A well known math theorem says that - if the spatial dimension is odd - D'Alembert equation gives rise to a solution containing a term which is completely supported on the light cone. A mathematical wrap up could be the following: "in dimension 3 (and in fact, for all odd dimensions), the solution of the wave equation at point x0, at time t0, depends only on the initial data in an infinitesimal neighbourhood of the sphere |x − x0| = ct0. This is a statement of Huygens principle. In particular, it says that information from a point source travels in the form of a sphere. The wavefront is thus sharp, with a sudden onset at the start, and sudden cutoff at the end. In dimension 2 (and all even dimensions), the behaviour is different. Wavefronts do have a sharp onset, but they decay with a long tail. This we see because the solution at x0, t0 depends on the initial conditions on the entire disk |x−x0| ≤ ct0. This behaviour can be observed in the ripples of a pond that are formed around a pebble that falls into the pond." from these lecture-notes From another point of view, the main mathematical point is the interpretation of the inverse Radon, the lack of the Hilbert transform in the even dimensions having a fundamental impact. Two questions: 1) does the failure of the Huygens Principle in even spatial dimension imply a breakdown of global Lorentz invariance? (I don't think so, but the issue would be with the wave equation for the scalar field in odd-dimensional Minkowski spacetime [=> even spatial dimensions], where one naively expects Lorentz invariance to hold, therefore Huygens' principle to hold? 2) is it true that "the Feynman propagator, for a massless field, in flat spacetime, is supported on the light cone, thereby realizing Huygens' principle, for all dimensions"? In other word is it true that "the distinction between even and odd number of space-like dimensions for the Huygens Principle is an artifact(*) of having made the choice of the retarded Green function (with causality plus natural boundary conditions at infinity) instead of the Feynman propagator? (I don't think so because I would expect that analogous expressions hold for the advanced propagator) (*) one way to show this would be by Wick rotating... (but, once more, as far as I know, the poles of the meromorphic resolvents in odd dimensional Minkowski space are responsible for Huygens principle) ref. from G+ Note: please, move the thread to Quantum Physics forum if you deem that the discussion is more appropriate there. I've asked this here because I found a previous post in the Classical forum, explaining the difference between 2D and 3D.