The deformation of the classical action for a point-like particle recently suggested by Staruszkiewicz gives rise to a spin structure which constrains the values of the invariant mass and the invariant spin to be the same for any solution of the equations of motion. Both these Casimir invariants, the square of the four-momentum vector and the square of the Pauli-Lubański pseudo-vector, are shown to preserve the same fixed values also in the presence of an arbitrary external electromagnetic field. In the "free" case, in the centre-of-mass reference frame, the particle moves along a circle of fixed radius with arbitrary varying frequency. In a homogeneous magnetic field, a number of rotational "states" is possible, with frequencies slightly different from the cyclotron frequency, and "phase-like" transitions with spin flops occure at some critical value of the particle's three-momentum. In the last section, the article of Kuzenko, Lyakhovich and Segal (1994) in which, in fact, an equivalent model had been earlier proposed and elaborated, is briefly reviewed and compared with Staruszkiewicz's approach and our results. PACS numbers: 03.30.+p; 03.50.De; 41.60.Ap 1 Introduction. The Staruszkiewicz model From the times of Frenkel [1] and Mathisson [2], or from later works [3, 4], a lot of attempts have been undertaken to unambiguously formulate the dynamics of a classical spinning particle [5]-[10].Most of them deal with generalizations of the classical point-mass Lagrangian (−mc √ẋẋ ) through the introduction of terms with higher derivatives or "inner" variables, and then try to restrict the undesirable freedom by making use of some geometrical [11,12] or symmetry [13,14] considerations. A thorough analysis of extra variables responsible for the spin structure has been carried out by Hanson and Regge [15]. Rivas [16] proposed to make use of a complete set of parameters of the kinematical symmetry group and obtained considerable restrictions on the spin dynamics (so-called "atomic hypothesis").However, a lot of problems arising within the classical description of spin still have to be solved. Corresponding Lagrangians, especially in their interaction part, are rather ambiguous, cumbersome and have no correspondence with generally accepted gauge theories and with the structure of the Lorentz force in the spinless limit in particular [17]. The Schrödinger zitterbewegung motion, being a common feature of different spin models, results in the problem of radiation of electromagnetic waves, and the invariant spin is not bound to preserve its value in the presence of external fields (as one expects for an innate characteristic of elementary particle). Thus, the "zitterbewegung" radius and the magnitude of spin are, as a rule, to be fixed "by hands". Generally, it is not quite clear which properties of the spin could arise in the framework of a successively classical relativistic model.Meanwhile, in a short note [18] Staruszkiewicz has offered a fairly simple relativistic model for a classical particle with spin 1 . Specifica...

First principles should predetermine physical geometry and dynamics both together. In the "algebrodynamics" they follow solely from the properties of biquaternion algebra B and the analysis over B . We briefly present the algebrodynamics over the Minkowski background based on a nonlinear generalization to B of the Cauchi-Riemann analyticity conditions. Further, we consider the effective real geometry uniquely resulting from the structure of multiplication in B and found it to be of the Minkowski type, with an additional phase invariant. Then we pass to study the primordial dynamics that takes place in the complex B space and brings into consideration a number of remarkable structures: an ensemble of identical correlated matter pre-elements ("duplicons"), caustic-like signals (interaction carriers), a concept of random complex time resulting in irreversibility of physical time at a macrolevel, etc. In partucular, the concept of "dimerous electron" naturally arises in the framework of complex algebrodynamics and, together with the above-mentioned phase invariant, allows for a novel approach to explanation of quantum interference phenomena alternative to the recently accepted paradigm of wave-particle dualism.

Making use of the Kerr theorem for shear-free null congruences and of Newman's representation for a virtual charge ``moving'' in complex space-time, we obtain an axisymmetric time-dependent generalization of the Kerr congruence, with a singular ring uniformly contracting to a point and expanding then to infinity. Electromagnetic and complex eikonal field distributions are naturally associated with the obtained congruence, with electric charge being necesssarily unit (``elementary''). We conjecture that the corresponding solution to the Einstein-Maxwell equations could describe the process of continious transition of the naked ringlike singularitiy into a rotating black hole and vice versa, under a particular current radius of the singular ring.Comment: 6 pages, twocolum

Consider a worldline of a pointlike particle parametrized by polynomial functions together with the light cone ("retardation") equation of an inertially moving observer. Then a set of apparent copies, R-or C-particles, defined by the (real or complex conjugate) roots of the retardation equation will be detected by the observer. We prove that for any "polynomial" worldline the induced collective dynamics of R-C particles obeys a whole set of canonical conservation laws (for total momentum, angular momentum and the analogue of mechanical energy). Explicit formulas for the values of total angular momentum and the analogue of total rest energy (rest mass) are obtained; the latter is "self-quantized", i.e. for any worldline takes only integer values. The dynamics is Lorentz invariant though different from the canonical relativistic mechanics. Asymptotically, at large values of the observer's proper time, the R-C particles couple and then assemble into compact incoming/outgoing clusters. As a whole, the evolution resembles the process of (either elastic or inelastic) scattering of a beam of composite particles. Throughout the paper the consideration is purely algebraic, with no resort to differential equations of motion, field equations, etc.

We consider a manifestly Lorentz invariant form L of the biquaternion algebra and its generalization to the case of curved manifold. The conditions of L-differentiability of L-functions are formulated and considered as the primary equations for fundamental fields modeled with such functions. The exact form of the effective affine connection induced by L-differentiability equations is obtained for the flat and curved cases. In the flat case, the integrability conditions of the latter leads to the self-duality of the corresponding curvature, thus ensuring that the source-free Maxwell and SL(2, C) Yang-Mills equations hold on the solutions of the L-differentiability equations.