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Gamma matrices and Pauli matrices

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Gamma matrices and Pauli matrices

Gamma matrices vs. Pauli matrices

In mathematical physics, the gamma matrices, \, also known as the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra Cℓ1,3(R). In mathematical physics and mathematics, the Pauli matrices are a set of three complex matrices which are Hermitian and unitary.

Similarities between Gamma matrices and Pauli matrices

Gamma matrices and Pauli matrices have 16 things in common (in Unionpedia): Clifford algebra, Commutator, Dirac equation, Einstein notation, Euclidean space, Gell-Mann matrices, Identity matrix, Kronecker delta, Levi-Civita symbol, Lie algebra, Mathematical physics, Matrix (mathematics), Orthogonality, Rotation, Spin-½, Trace (linear algebra).

Clifford algebra

In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra.

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Commutator

In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative.

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Dirac equation

In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928.

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Einstein notation

In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving notational brevity.

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Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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Gell-Mann matrices

The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3x3 traceless Hermitian matrices used in the study of the strong interaction in particle physics.

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Identity matrix

In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.

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Kronecker delta

In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.

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Levi-Civita symbol

In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol represents a collection of numbers; defined from the sign of a permutation of the natural numbers, for some positive integer.

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Lie algebra

In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.

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Mathematical physics

Mathematical physics refers to the development of mathematical methods for application to problems in physics.

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Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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Orthogonality

In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.

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Rotation

A rotation is a circular movement of an object around a center (or point) of rotation.

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Spin-½

In quantum mechanics, spin is an intrinsic property of all elementary particles.

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Trace (linear algebra)

In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii denotes the entry on the ith row and ith column of A. The trace of a matrix is the sum of the (complex) eigenvalues, and it is invariant with respect to a change of basis.

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The list above answers the following questions

Gamma matrices and Pauli matrices Comparison

Gamma matrices has 52 relations, while Pauli matrices has 90. As they have in common 16, the Jaccard index is 11.27% = 16 / (52 + 90).

References

This article shows the relationship between Gamma matrices and Pauli matrices. To access each article from which the information was extracted, please visit:

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