A note on Lie superalgebras

Loide, R.-K.; Suurvarik, P

doi:10.3176/proc.2010.4.12

Cited by 1 publication

(2 citation statements)

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“…Let us consider the problem of massless fields [4]. It turns out that the same formalism of spin projection operators is useful to derive massless gauge invariant equations for a given helicity.…”

Section: Massless Gauge Invariant Equationsmentioning

confidence: 99%

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Supersymmetry: superfield equations of motion

Loide

Suurvarik

2014

J. Phys.: Conf. Ser.

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Abstract. Supersymmetry and superfields are considered in connection with Poincaré superalgebras. A formalism of projection operators for deriving wave equations for ordinary fields and superfields is developed. Superfield equations of motion in the case of massive and massless fields are presented together with an application in linear supergravity.1. Supersymmetry, superfields, Poincaré superalgebra Supersymmetry has been known more than few decades, but it is still alive despite the absence of experimental verification. Supersymmetry offers several relevant theoretical solutions for modern physics. Supersymmetry (Bose-Fermi symmetry)Let us consider a general N = 1 superfieldwhere θ α is a four-component anticommuting Majorana spinor and i is a Lorentz index. Now we introduce the most general Poincaré superalgebra [1]. The generators of the Poincaré group P µ and M µν , and n supergenerators S α (α = 1, 2, . . . , n) satisfy the following relations:where η µν = diag(+ ---). The simple N = 1 supersymmetry algebra is related to the bispinor representation of the Lorentz group. We have four bispinor generators S α , B µν = 1 2 σ µν and A µ = γ µ C. The Nextended Poincaré superalgebra is related to the direct sum of N bispinor representations. New possibilities [2]• In the most general case the matrices A µ are related to the β-matrices of an invariant first order wave equation

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Section: Massless Gauge Invariant Equationsmentioning

confidence: 99%

“…Analogous considerations are applicable in the superfield case [5,6,7]. To consider irreducible Lorentz superfields ψ i (x, θ), ψ j (x, θ), .…”

Section: Superfield Equations Of Motion Superspin Projection Operatorsmentioning

confidence: 99%