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

contains gamma matrices and a parameter m > 0 {\displaystyle m>0} interpreted as the mass, as well as other physical constants. Dirac first obtained his...

three dimensions Gamma matrices § Dirac basis Angular momentum Gell-Mann matrices Poincaré group Generalizations of Pauli matrices Bloch sphere Euler's...

Paul Adrien Maurice Dirac OM FRS (/dɪˈræk/; 8 August 1902 – 20 October 1984) was an English mathematical and theoretical physicist who is considered to...

physicist P. A. M. Dirac in 1928 in developing the Dirac equation for spin-1/2 particles with a matrix representation of the gamma matrices, which represent...

{\alpha }}=(\alpha _{1},\alpha _{2},\alpha _{3})} are the off-diagonal Dirac matrices α i = β γ i {\displaystyle \alpha _{i}=\beta \gamma _{i}} , with β =...

trivialization. Just as with the Dirac equation on flat spacetime, we make use of the Clifford algebra, a set of four gamma matrices {γμ}{\displaystyle \{\gamma...

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

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 all spin-1⁄2 particles...

is the study of Dirac operators, and Dirac type operators in analysis and geometry, together with their applications. Examples of Dirac type operators...

packaged into a matrix Z a b {\displaystyle Z_{ab}} defined using the Dirac matrices Z a b = ∑ H ( − 1 ) h ( h − 1 ) / 2 ( γ H ) a b T d x H . {\displaystyle...

relativistic quantum mechanics. Likewise using the 4 × 4 Dirac gamma matrices gives rise to the 4 component Dirac spinors used in 3+1 dimensional relativistic quantum...

\gamma ^{\mu }} are the gamma matrices (known as Dirac matrices) and i is the imaginary unit. A second application of the Dirac operator will now reproduce...

acts. Augustin-Louis Cauchy proved the spectral theorem for symmetric matrices, i.e., that every real, symmetric matrix is diagonalizable. In addition...

influenced Paul Dirac in his creation of the Dirac equation for the relativistic electron, though Dirac said that he invented these same matrices himself independently...

}=-i{\frac {\partial }{\partial x_{\mu }}}} and γμ are the gamma matrices. The two-body Dirac equations (TBDE) have the property that if one of the masses...

matrix multiplication of the two matrices. When two matrices are multiplied, the answer is a third matrix. Paul Dirac decided that the essence of Heisenberg's...

quantum mechanics uses 4×4 matrices to describe spin operators and observables.[citation needed] When physicist Paul Dirac tried to modify the Schrödinger...

particles as matrices that evolve in time. It is equivalent to the Schrödinger wave formulation of quantum mechanics, as manifest in Dirac's bra–ket notation...

equation in terms of the Pauli matrices; the Weyl equation, for massless spin-1/2 fermions. The problem was resolved by Dirac in the late 1920s, when he furthered...

matrices multiplying ψ suggest it isn't a scalar wavefunction as permitted in the KG equation, but must instead be a four-component entity. The Dirac...

or wavefunctions: while those can only represent pure states, density matrices can also represent mixed states. Mixed states arise in quantum mechanics...

}} are the Dirac matrices, and e μ i {\displaystyle e_{\mu }^{i}} is a tetrad. If the wave function propagates according to the curved Dirac equation,...

Ettore Majorana in 1937. The term is sometimes used in opposition to a Dirac fermion, which describes fermions that are not their own antiparticles....

of the γμ matrices, and the mc term scalar-multiplies the 4 × 4 identity matrix (usually not written for simplicity). Explicitly, in the Dirac representation...

Nevertheless, spin appears in the Dirac equation, and thus the relativistic Hamiltonian of the electron, treated as a Dirac field, can be interpreted as including...

Schrödinger in 1930 as a result of analysis of the wave packet solutions of the Dirac equation for relativistic electrons in free space, in which an interference...

{m^{2}}{\kappa }}. Dirac equation Dirac equation in the algebra of physical space Dirac–Kähler equation Gross–Neveu model Higher-dimensional gamma matrices Nonlinear...

replaces the velocity of light in the Dirac theory; σ → {\displaystyle {\vec {\sigma }}} is the vector of the Pauli matrices; ψ ( r ) {\displaystyle \psi (\mathbf...

This definition can be extended to 2 n × 2 n {\displaystyle 2n\times 2n} matrices with entries in other fields, such as the complex numbers, finite fields...