Some comments about classical conservation laws in Zero Energy Ontology
In Zero Energy Ontology (ZEO), the basic geometric structure is causal diamond (CD), which is a subset of M^{4}× CP_{2} identified as an intersection of future and past directed light cones of M^{4} with points replaced with CP_{2}. Poincare symmetries are isometries of M^{4}× CP_{2} but CD itself breaks Poincare symmetry.
Whether Poincare transformations can act as global symmetries in the "world of classical worlds" (WCW), the space of spacetime surfaces  preferred extremals  connecting 3surfaces at opposite boundaries of CD, is not quite clear since CD itself breaks Poincare symmetry. One can even argue that ZEO is not consistent with Poincare invariance. By holography one can either talk about WCW as pairs of 3surfaces or about space of preferred extremals connecting the members of the pair.
First some background.
 Poincare transformations act symmetries of spacetime surfaces representing extremals of the classical variational principle involved, and one can hope that this is true also for preferred extremals. Preferred extremal property is conjectured to be realized as a minimal surface property implied by appropriately generalized holomorphy property meaning that field equations are separately satisfied for Kähler action and volume action except at 2D string world sheets and their boundaries. Twistor lift of TGD allows to assign also to string world sheets the analog of Kähler action.
 String world sheets and their lightlike boundaries carry elementary particle quantum numbers identified as conserved Noether charges assigned with second quantized induced spinors solving modified Dirac equation determined by the action principle determining the preferred extremals  this gives rise to superconformal symmetry for fermions.
 The ground states of supersymplectic and superKacMoody representations correspond to spinor harmonics with welldefined Poincare quantum numbers. Excited states are obtained using generators of symplectic algebra and have welldefined fourmomenta identifiable also as classical momenta. Quantum classical correspondence (QCC) states that classical charges are equal to the eigenvalues of Poincare generators in the Cartan algebra of Poincare algebra. This would hold quite generally.
 In ZEO one assigns opposite total quantum numbers to the boundaries of CD: this codes for the conservation laws. The action of Poincare transformations can be nontrivial at second (active) boundary of CD only and one has two kinds of realizations of Poincare algebra leaving either boundary of CD invariant. Since Poincare symmetries extend to KacMoody symmetries analogous to local gauge symmetries, it should be possible to achieve trivial action at the passive boundary of CD so that the Cartan algebra of symmetries act nontrivially only at the active boundary of CD. Physical intuition suggests that Poincare transformations on the entire CD treating it as a rigid body correspond to trivial center of mass quantum numbers.
How do Poincare transformations act on 3surfaces at the active boundary of CD?
 Zero energy states are superpositions of 4D preferred extremals connecting 3D surfaces at boundaries of CD, the ends of spacetime. One should be able to construct the analogs of plane waves as superpositions of spacetime surfaces obtained by translating the active boundary of CD and 3surfaces at it so that the size of CD increases or decreases. The translate of a preferred extremal is a preferred extremal associated with the new pair of 3surfaces and has size and thus also shape different from those of the original. Clearly, classical theory becomes an essential part of quantum theory.
 Fourmomentum eigenstate is an analog of plane wave which is superposition of the translates of a preferred extremal. In practice it is enough to have wave packets so that in given resolution one has a cutoff for the size of translations in various directions. As noticed, QCC requires that the eigenvalues of Cartan algebra generators such as momentum components are equal to the classical charges.
See the chapter Zero Energy Ontology and Matrices.
