mathematical physics, higher-dimensional gamma matrices generalize to arbitrary dimension the four-dimensional Gamma matrices of Dirac, which are a mainstay...

3}(\mathbb {R} )~.} It is also possible to define higher-dimensional gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis...

of Pauli matrices Gamma matrices, which can be represented in terms of the Pauli matrices. Higher-dimensional gamma matrices In pure mathematics and physics:...

article. Rotation matrices are square matrices, with real entries. More specifically, they can be characterized as orthogonal matrices with determinant...

In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are traceless, Hermitian, involutory and unitary...

physics, 4×4 complex matrices or 8×8 real matrices are needed. Weyl–Brauer matrices Higher-dimensional gamma matrices Clifford module bundle Atiyah, Michael;...

matrices to n dimensions, and are a specific construction of higher-dimensional gamma matrices. They are named for Richard Brauer and Hermann Weyl, and were...

Exterior algebra Fierz identity Gamma matrices Generalized Clifford algebra Geometric algebra Higher-dimensional gamma matrices Hypercomplex number Octonion...

defined for higher-dimensional gamma matrices, with an explicit construction for Weyl spinors given in the article on Weyl–Brauer matrices. Note, however...

four-dimensional supergravity with one gravitino. One important direction in the supergravity program was to try to construct four-dimensional N = 8...

Square matrices, matrices with the same number of rows and columns, play a major role in matrix theory. Square matrices of a given dimension form a noncommutative...

identified with the group of these matrices under matrix multiplication. These matrices are known as "special orthogonal matrices", explaining the notation SO(3)...

transformations from the vector space into itself and n-by-n square matrices. Hence, in a finite-dimensional vector space, it is equivalent to define eigenvalues and...

rotation matrices X, Y, Z, and their multiplication order depend on the choices taken by the user about the definition of both rotation matrices and Euler...

Throughout, italic non-bold capital letters are 4 × 4 matrices, while non-italic bold letters are 3 × 3 matrices. Writing the coordinates in column vectors and...

n\rfloor }} -dimensional representation of the Clifford algebra, the representation that acts on the Dirac spinors, consists of the gamma matrices. When n...

the gamma matrices, which represent the generators of the algebra. The gamma matrices are a set of four 4 × 4 {\displaystyle 4\times 4} matrices { γ μ...

terms of the gamma function. The gamma function can also be used to calculate "volume" and "area" of n-dimensional hyperspheres. The gamma function's ability...

Optical Society of America. The Jones matrices are operators that act on the Jones vectors defined above. These matrices are implemented by various optical...

{\left({\tfrac {1}{8}}\omega _{\mu \nu }[\gamma _{\mu },\gamma _{\nu }]\right)}\psi ,} where γν are gamma matrices, and ωμν is an antisymmetric 4 × 4 matrix...

positive-definite random matrices (i.e. matrix-valued random variables). These distributions are of great importance in the estimation of covariance matrices in multivariate...

matrix gamma distribution and the Wishart distribution are multivariate generalizations of the gamma distribution (samples are positive-definite matrices rather...

"flat" 4-dimensional Minkowski space – an example of a spacetime. Minkowski spacetime appears to be very similar to the standard 3-dimensional Euclidean...

mathematically as problems concerning large, random matrices. In nuclear physics, random matrices were introduced by Eugene Wigner to model the nuclei...

equation Generalizations of Pauli matrices Wigner D-matrix Weyl–Brauer matrices Higher-dimensional gamma matrices Joos–Weinberg equation, alternative...

applications of higher dimensional objects. In 1987, Eric Bergshoeff, Ergin Sezgin, and Paul Townsend showed that eleven-dimensional supergravity includes...

well as rows. The n-dimensional parallelotope spanned by the rows of an n × n Hadamard matrix has the maximum possible n-dimensional volume among parallelotopes...

based on matrices (the holonomy) and these matrices satisfy identities. Given any two SU ⁡ ( 2 ) {\displaystyle \operatorname {SU} (2)} matrices A {\displaystyle...

of physical space Dirac–Kähler equation Gross–Neveu model Higher-dimensional gamma matrices Nonlinear Schrödinger equation Pokhozhaev's identity for the...

distribution describes the spectrum of random matrices with mean 0, the eigenvalues of correlation matrices that fall inside of the aforementioned interval...