This is a list of topics named after

Hermann Weyl Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is assoc ...

, the influential German mathematician from the 20th century.

Mathematics and physics

* Cartan–Weyl theory ** Cartan–Weyl basis * Courant–Fischer–Weyl min-max principle *

De Donder–Weyl theory In mathematical physics, the De Donder–Weyl theory is a generalization of the Hamiltonian formalism in the calculus of variations and classical field theory over spacetime which treats the space and time coordinates on equal footing. In this frame ...

* Hodge−Weyl decomposition * Majorana–Weyl spinor * Peter–Weyl theorem *

Schur–Weyl duality Schur–Weyl duality is a mathematical theorem in representation theory that relates irreducible finite-dimensional representations of the general linear and symmetric groups. It is named after two pioneers of representation theory of Lie groups, I ...

Weyl–Berry conjecture To hear the shape of a drum is to infer information about the shape of the drumhead from the sound it makes, i.e., from the list of overtones, via the use of mathematical theory. "Can One Hear the Shape of a Drum?" is the title of a 1966 article ...

* Weyl–Groenewold product *

Wigner–Weyl transform In quantum mechanics, the Wigner–Weyl transform or Weyl–Wigner transform (after Hermann Weyl and Eugene Wigner) is the invertible mapping between functions in the quantum phase space formulation and Hilbert space operators in the Schrödin ...

* Weyl algebra * Weyl almost periodic functions * Weyl anomaly *

Weyl basis In mathematical physics, the gamma matrices, \left\ , also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra Cl1,3(\ma ...

of the gamma matrices * Weyl chamber * Weyl character formula ** Weyl denominator formula ** Weyl dimension formula ** Weyl–Kac character formula *

Weyl curvature In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold. Like the Riemann curvature tensor, the Weyl tensor expresses the tidal f ...

: see Weyl tensor *

Weyl curvature hypothesis The Weyl curvature hypothesis, which arises in the application of Albert Einstein's general theory of relativity to physical cosmology, was introduced by the British mathematician and theoretical physicist Roger Penrose in an article in 1979 in ...

* Weyl dimension formula, a specialization of the character formula * Weyl distance function *

Weyl equation In physics, particularly in quantum field theory, the Weyl equation is a relativistic wave equation for describing massless spin-1/2 particles called Weyl fermions. The equation is named after Hermann Weyl. The Weyl fermions are one of the three ...

, a relativistic wave equation * Weyl expansion * Weyl fermion *

Weyl gauge In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct con ...

* Weyl gravity *

Weyl group In mathematics, in particular the theory of Lie algebras, the Weyl group (named after Hermann Weyl) of a root system Φ is a subgroup of the isometry group of that root system. Specifically, it is the subgroup which is generated by reflections th ...

** Length of a Weyl group element **

Restricted Weyl group In mathematics, restricted root systems, sometimes called relative root systems, are the root systems associated with a symmetric space. The associated finite reflection group is called the restricted Weyl group. The restricted root system of a s ...

Weyl integral In mathematics, the Weyl integral (named after Hermann Weyl) is an operator defined, as an example of fractional calculus, on functions ''f'' on the unit circle having integral 0 and a Fourier series. In other words there is a Fourier series for ...

Weyl integration formula In mathematics, the Weyl integration formula, introduced by Hermann Weyl, is an integration formula for a compact connected Lie group ''G'' in terms of a maximal torus ''T''. Precisely, it says there exists a real-valued continuous function ''u' ...

* Weyl law *

Weyl metrics In general relativity, the Weyl metrics (named after the German-American mathematician Hermann Weyl) are a class of ''static'' and ''axisymmetric'' solutions to Einstein's field equation. Three members in the renowned Kerr–Newman family solution ...

* Weyl module * Weyl notation *

Weyl quantization Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is assoc ...

* Weyl relations *

Weyl scalar In the Newman–Penrose (NP) formalism of general relativity, Weyl scalars refer to a set of five complex scalars \ which encode the ten independent components of the Weyl tensor of a four-dimensional spacetime. Definitions Given a complex null ...

Weyl semimetal Weyl fermions are massless chiral fermions embodying the mathematical concept of a Weyl spinor. Weyl spinors in turn play an important role in quantum field theory and the Standard Model, where they are a building block for fermions in quantum ...

Weyl sequence In mathematics, a Weyl sequence is a sequence from the equidistribution theorem proven by Hermann Weyl Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although ...

