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  2. Dirac algebra - Wikipedia

    en.wikipedia.org/wiki/Dirac_algebra

    In mathematical physics, the Dirac algebra is the Clifford algebra, ().This was introduced by the mathematical 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 the generators of the algebra.

  3. Higher-dimensional gamma matrices - Wikipedia

    en.wikipedia.org/wiki/Higher-dimensional_gamma...

    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 are utilized in relativistically invariant wave equations for fermions (such as spinors) in arbitrary space-time dimensions, notably in string ...

  4. Spin network - Wikipedia

    en.wikipedia.org/wiki/Spin_network

    A unit with spin number n is called an n-unit and has angular momentum nħ/2, where ħ is the reduced Planck constant. For bosons, such as photons and gluons, n is an even number. For fermions, such as electrons and quarks, n is odd. Given any closed spin network, a non-negative integer can be calculated which is called the norm of the

  5. Loop quantum gravity - Wikipedia

    en.wikipedia.org/wiki/Loop_quantum_gravity

    A spin network state assigns an amplitude to a set of spin half particles tracing out a path in space, merging and splitting. These are described by spin networks γ {\displaystyle \gamma } : the edges are labelled by spins together with 'intertwiners' at the vertices which are prescription for how to sum over different ways the spins are rerouted.

  6. Mathematical formulation of the Standard Model - Wikipedia

    en.wikipedia.org/wiki/Mathematical_formulation...

    The sum over r covers other degrees of freedom specific for the field, such as polarization or spin; it usually comes out as a sum from 1 to 2 or from 1 to 3. E p is the relativistic energy for a momentum p quantum of the field, = m 2 c 4 + c 2 p 2 {\textstyle ={\sqrt {m^{2}c^{4}+c^{2}\mathbf {p} ^{2}}}} when the rest mass is m .

  7. Pauli matrices - Wikipedia

    en.wikipedia.org/wiki/Pauli_matrices

    That is, the resulting spin operators for higher spin systems in three spatial dimensions, for arbitrarily large j, can be calculated using this spin operator and ladder operators. They can be found in Rotation group SO(3) § A note on Lie algebras. The analog formula to the above generalization of Euler's formula for Pauli matrices, the group ...

  8. Dirac equation in curved spacetime - Wikipedia

    en.wikipedia.org/wiki/Dirac_equation_in_curved...

    The vierbein defines a local rest frame, allowing the constant Gamma matrices to act at each spacetime point. In differential-geometric language, the vierbein is equivalent to a section of the frame bundle, and so defines a local trivialization of the frame bundle.

  9. Gamma matrices - Wikipedia

    en.wikipedia.org/wiki/Gamma_matrices

    The defining property for the gamma matrices to generate a Clifford algebra is the anticommutation relation {,} = + = ,where the curly brackets {,} represent the anticommutator, is the Minkowski metric with signature (+ − − −), and is the 4 × 4 identity matrix.

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