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Quantum algebra is one of the top-level mathematics categories used by the arXiv. It is the study of noncommutative analogues and generalizations of commutative algebras, especially those arising in Lie theory.[1]
Subjects include:
Quantum groups
Skein theories
Operadic algebra
Diagrammatic algebra
Quantum field theory
Racks and quandles
^"What is quantum algebra?". mathoverflow.net. Retrieved 2018-01-22.
commutative algebras, especially those arising in Lie theory. Subjects include: Quantum groups Skein theories Operadic algebra Diagrammatic algebraQuantum field...
term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups...
Algebraicquantum field theory (AQFT) is an application to local quantum physics of C*-algebra theory. Also referred to as the Haag–Kastler axiomatic framework...
theory, differential geometry, quantum statistical mechanics, quantum information, and quantum field theory. Operator algebras can be used to study arbitrary...
physics CCR algebras (after canonical commutation relations) and CAR algebras (after canonical anticommutation relations) arise from the quantum mechanical...
mathematics, a quantum affine algebra (or affine quantum group) is a Hopf algebra that is a q-deformation of the universal enveloping algebra of an affine...
a quantum spacetime, and to Robert Oppenheimer, who carried it to Hartland Snyder, who published the first concrete example. Snyder's Lie algebra was...
operators in quantum field theories define an infinite-dimensional Lie algebra called a current algebra. Mathematically these are Lie algebras consisting...
quantizations (cf. quantum group) of the exterior algebra, in the same way that the Weyl algebra is a quantization of the symmetric algebra. Weyl algebras and Clifford...
from condensed-matter physics and quantum field theory to string theory and LHC phenomenology. Formally, a Hopf algebra is an (associative and coassociative)...
and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological...
Poisson algebras appear naturally in Hamiltonian mechanics, and are also central in the study of quantum groups. Manifolds with a Poisson algebra structure...
tests in classical mechanics forms a Boolean algebra, but the structure of experimental tests in quantum mechanics forms a much more complicated structure...
A quantum computer is a computer that takes advantage of quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles...
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction...
In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information....
(CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local...
commute. Jordan algebras were introduced by Pascual Jordan (1933) in an effort to formalize the notion of an algebra of observables in quantum electrodynamics...
Linear algebra is the branch of mathematics concerning linear equations such as: a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...
the field have studied irreversible quantum mechanical systems on von Neumann algebras. Equations to describe quantum systems can be seen as equivalent...
In mathematics, a quantum or quantized enveloping algebra is a q-analog of a universal enveloping algebra. Given a Lie algebra g {\displaystyle {\mathfrak...
algebra requires the introduction of a Z2-grading under which the bosons are the even elements and the fermions are the odd elements. Such an algebra...
the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises...
the Bethe ansatz. In the algebraic formulation, these are related to particular quantum affine algebras and elliptic quantum groups in the XXZ and XYZ...
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