Quantum topology

Quantum mechanics
${\hat {H}}\|\psi (t)\rangle =i\hbar {\frac {\partial }{\partial t}}\|\psi (t)\rangle$ Schrödinger equation
Introduction Glossary History
Background Classical mechanics Old quantum theory Bra–ket notation Hamiltonian Interference
Fundamentals Complementarity Decoherence Entanglement Energy level Measurement Nonlocality Quantum number State Superposition Symmetry Tunnelling Uncertainty Wave function (collapse)
Experiments Afshar Bell's inequality Davisson–Germer Double-slit Elitzur–Vaidman Franck–Hertz Leggett–Garg inequality Mach–Zehnder Popper Quantum eraser (delayed-choice) Schrödinger's cat Stern–Gerlach Wheeler's delayed-choice
Formulations Overview Heisenberg Interaction Matrix Phase-space Schrödinger Sum-over-histories (path integral)
Equations Dirac Klein–Gordon Pauli Rydberg Schrödinger
Interpretations Overview Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective collapse Bayesian Quantum logic Relational Stochastic Scale relativity Transactional
Advanced topics Relativistic quantum mechanics Quantum field theory Quantum information science Quantum computing Quantum chaos Density matrix Fractional quantum mechanics Scattering theory Quantum statistical mechanics Quantum machine learning
Scientists Aharonov Bell Blackett Bloch Bohm Bohr Born Bose de Broglie Candlin Compton Dirac Davisson Debye Ehrenfest Einstein Everett Fock Fermi Feynman Glauber Gutzwiller Heisenberg Hilbert Jordan Kramers Pauli Lamb Landau Laue Moseley Millikan Onnes Planck Rabi Raman Rydberg Schrödinger Sommerfeld von Neumann Weyl Wien Wigner Zeeman Zeilinger

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

Dirac notation provides a viewpoint of quantum mechanics which becomes amplified into a framework that can embrace the amplitudes associated with topological spaces and the related embedding of one space within another such as knots and links in three-dimensional space. This bra–ket notation of kets and bras can be generalised, becoming maps of vector spaces associated with topological spaces that allow tensor products.^[1]

Topological entanglement involving linking and braiding can be intuitively related to quantum entanglement.^[1]

References

Quantum topology by Louis H. Kauffman and Randy A. Baadhio, World Scientific Publishing Co Pte Ltd, 1993

1 2 Quantum Topology and Quantum Computing by Louis H. Kauffman

External links

Quantum Topology at EMS Publishing House.

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Quantum topology

See also

References

External links