field K is called a non-Archimedean local field if it is complete with respect to a metric induced by a discrete valuation v and if its residue field...

Local field potentials (LFP) are transient electrical signals generated in nerves and other tissues by the summed and synchronous electrical activity...

mathematics, local class field theory, introduced by Helmut Hasse, is the study of abelian extensions of local fields; here, "local field" means a field which...

into English as Local Fields by Marvin Jay Greenberg in 1979, is a seminal graduate-level algebraic number theory text covering local fields, ramification...

known fields are the field of rational numbers, the field of real numbers and the field of complex numbers. Many other fields, such as fields of rational...

of local fields where a more detailed analysis can be carried out with the aid of tools such as ramification groups. In this article, a local field is...

(-dimensional) local field is an important example of a complete discrete valuation field. Such fields are also sometimes called multi-dimensional local fields. On...

mathematics, an algebraic number field (or simply number field) is an extension field K {\displaystyle K} of the field of rational numbers Q {\displaystyle...

the complex representations of a reductive algebraic group G over a local field F, and representations of the Langlands group of F into the L-group of...

class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global...

more specifically in local class field theory, the ramification groups are a filtration of the Galois group of a local field extension, which gives...

the central nervous system at all levels, and include spike trains, local field potentials and large-scale oscillations which can be measured by electroencephalography...

Field electron emission, also known as field-induced electron emission, field emission (FE) and electron field emission, is the emission of electrons from...

automorphic forms and representation theory of algebraic groups over local fields and adeles. It was described by Edward Frenkel as the "grand unified...

global field is one of two types of fields (the other one is local fields) that are characterized using valuations. There are two kinds of global fields: Algebraic...

cohomology, local Tate duality (or simply local duality) is a duality for Galois modules for the absolute Galois group of a non-archimedean local field. It is...

infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. Conformal field theory has important...

momentum transfer to the spacecraft from some external source such as a local force field, which in turn must obtain it from still other momentum and/or energy...

Algebraic quantum field theory (AQFT) is an application to local quantum physics of C*-algebra theory. Also referred to as the Haag–Kastler axiomatic framework...

Galois group of a certain type of field extension is a specific group associated with the field extension. The study of field extensions and their relationship...

extensions of a valuation of a field K to an extension field of K. This generalizes the notions in algebraic number theory, local fields, and Dedekind domains...

moment to the local electric field; in a crystalline solid, one considers the dipole moment per unit cell. Note that the local electric field seen by a molecule...

be local, or it might be nonlocal. Noether fields are often composite fields and they are local. In the generalized LSZ formalism, composite fields, which...

of global fields rather than for the larger local fields. The Hilbert symbol has been generalized to higher local fields. Over a local field K {\displaystyle...

Formally real field Real closed field Global field A number field or a function field of one variable over a finite field. Local field A completion of...

usual notion of admissible representation when the local field is non-Archimedean. When the local field is Archimedean, admissible representation instead...

theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according...

not be a field. Such a notion was introduced in a 1951 paper of Goro Azumaya, for the case where R {\displaystyle R} is a commutative local ring. The...

to the group ring (Z/2Z)[F*/F*2] if q ≡ 1 mod 4. The Witt ring of a local field with maximal ideal of norm congruent to 1 modulo 4 is isomorphic to the...

axioms for geometry, and the theories of ordered groups, ordered fields, and local fields. An algebraic structure in which any two non-zero elements are...