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Conformal may refer to: Conformal (software), in ASIC Software; Conformal coating in electronics; Conformal cooling channel, in injection or blow moulding; Conformal field theory in physics, such as: Boundary conformal field theory; Coset conformal field theory; Logarithmic conformal field theory; Rational conformal field theory
The conformal property may be described in terms of the Jacobian derivative matrix of a coordinate transformation. The transformation is conformal whenever the Jacobian at each point is a positive scalar times a rotation matrix (orthogonal with determinant one). Some authors define conformality to include orientation-reversing mappings whose ...
Alternatively any conformal linear transformation can be represented as a versor (geometric product of vectors); [1] every versor and its negative represent the same transformation, so the versor group (also called the Lipschitz group) is a double cover of the conformal orthogonal group.
An equivalence class of such metrics is known as a conformal metric or conformal class. Thus, a conformal metric may be regarded as a metric that is only defined "up to scale". Often conformal metrics are treated by selecting a metric in the conformal class, and applying only "conformally invariant" constructions to the chosen metric.
The term conformal field theory has sometimes been used with the meaning of two-dimensional conformal field theory, as in the title of a 1997 textbook. [5] Higher-dimensional conformal field theories have become more popular with the AdS/CFT correspondence in the late 1990s, and the development of numerical conformal bootstrap techniques in the ...
In complex analysis, a Schwarz–Christoffel mapping is a conformal map of the upper half-plane or the complex unit disk onto the interior of a simple polygon.Such a map is guaranteed to exist by the Riemann mapping theorem (stated by Bernhard Riemann in 1851); the Schwarz–Christoffel formula provides an explicit construction.
Bateman and Cunningham showed that this conformal group is "the largest group of transformations leaving Maxwell’s equations structurally invariant." [9] The conformal group of spacetime has been denoted C(1,3) [10] Isaak Yaglom has contributed to the mathematics of spacetime conformal transformations in split-complex and dual numbers. [11]
A conformal connection on an n-manifold M is a Cartan geometry modelled on the conformal sphere, where the latter is viewed as a homogeneous space for O + (n+1,1). In other words, it is an O + (n+1,1)-bundle equipped with a O + (n+1,1)-connection (the Cartan connection)