Related papers: Hamilton-Dirac systems for charged particles in ga…
We show how to obtain all covariant field equations for massless particles of arbitrary integer, or half-integer, helicity in four dimensions from the quantization of the rigid particle, whose action is given by the integrated extrinsic…
Using the approach the modified Euler-Lagrange field equation together with the corresponding Seiberg-Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative…
Wigner's quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincar\'e group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase…
The gauge field theory of the standard electroweak model in the presence of the electroweak bubble wall is investigated with a view to its applications to microscopic phenomena, which are believed to have occurred during the phase…
The dynamics of particles with intrinsic angular momentum (spin) described by the Dirac equation is considered in a homogeneous space with rotation in the presence of a homogeneous vortex gravitational field. The effects of the interaction…
The kinematical formalism for describing spinning particles developped by the author is based upon the idea that an elementary particle is a physical system with no excited states. It can be annihilated by the interaction with its…
Hamiltonian models based on a localized basis set are widely used in condensed matter physics, as, for example, for the calculation of electronic structures or transport properties. The presence of a weak and homogeneous magnetic field can…
We explore the Higgs-Gauge configuration space in the standard electroweak theory. We outline a general prescription that uses the non-trivial topology associated with the gauge group of the theory, to find known solutions of the Euclidean…
We find a relationship between unitary transformations of the dynamics of quantum systems with time-dependent Hamiltonians and gauge theories. In particular, we show that the nonrelativistic dynamics of spin-$\frac12$ particles in a…
In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of the Clifford bundle (over the…
In this paper, we present the results of our investigation relating particle dynamics and non-commutativity of space-time by using Dirac's constraint analysis. In this study, we re-parameterise the time $t=t(\tau)$ along with $x=x(\tau)$…
We prove the possibility of existence of stationary bound states of spin-half particles in the Reissner-Nordstroem gravitational field using a self-conjugate Hamiltonian with a flat scalar product of wave functions. Bound states of Dirac…
Using the Clifford and the Spin-Clifford formalisms we prove that the classical relativistic Hamilton Jacobi equation for a charged massive (and spinning) particle interacting with an external electromagnetic field is equivalent to a…
In this paper we analyze again a transition from the classical to quantum description of bound charged particles, which involves a substantial modification of the structure of their electromagnetic (EM) fields related to the well-known fact…
An equation, we call Dirac gamma-equation, is introduced with the help of the mathematical tools connected with the Clifford algebra. This equation can be considered as a generalization of the Dirac equation for the electron. Some features…
We consider a class of electromagnetic fields that contains crossed fields combined with longitudinal electric and magnetic fields. We study the motion of a classical particle (solutions of the Lorentz equations) in such fields. Then, we…
The Dirac equation offers a precise analytical description of relativistic two-particle bound states, when one of the constituent is very heavy and radiative corrections are neglected. Looking at the high-Z hydrogen-like atom in the…
We present a unified approach to constrained implicit Lagrangian and Hamiltonian systems based on the introduced concept of Dirac algebroid. The latter is a certain almost Dirac structure associated with the Courant algebroid on the dual…
Given a Lie group $G$, we elaborate the dynamics on $T^*T^*G$ and $T^*TG$, which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew symplectic space $TT^*G$, which may be defined by a Lagrangian or a Hamiltonian function.…
We propose a conservative two-dimensional particle model in which particles carry a continuous and classical spin. The model includes standard ferromagnetic interactions between spins of two different particles, and a nonstandard coupling…