24 relations: Affine Lie algebra, Bosonic field, Compact group, Conformal field theory, Coset construction, Eigenvalues and eigenvectors, Fermionic field, Hermitian symmetric space, Infinite dihedral group, Inner product space, Kähler manifold, Lie superalgebra, Mathematical physics, Maximal torus, Mirror symmetry (string theory), Normal order, Special unitary group, State of matter, String theory, Super Virasoro algebra, Supersymmetry, Type II string theory, Virasoro algebra, Weyl character formula.
In mathematics, an affine Lie algebra is an infinite-dimensional Lie algebra that is constructed in a canonical fashion out of a finite-dimensional simple Lie algebra.
In quantum field theory, a bosonic field is a quantum field whose quanta are bosons; that is, they obey Bose–Einstein statistics.
In mathematics, a compact (topological, often understood) group is a topological group whose topology is compact.
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations.
In mathematics, the coset construction (or GKO construction) is a method of constructing unitary highest weight representations of the Virasoro algebra, introduced by Peter Goddard, Adrian Kent and David Olive (1986).
In linear algebra, an eigenvector or characteristic vector of a square matrix is a vector that does not change its direction under the associated linear transformation.
In quantum field theory, a fermionic field is a quantum field whose quanta are fermions; that is, they obey Fermi–Dirac statistics.
In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has as an inversion symmetry preserving the Hermitian structure.
In mathematics, the infinite dihedral group Dih∞ is an infinite group with properties analogous to those of the finite dihedral groups.
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures; a complex structure, a Riemannian structure, and a symplectic structure.
In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z2-grading.
Mathematical physics refers to development of mathematical methods for application to problems in physics.
In the mathematical theory of compact Lie groups a special role is played by torus subgroups, in particular by the maximal torus subgroups.
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds.
In quantum field theory a product of quantum fields, or equivalently their creation and annihilation operators, is usually said to be normal ordered (also called Wick order) when all creation operators are to the left of all annihilation operators in the product.
In mathematics, the special unitary group of degree, denoted, is the Lie group of unitary matrices with determinant 1 (i.e., real-valued determinant, not complex as for general unitary matrices).
In physics, a state of matter is one of the distinct forms that matter takes on.
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.
In mathematical physics, a super Virasoro algebra is an extension of the Virasoro algebra to a Lie superalgebra.
Supersymmetry (SUSY), a theory of particle physics, is a proposed type of spacetime symmetry that relates two basic classes of elementary particles: bosons, which have an integer-valued spin, and fermions, which have a half-integer spin.
In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings theories.
In mathematics, the Virasoro algebra (named after the physicist Miguel Angel Virasoro) is a complex Lie algebra, given as a central extension of the complex polynomial vector fields on the circle, and is widely used in conformal field theory and string theory.
In mathematics, the Weyl character formula in representation theory describes the characters of irreducible representations of compact Lie groups in terms of their highest weights.