Topological Quantum Field Theory

Topological Quantum Field Theory (TQFT) is a branch of physics and mathematics that studies how quantum fields behave in ways that depend only on the shape or topology of the space, not on its exact geometry. Essentially, TQFT focuses on properties that remain unchanged when objects are smoothly transformed without tearing or gluing. It provides tools to understand phenomena like quantum states linked to the shape of spaces—useful in areas like quantum computing and understanding fundamental particles—by linking shapes and patterns to quantum behavior in a mathematically rigorous way.