# Category: Spinors

Spinors in three dimensions
In mathematics, the spinor concept as specialised to three dimensions can be treated by means of the traditional notions of dot product and cross product. This is part of the detailed algebraic discus
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 2⌊n/2⌋ × 2⌊n/2⌋ matrices. They generalize the P
Feynman checkerboard
The Feynman checkerboard, or relativistic chessboard model, was Richard Feynman’s sum-over-paths formulation of the kernel for a free spin-½ particle moving in one spatial dimension. It provides a rep
Anti-twister mechanism
The anti-twister or antitwister mechanism is a method of connecting a flexible link between two objects, one of which is rotating with respect to the other, in a way that prevents the link from becomi
Orientation entanglement
In mathematics and physics, the notion of orientation entanglement is sometimes used to develop intuition relating to the geometry of spinors or alternatively as a concrete realization of the failure
Spin representation
In mathematics, the spin representations are particular projective representations of the orthogonal or special orthogonal groups in arbitrary dimension and signature (i.e., including indefinite ortho
Spin connection
In differential geometry and mathematical physics, a spin connection is a connection on a spinor bundle. It is induced, in a canonical manner, from the affine connection. It can also be regarded as th
Chandrasekhar–Page equations
Chandrasekhar–Page equations describe the wave function of the spin-½ massive particles, that resulted by seeking a separable solution to the Dirac equation in Kerr metric or Kerr–Newman metric. In 19
Bispinor
In physics, and specifically in quantum field theory, a bispinor, is a mathematical construction that is used to describe some of the fundamental particles of nature, including quarks and electrons. I
Spinor
In geometry and physics, spinors /spɪnər/ are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearl
Spin group
In mathematics the spin group Spin(n) is the double cover of the special orthogonal group SO(n) = SO(n, R), such that there exists a short exact sequence of Lie groups (when n ≠ 2) As a Lie group, Spi
Dirac equation
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all s
Fermionic field
In quantum field theory, a fermionic field is a quantum field whose quanta are fermions; that is, they obey Fermi–Dirac statistics. Fermionic fields obey canonical anticommutation relations rather tha
Plate trick
In mathematics and physics, the plate trick, also known as Dirac's string trick, the belt trick, or the Balinese cup trick, is any of several demonstrations of the idea that rotating an object with st
Fierz identity
In theoretical physics, a Fierz identity is an identity that allows one to rewrite bilinears of the product of two spinors as a linear combination of products of the bilinears of the individual spinor
Dirac equation in curved spacetime
In mathematical physics, the Dirac equation in curved spacetime is a generalization of the Dirac equation from flat spacetime (Minkowski space) to curved spacetime, a general Lorentzian manifold.
Dirac spinor
In quantum field theory, the Dirac spinor is the spinor that describes all known fundamental particles that are fermions, with the possible exception of neutrinos. It appears in the plane-wave solutio
Tangloids
Tangloids is a mathematical game for two players created by Piet Hein to model the calculus of spinors. A description of the game appeared in the book "Martin Gardner's New Mathematical Diversions fro
Gamma matrices
In mathematical physics, the gamma matrices, , also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representat
Van der Waerden notation
In theoretical physics, Van der Waerden notation refers to the usage of two-component spinors (Weyl spinors) in four spacetime dimensions. This is standard in twistor theory and supersymmetry. It is n
Pure spinor
In the domain of mathematics known as representation theory, pure spinors (or simple spinors) are spinors that are annihilated under the Clifford action by a maximal isotropic subspace of the space of
Infeld–Van der Waerden symbols
The Infeld–Van der Waerden symbols, sometimes called simply Van der Waerden symbols, are an invariant symbol associated to the Lorentz group used in quantum field theory. They are named after Leopold
In quantum field theory, the Dirac adjoint defines the dual operation of a Dirac spinor. The Dirac adjoint is motivated by the need to form well-behaved, measurable quantities out of Dirac spinors, re
Triality
In mathematics, triality is a relationship among three vector spaces, analogous to the duality relation between dual vector spaces. Most commonly, it describes those special features of the Dynkin dia
Killing spinor
Killing spinor is a term used in mathematics and physics. By the more narrow definition, commonly used in mathematics, the term Killing spinor indicates those twistorspinors which are also eigenspinor
Rarita–Schwinger equation
In theoretical physics, the Rarita–Schwinger equation is therelativistic field equation of spin-3/2 fermions. It is similar to the Dirac equation for spin-1/2 fermions. This equation was first introdu
Local twistor
In differential geometry, the local twistor bundle is a specific vector bundle with connection that can be associated to any conformal manifold, at least locally. Intuitively, a local twistor is an as
Spinor spherical harmonics
In quantum mechanics, the spinor spherical harmonics (also known as spin spherical harmonics, spinor harmonics and Pauli spinors) are special functions defined over the sphere. The spinor spherical ha
Feynman slash notation
In the study of Dirac fields in quantum field theory, Richard Feynman invented the convenient Feynman slash notation (less commonly known as the Dirac slash notation). If A is a covariant vector (i.e.
Higher-dimensional gamma matrices
In mathematical physics, higher-dimensional gamma matrices generalize to arbitrary dimension the four-dimensional Gamma matrices of Dirac, which are a mainstay of relativistic quantum mechanics. They
Majorana equation
In physics, the Majorana equation is a relativistic wave equation. It is named after the Italian physicist Ettore Majorana, who proposed it in 1937 as a means of describing fermions that are their own