Conformal groupIn mathematics, the conformal group of an inner product space is the group of transformations from the space to itself that preserve angles. More formally, it is the group of transformations that preserve the conformal geometry of the space. Several specific conformal groups are particularly important: The conformal orthogonal group. If V is a vector space with a quadratic form Q, then the conformal orthogonal group CO(V, Q) is the group of linear transformations T of V for which there exists a scalar λ such that for all x in V For a definite quadratic form, the conformal orthogonal group is equal to the orthogonal group times the group of dilations.
Phénomène critiquevignette|Point critique de l'éthane : 1. état subcritique, liquide et gaz ; 2. opalescence critique ; 3. fluide supercritique. En physique, un phénomène critique est un phénomène associé à une transition de phase du deuxième ordre d'un système thermodynamique. Par exemple la transition de phase ferromagnétique et le comportement au voisinage du point critique liquide-gaz. La plupart des phénomènes critiques proviennent d'une divergence de la ou d'un ralentissement de la dynamique.
Operator product expansionIn quantum field theory, the operator product expansion (OPE) is used as an axiom to define the product of fields as a sum over the same fields. As an axiom, it offers a non-perturbative approach to quantum field theory. One example is the vertex operator algebra, which has been used to construct two-dimensional conformal field theories. Whether this result can be extended to QFT in general, thus resolving many of the difficulties of a perturbative approach, remains an open research question.
Landau poleIn physics, the Landau pole (or the Moscow zero, or the Landau ghost) is the momentum (or energy) scale at which the coupling constant (interaction strength) of a quantum field theory becomes infinite. Such a possibility was pointed out by the physicist Lev Landau and his colleagues. The fact that couplings depend on the momentum (or length) scale is the central idea behind the renormalization group. Landau poles appear in theories that are not asymptotically free, such as quantum electrodynamics (QED) or φ4 theory—a scalar field with a quartic interaction—such as may describe the Higgs boson.
Scalar field theoryIn theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under any Lorentz transformation. The only fundamental scalar quantum field that has been observed in nature is the Higgs field. However, scalar quantum fields feature in the effective field theory descriptions of many physical phenomena. An example is the pion, which is actually a pseudoscalar.
Méthode itérativeEn analyse numérique, une méthode itérative est un procédé algorithmique utilisé pour résoudre un problème, par exemple la recherche d’une solution d’un système d'équations ou d’un problème d’optimisation. En débutant par le choix d’un point initial considéré comme une première ébauche de solution, la méthode procède par itérations au cours desquelles elle détermine une succession de solutions approximatives raffinées qui se rapprochent graduellement de la solution cherchée. Les points générés sont appelés des itérés.
Algebraic quantum field theoryAlgebraic quantum field theory (AQFT) is an application to local quantum physics of C*-algebra theory. Also referred to as the Haag–Kastler axiomatic framework for quantum field theory, because it was introduced by . The axioms are stated in terms of an algebra given for every open set in Minkowski space, and mappings between those. Let be the set of all open and bounded subsets of Minkowski space. An algebraic quantum field theory is defined via a net of von Neumann algebras on a common Hilbert space satisfying the following axioms: Isotony: implies .
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
Icosahedral symmetryIn mathematics, and especially in geometry, an object has icosahedral symmetry if it has the same symmetries as a regular icosahedron. Examples of other polyhedra with icosahedral symmetry include the regular dodecahedron (the dual of the icosahedron) and the rhombic triacontahedron. Every polyhedron with icosahedral symmetry has 60 rotational (or orientation-preserving) symmetries and 60 orientation-reversing symmetries (that combine a rotation and a reflection), for a total symmetry order of 120.
Topological quantum field theoryIn gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants. Although TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, knot theory and the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry. Donaldson, Jones, Witten, and Kontsevich have all won Fields Medals for mathematical work related to topological field theory.
