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Quantum topology

Index Quantum topology

Quantum topology is a branch of mathematics that connects quantum mechanics with low-dimensional topology. [1]

11 relations: Bra–ket notation, Braid theory, Link (knot theory), Low-dimensional topology, Quantum entanglement, Quantum mechanics, Tangle (mathematics), Tensor product, Topological quantum field theory, Topological space, Vector space.

Bra–ket notation

In quantum mechanics, bra–ket notation is a standard notation for describing quantum states.

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Braid theory

In topology, a branch of mathematics, braid theory is an abstract geometric theory studying the everyday braid concept, and some generalizations.

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Link (knot theory)

In mathematical knot theory, a link is a collection of knots which do not intersect, but which may be linked (or knotted) together.

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Low-dimensional topology

In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions.

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Quantum entanglement

Quantum entanglement is a physical phenomenon which occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the other(s), even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole.

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Quantum mechanics

Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

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Tangle (mathematics)

In mathematics, a tangle is generally one of two related concepts.

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Tensor product

In mathematics, the tensor product of two vector spaces and (over the same field) is itself a vector space, together with an operation of bilinear composition, denoted by, from ordered pairs in the Cartesian product into, in a way that generalizes the outer product.

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Topological quantum field theory

A topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants.

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Topological space

In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.

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Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

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References

[1] https://en.wikipedia.org/wiki/Quantum_topology

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