Polyharmonic Green functions and nonlocal Bondi-Metzner-Sachs transformations of a free scalar field

We express the nonlocal Bondi-Metzner-Sachs (BMS) charges of a free massless Klein-Gordon scalar field in 2 thorn 1 in terms of the Green functions of the polyharmonic operators. Using the properties of these Green functions, we are able to discuss the asymptotic behavior of the fields that ensures the existence of the charges and prove that one obtains a realization of the 2 thorn 1 BMS algebra in canonical phase space. We also discuss the transformations in configuration space and show that in this case the algebra closes only up to skew-symmetric combinations of the equations of motion. The formulation of the charges in terms of Green functions opens the way to the generalization of the formalism to other dimensions and systems.

Automated summary

We express the nonlocal BMS charges of a free massless Klein-Gordon scalar field in 2 thorn 1 in terms of the Green functions of the polyharmonic operators. Using these Green functions, we discuss the asymptotic behavior of the fields that ensures the existence of the charges and prove the realization of the 2 thorn 1 BMS algebra in canonical phase space. We also show that the algebra closes only up to skew-symmetric combinations of the equations of motion in configuration space. The formulation of charges in terms of Green functions allows for generalization to other dimensions and systems.