topological quantum field theories
Topological quantum field theories (TQFTs) are mathematical frameworks that study quantum field theories with a focus on topological properties rather than geometric ones. They are used to understand how physical systems behave under continuous deformations, such as stretching or bending, without tearing or gluing. TQFTs are particularly important in areas like string theory and quantum gravity.
In TQFTs, the observables are often linked to the topology of the underlying space, such as manifolds. This means that the physical phenomena described by TQFTs remain invariant under changes in shape, making them useful for classifying different types of quantum states. They also have applications in mathematics, particularly in knot theory and the study of 3-manifolds.