Speaker: Saverio Pascazio
Affiliation: Universita di Bari/INFN
Date: Tuesday, 25 April 2017 at 10:00
Location: Seminar Room, Serrano 121 (CFMAC)
Every point on the wave front of a propagating wave is a source of secondary wavelets, which spread forward at the same speed as the source wave. The wave front at later times is then given by the surface tangent to the secondary wavelets. This principle was proposed by Christiaan Huygens in 1678, to explain the laws of reflection and refraction. It was used again more than a century later, in 1816, by Augustin-Jean Fresnel, to intepret the diffraction effects that occur when visible light encounters slits, edges and screens.
The principle provides crucial insight into the nature of wave propagation and it is a milestone in the physics of ondulatory phenomena. For this reason, its universal validity is usually taken for granted. However, yet one century later, Jacques Hadamard noticed that Huygens’ principle is valid only when waves propagate in an odd number n>1 of spatial dimensions.
Both quantum mechanics and quantum field theory make use of wave equations in their formulation. It is therefore interesting to ask whether Huygens’ principle holds for the seminal equations that are the backbone of these theories. The Schrodinger equation, being non-relativistic, does not admit a satisfactory formulation of this question. What about the Dirac equation?
We discuss the validity of Huygens’ principle for the massless Dirac-Weyl equation. We find that the principle holds for odd space dimension n, while it is invalid for even n. We explicitly discuss the cases n=1,2 and 3.