3+1 is more than enough - particles in lower dimensions

A.Khodin, National Academy of Sciences of Belarus, Minsk

The topological approach is developed where an elementary particle is considered as corresponding to a localized space-time configuration [1]. The key of the approach is the standard relativistic limit for space-time curvature. In general case, the space-time configurations, for which this limit is maintained, are shown to be three-, two-, and one-dimensional as space objects. The real space-time is proposed to consider as evolution of a mixture of one-, two-, and three-dimensional micro-objects, which interacts and compose macro-objects corresponding to its degrees of freedom in space coordinates.
In the frames of the approach presented, a photon is described as 2+1 configuration where above mentioned condition is valid in its centre point. The configuration possesses of Doppler effect behavior in the case it propagates with light velocity only. Topological charge of the configuration is zero. The photon spin is represented as configuration' rotation around the propagation direction; the only permissible rotation period corresponding to the photon wavelength. It is shown that ordered one-dimensional superposition of single-photon configurations composes a restricted stable coherent harmonic-type packet which wavelength equals to the constitutive photon configurations' wavelength. Two- and three-dimensional coherent superposition of single-photon configurations are shown to form some types of photons ordering symmetry inside the coherent packet.

1. A.Khodin. EPS-11: Trends in Physics. 11th Gen. Conf. of Europ. Phys. Soc. London, UK, 6-10 Sept.1999.