%0 Book Section %T Localization in Symplectic Geometry and Application to Path Integral and Supersymmetry %+ Modélisation mathématique et numérique (M2N) %A Durand, Philippe %B Transactions on Engineering Technologies %I Springer Singapore %C Singapore %P 67-82 %8 2021-10-25 %D 2021 %R 10.1007/978-981-15-8273-8_6 %Z Mathematics [math] %Z Physics [physics]Book sections %X 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. %G English %L hal-04101513 %U https://cnam.hal.science/hal-04101513 %~ CNAM %~ INSMI %~ M2N-CNAM %~ HESAM-CNAM %~ HESAM