory to study and formalize physical theories. Emerging from the observation that many physical concepts are inherently compositional, it seeks to describe systems, processes, and their interrelations in a language that emphasizes structure over representation.

Foundations: In a categorical formulation, objects represent physical systems; morphisms correspond to physical processes or state changes; a monoidal structure provides a formal account of composing systems in parallel. Functors relate different theories or regimes, and natural transformations compare alternative process descriptions. Higher category theory and enriched categories extend these ideas to more complex notions such as processes between processes and multi-level descriptions.

Prominent strands: Categorical quantum mechanics employs dagger compact categories to model quantum states and operations abstractly, enabling diagrammatic calculi such as the ZX-calculus. Functorial quantum field theory treats a quantum field theory as a functor from a category of spacetime cobordisms to a category of vector spaces or other targets. Topos-theoretic and higher-categorical approaches model the logic, geometry, and algebraic structure of physical theories, with contributors such as Baez, Dolan, Abramsky, and Coecke advancing the framework.

Applications: The formalism supports quantum information, quantum computing, and the study of topological phases, quantum gravity, and extended quantum field theories. It provides a unifying perspective for comparing theories and constructing compositional models of complex experimental setups.

Criticism: The framework is highly abstract, and translating categorical structures into concrete predictions can be challenging. Adoption varies across subfields, and some researchers seek closer ties to experimental practice.

See also: category theory, quantum mechanics, tensor categories, monoidal categories, topos theory, functorial quantum field theory.