mathematical physics, the gamma matrices,   { γ 0 , γ 1 , γ 2 , γ 3 }   , {\displaystyle \ \left\{\gamma ^{0},\gamma ^{1},\gamma ^{2},\gamma ^{3}\right\}\ ,} also...

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

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

by gamma matrices, matrices that satisfy a set of canonical anti-commutation relations. The spinors are the column vectors on which these matrices act...

Let γμ denote a set of four 4-dimensional gamma matrices, here called the Dirac matrices. The Dirac matrices satisfy where { , } is the anticommutator...

{\stackrel {\mathrm {def} }{=}}\ \gamma ^{0}A_{0}+\gamma ^{1}A_{1}+\gamma ^{2}A_{2}+\gamma ^{3}A_{3}} where γ are the gamma matrices. Using the Einstein summation...

4-gradient. In practice one often writes the gamma matrices in terms of 2 × 2 sub-matrices taken from the Pauli matrices and the 2 × 2 identity matrix. Explicitly...

article. Rotation matrices are square matrices, with real entries. More specifically, they can be characterized as orthogonal matrices with determinant 1;...

{I} \end{bmatrix}}} These two 4×4 matrices are related to the Dirac gamma matrices. Note that 0 and I are 2×2 matrices here. The next step is to look for...

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...

The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the...

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

of the gamma matrices, including the Dirac, Weyl, and Majorana representations, that C γ μ = − γ μ T C {\displaystyle \,C\,\gamma _{\mu }=-\gamma _{\mu...

the subspace spanned by the gamma matrices inside the Dirac algebra. The Lorentz group may be represented by 4×4 matrices Λ. The action of a Lorentz transformation...

{\displaystyle 2\times 3} . Matrices are commonly related to linear algebra. Notable exceptions include incidence matrices and adjacency matrices in graph theory...

of matrices, which are related to Spin (physics). Pauli matrices, also called the "Pauli spin matrices". Generalizations of Pauli matrices Gamma matrices...

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

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

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

written as ln(x) or loge(x). In mathematics, the gamma function (represented by Γ, capital Greek letter gamma) is the most common extension of the factorial...

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

{\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...

}^{ab}\gamma _{ab}\psi _{\nu },} where γ a b = γ [ a γ b ] {\displaystyle \gamma _{ab}=\gamma _{[a}\gamma _{b]}} . The regular gamma matrices satisfying...

transform under Lorentz transformations generated by the gamma matrices ( γ μ {\displaystyle \gamma _{\mu }} ). It can be shown that the scalar product ⟨...

{j}})} . Taking μ = 0 and using the relation for gamma matrices ( γ 0 ) 2 = I {\displaystyle \left(\gamma ^{0}\right)^{2}=I} , the probability density becomes...

article lists some important classes of matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular...

★. Consider the gamma matrices in the examples given above. The formula defining the fifth gamma matrix ( γ 5 {\displaystyle \gamma _{5}} ) shows that...

numbers can be represented as matrices, so can quaternions. There are at least two ways of representing quaternions as matrices in such a way that quaternion...

compartmented information Gamma matrices, in mathematical physics The Gamma People, a 1956 British-American film Gama (disambiguation) Gamma ray (disambiguation)...

^{0}q\varphi \right],} in which the γ = (γ1, γ2, γ3) and γ0 are the Dirac gamma matrices related to the spin of the particle. The Dirac equation is true for...