Can Hamiltonians be boundary observables in parametrized field theories? (English) Zbl 1217.83008
Summary: It has been argued that holography in gravitational theories is related to the existence of a particularly useful Gauss Law that allows energy to be measured at the boundary. This work investigates the extent to which such Gauss Laws follow from diffeomorphism invariance. We study parametrized field theories, which are a class of diffeomorphism-invariant theories without gravity. We find that the Hamiltonian for non-gravitational parametrized field theories vanishes on shell even in the presence of a boundary and under a variety of boundary conditions. We conclude that such theories have no useful Gauss Law, consistent with the absence of holography.
MSC:
83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
83C40 | Gravitational energy and conservation laws; groups of motions |
81P15 | Quantum measurement theory, state operations, state preparations |
35L15 | Initial value problems for second-order hyperbolic equations |
83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
37K65 | Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics |
83C75 | Space-time singularities, cosmic censorship, etc. |
81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
83C35 | Gravitational waves |