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N = 1 supersymmetry algebra in 1 + 1 dimensions

In 1 + 1 dimensions the N. [1]

12 relations: Algebra over a field, Center (algebra), Generator (mathematics), Graded ring, Identity element, Lorentz transformation, Representation theory, Sine-Gordon equation, Supercharge, Supersymmetry, Translation (geometry), (−1)F.

Algebra over a field

In mathematics, an algebra over a field is a vector space (a module over a field) equipped with a bilinear product.

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Center (algebra)

The term center or centre is used in various contexts in abstract algebra to denote the set of all those elements that commute with all other elements.

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Generator (mathematics)

In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts.

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Graded ring

In mathematics, in particular abstract algebra, a graded ring is a ring that is a direct sum of abelian groups R_i such that R_i R_j \subset R_.

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Identity element

In mathematics, an identity element (or neutral element) is a special type of element of a set with respect to a binary operation on that set.

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Lorentz transformation

In physics, the Lorentz transformation (or transformations) is named after the Dutch physicist Hendrik Lorentz.

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Representation theory

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.

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Sine-Gordon equation

The sine-Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and the sine of the unknown function.

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Supercharge

In theoretical physics, a supercharge is a generator of supersymmetry transformations.

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Supersymmetry

Supersymmetry (SUSY), a theory of particle physics, is a proposed type of spacetime symmetry that relates two basic classes of elementary particles: bosons, which have an integer-valued spin, and fermions, which have a half-integer spin.

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Translation (geometry)

In Euclidean geometry, a translation is a function that moves every point a constant distance in a specified direction.

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(−1)F

In a quantum field theory with fermions, (−1)F is a unitary, Hermitian, involutive operator where F is the fermion number operator and is equal to the sum of the lepton number plus the baryon number, F.

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N=1 supersymmetry algebra in 1+1 dimensions.

References

[1] https://en.wikipedia.org/wiki/N_=_1_supersymmetry_algebra_in_1_%2B_1_dimensions

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