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QuantumA quantum is the smallest increment into which many physical properties are subdivided.
Most commonly, quanta are the fundamental units of something measurable. Energy, for example, is quantized into photons, wavelike packets of fixed frequency. Quantum physics was founded at the beginning of the twentieth century, incorporating at a foundational level the idea that electromagnetic radiation comes in such packets; the concepts of quantum theory have proved paradoxical, and difficult to articulate in any familiar terms, but the theory built up into quantum field theory was the largest single step in the physical sciences between 1900 and 1950.
Etymology
The word quantum comes from the Latin word for "quantity".
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Topological Quantum Field Theory Club
A club which holds monthly and yearly meetings in Portugal to discuss topics in quantum field theory.
http://www.math.ist.utl.pt/~rpicken/tqft/
An Introduction to Topological Quantum Field Theories
A topological quantum field theory (TQFT) is an, almost, metric independent quantum field theory that gives rise to topological invariants of the background manifold
http://www.math.lsa.umich.edu/~ruthjl/papers/itft.html
Topological Geometrodynamics
An attempt to unify fundamental interactions by assuming that physical spacetimes can be regarded as submanifolds of certain 8-dimensional space. Book in PDF by Matti Pitkänen, Helsinki.
http://www.physics.helsinki.fi/~matpitka/tgd.html
Quantum Topology Project
The objective of the Project are to use topological quantum field theories to explore low-dimensional topological objects. The field theories to be used are combinatorially and algebraically defined, and the emphasis is on numerical computation and detection of counterexamples rather than general structure.
http://www.math.vt.edu/quantum_topology/
Research Group on Topological Quantum Field Theory and Knots
Research Group on Topological Quantum Field Theories in any dimension and their relation to topological invariants. Particular attention is given to BF theories and knots in any dimension.
http://wwwteor.mi.infn.it/users/cotta/tqft.html
Ahmed, Diaa A: Quantum Field Theories: Quantum Topology
Includes links to research papers, quotations on the development of the quantum theory, brief notes on the field and related links.
http://homestead.com/qft/
Math and Physics
A brief review on some of the recent developments in topological quantum field theory. These include topological string theory, topological Yang-Mills theory and Chern-Simons gauge theory.
http://arxiv.org/abs/hep-th/0107079
Topological Quantum Field Theories
Topological quantum field theories can be used as a powerful tool to probe geometry and topology in low dimensions. Chern-Simons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots and links in three dimensions.
http://arxiv.org/abs/hep-th/9907119
New Results in Topological Field Theory and Abelian Gauge Theory
These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. Much of the necessary background material is given, including a crash course in topological field theory, cohomology of manifolds, topological gauge theory and the rudiments of four manifold theory.
http://arxiv.org/abs/hep-th/9511038
Geometry of 2D Topological Field Theory
These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories.
http://arxiv.org/abs/hep-th/9407018
Lectures in Topological Quantum Field Theory
A set of introductory notes on Topological Quantum Field Theories
http://arxiv.org/abs/hep-th/9709192
Topological Quantum Field Theory, a Progress Report
A brief introduction to Topological Quantum Field Theory as well as a description of recent progress made in the field is presented. I concentrate mainly on the connection between Chern-Simons gauge theory and Vassiliev invariants, and Donaldson theory and its generalizations and Seiberg-Witten invariants. Emphasis is made on the usefulness of these relations to obtain explicit expressions for topological invariants, and on the universal structure underlying both systems.
http://arxiv.org/abs/hep-th/9511037
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