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Chern-Simons--Antoniadis-Savvidy forms and standard supergravity
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In the context of the so called the Chern--Simons--Antoniadis--Savvidy (ChSAS) forms, we use the methods for FDA decomposition in 1-forms to construct a four-dimensional ChSAS supergravity action for the Maxwell superalgebra. On the another hand, we use the Extended Cartan Homotopy Formula to find a method that allows the separation of the ChSAS action into bulk and boundary contributions and permits the splitting of the bulk Lagrangian into pieces that reflect the particular subspace structure of the gauge algebra.
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Schwinger's non-commutative coordinates and duality between helicity and Dirac quantisation conditions
Demanding associativity of the momentum translation operator for Schwinger's non-commuting coordinates of massless particles yields the helicity quantization λ=(ℏ/2)n, shown to be dual to Dirac's monopole quantization.
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