Weyl spinor In physics, particularly in quantum field theory, the Weyl equation is a relativistic wave equation for describing massless spin-1/2 particles called Weyl fermions. The equation is named after Hermann Weyl. The Weyl fermions are one of the three p ...

Weyl representation Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is assoc ...

Weyl sum In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function :e(x) = \exp(2\pi ix).\, Therefore, a typ ...

, a type of exponential sum *

Weyl symmetry :''See also Wigner–Weyl transform, for another definition of the Weyl transform.'' In theoretical physics, the Weyl transformation, named after Hermann Weyl, is a local rescaling of the metric tensor: :g_\rightarrow e^g_ which produces another ...

: see Weyl transformation *

Weyl tensor In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold. Like the Riemann curvature tensor, the Weyl tensor expresses the tidal f ...

Weyl transform Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is assoc ...

Weyl transformation :''See also Wigner–Weyl transform, for another definition of the Weyl transform.'' In theoretical physics, the Weyl transformation, named after Hermann Weyl, is a local rescaling of the metric tensor: :g_\rightarrow e^g_ which produces anothe ...

Weyl vector 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. It was proved by . There is a closely related formula for the char ...

of a compact Lie group *

Weyl–Brauer matrices In mathematics, particularly in the theory of spinors, the Weyl–Brauer matrices are an explicit realization of a Clifford algebra as a matrix algebra of matrices. They generalize the Pauli matrices to dimensions, and are a specific constructi ...

* Weyl−Lewis−Papapetrou coordinates *

Weyl–Schouten theorem In the mathematical field of differential geometry, the existence of isothermal coordinates for a ( pseudo-)Riemannian metric is often of interest. In the case of a metric on a two-dimensional space, the existence of isothermal coordinates is uncon ...

Weyl–von Neumann theorem In mathematics, the Weyl–von Neumann theorem is a result in operator theory due to Hermann Weyl and John von Neumann. It states that, after the addition of a compact operator () or Hilbert–Schmidt operator () of arbitrarily small norm, a bound ...

* Weyl-squared theories * Weyl's axioms * Weyl's construction *

Weyl's criterion In mathematics, a sequence (''s''1, ''s''2, ''s''3, ...) of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling in a subinterval is proportional to the length of that subinterval. Such sequences ...

* Weyl's criterion for essential spectrum *

Weyl's criterion for equidistribution In mathematics, a sequence (''s''1, ''s''2, ''s''3, ...) of real numbers is said to be equidistributed, or uniformly distributed, if the proportion of terms falling in a subinterval is proportional to the length of that subinterval. Such sequences ...

* Weyl's inequality *

Weyl's inequality (number theory) In number theory, Weyl's inequality, named for Hermann Weyl, states that if ''M'', ''N'', ''a'' and ''q'' are integers, with ''a'' and ''q'' coprime, ''q'' > 0, and ''f'' is a real polynomial of degree ''k'' whose leading coefficient ''c'' ...

* Weyl's infinitesimal geometry * Weyl's lemma: several results, for example; ** Weyl's lemma on the "very weak" form of the

Laplace equation In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as \nabla^2\! f = 0 or \Delta f = 0, where \Delta = \nab ...

** Weyl's lemma on

hypoellipticity In the theory of partial differential equations, a partial differential operator P defined on an open subset :U \subset^n is called hypoelliptic if for every distribution u defined on an open subset V \subset U such that Pu is C^\infty (smo ...

** Weyl's paradox (properly the Grelling–Nelson paradox) * Weyl's postulate * Weyl's theorem on complete reducibility *

Weyl's tile argument In philosophy, the Weyl's tile argument, introduced by Hermann Weyl in 1949, is an argument against the notion that physical space is "discrete", as if composed of a number of finite sized units or cubical complex, tiles. The argument purports to s ...

* Weyl–Titchmarsh–Kodaira theory * Weyl's tube formula *

Weyl's unitary trick In mathematics, the unitarian trick is a device in the representation theory of Lie groups, introduced by for the special linear group and by Hermann Weyl for general semisimple groups. It applies to show that the representation theory of some g ...

Other

Weyl (crater) Weyl is a lunar impact crater that is located on the far side of the Moon, behind the western limb as seen from the Earth. It lies to the east-southeast of the larger crater Fersman. To the southeast is Kamerlingh Onnes, and to the northeast is ...

References

{{DEFAULTSORT:Weyl, Hermann Lists of things named after mathematicians

Weyl Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is assoc ...