Quasi-local structure of p-form theory

TL;DR

This paper demonstrates that the Hamiltonian dynamics of self-interacting abelian p-form theories in specific dimensions results in a quasi-local energy distribution on closed surfaces, with implications for boundary conditions and duality transformations.

Contribution

It introduces a quasi-local Hamiltonian framework for p-form theories, connecting boundary value problems with gauge-invariant, positive Hamiltonians and local duality transformations.

Findings

Field energy is localized on closed 2p-dimensional surfaces.

Different boundary conditions lead to distinct Hamiltonian dynamics.

The approach aligns with standard formulations and reveals a similar structure in quantization conditions.

Abstract

We show that the Hamiltonian dynamics of the self-interacting, abelian p-form theory in D=2p+2 dimensional space-time gives rise to the quasi-local structure. Roughly speaking, it means that the field energy is localized but on closed 2p-dimensional surfaces (quasi-localized). From the mathematical point of view this approach is implied by the boundary value problem for the corresponding field equations. Various boundary problems, e.g. Dirichlet or Neumann, lead to different Hamiltonian dynamics. Physics seems to prefer gauge-invariant, positively defined Hamiltonians which turn out to be quasi-local. Our approach is closely related with the standard two-potential formulation and enables one to generate e.g. duality transformations in a perfectly local way (but with respect to a new set of nonlocal variables). Moreover, the form of the quantization condition displays very similar structure to that of the symplectic form of the underlying p-form theory expressed in the quasi-local language.