Localization in Symplectic Geometry and Application to Path Integral and Supersymmetry

Philippe Durand (1)

1 M2N - Modélisation mathématique et numérique

Equivariant geometry involves a group action on a manifold. This is the starting point to consider a super-geometry showing even and odd variables (bosons, fermions). The localization methods that provide source in the symplectic geometry (Duistermaat-Heckman formula), allow in certain cases to compute path integrals in an explicit way by using the concept of localization. Applications are important in topological field theory: They lead to the definition of new symplectics invariants.

Domains: Mathematics [math]; Physics [physics]

Philippe Durand. Localization in Symplectic Geometry and Application to Path Integral and Supersymmetry. Transactions on Engineering Technologies, Springer Singapore, pp.67-82, 2021, ⟨10.1007/978-981-15-8273-8_6⟩. ⟨hal-04101513⟩