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...

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...

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...

{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...

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

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 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 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...

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

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...

{\displaystyle 2\times 3} ⁠. In linear algebra, matrices are used as linear maps. In geometry, matrices are used for geometric transformations (for example...

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

matrices arise in the study of operator algebras and the theory of quantum computation. Butson-type Hadamard matrices are complex Hadamard matrices in...

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

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...

}^{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...

{\displaystyle \left(i\gamma ^{\mu }\partial _{\mu }-m\right)\psi (x)=0.\,} where γ μ {\displaystyle \gamma ^{\mu }} are gamma matrices and m {\displaystyle...

for contracting the vector with the Dirac gamma matrices, so A / = γ μ A μ {\displaystyle A\!\!\!/=\gamma ^{\mu }A_{\mu }} ; what one gains is not only...

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

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

γ-Hydroxybutyric acid, also known as gamma-hydroxybutyric acid, GHB, or 4-hydroxybutanoic acid, is a naturally occurring neurotransmitter and a depressant...

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

matrices γ0, ..., γ3, called Dirac matrices, which have the property that γ i γ j + γ j γ i = 2 η i j , {\displaystyle \gamma _{i}\gamma _{j}+\gamma _{j}\gamma...

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

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

{\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...