Classical-mechanical models without observable trajectories and the Dirac electron

We construct a non-Grassmann spinning-particle model which, by analogy with quantum mechanics, does not admit the notion of a trajectory within the position space. The pseudo-classical character of the model allows us to avoid the inconsistencies arising in the quantum-mechanical interpretation of a one-particle sector of the Dirac equation.Comment: 6 pages, published versio

Bosonic sector of D=11 superstring action and the critical dimension. Toy model

Bosonic model inspired by D=11 superstring action is investigated. An appropriate set of variables is find, in which the light-cone quantization turns out to be possible. It is shown that anomaly terms in the algebra of the light-cone Poincare generators are absent for the case D=27.Comment: 8 pages, LaTex file, twic

Poincare covariant mechanics on noncommutative space

The Dirac approach to constrained systems can be adapted to construct relativistic invariant theories on a noncommutative (NC) space. As an example, we propose and discuss relativistic invariant NC particle coupled to electromagnetic field by means of the standard term $A^\mu\dot x_\mu$. Poincare invariance implies deformation of the free particle NC algebra in the interaction theory. The corresponding corrections survive in the nonrelativistic limit.Comment: 7 pages, JHEP style, final versio

Analysis of constrained theories without use of primary constraints

It is shown that the Dirac approach to Hamiltonization of singular theories can be slightly modified in such a way that primary Dirac constraints do not appear in the process. According to the modified scheme, Hamiltonian formulation of singular theory is first order Lagrangian formulation, further rewritten in special coordinates.Comment: LaTex file, 10 pages, published versio

Semiclassical Description of Relativistic Spin without use of Grassmann variables and the Dirac equation

We propose a relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation. Both $\Gamma$\,-matrices and the relativistic spin tensor are produced through the canonical quantization of the classical variables which parametrize the properly constructed relativistic spin surface. Although there is no mass-shell constraint in our model, our particle's speed cannot exceed the speed of light. The classical dynamics of the model is in correspondence with the dynamics of mean values of the corresponding operators in the Dirac theory. In particular, the position variable experiences {\it Zitterbewegung} in noninteracting theory. The classical equations for the spin tensor are the same as those of the Barut-Zanghi model of a spinning particle.Comment: 16 pages, misprints correcte

Spinning-particle model for the Dirac equation and the relativistic Zitterbewegung

We construct the relativistic particle model without Grassmann variables which meets the following requirements. A) Canonical quantization of the model implies the Dirac equation. B) The variable which experiences {\it Zitterbewegung}, represents a gauge non-invariant variable in our model. Hence our particle does not experiences the undesirable {\it Zitterbewegung}. C) In the nonrelativistic limit spin is described by three-vector, as it could be expected.Comment: 6 pages, misprints correcte

From Noncommutative Sphere to Nonrelativistic Spin

Reparametrization invariant dynamics on a sphere, being parameterized by angular momentum coordinates, represents an example of noncommutative theory. It can be quantized according to Berezin-Marinov prescription, replacing the coordinates by Pauli matrices. Following the scheme, we present two semiclassical models for description of spin without use of Grassman variables. The first model implies Pauli equation upon the canonical quantization. The second model produces nonrelativistic limit of the Dirac equation implying correct value for the electron spin magnetic moment

String action with multiplet of Θ\Theta-terms and the hidden Poincare symmetry

We study string action with multiplet of $\Theta$-terms added, which turns out to be closely related with the bosonic sector of D=11 superstring action [3,4]. Alternatively, the model can be considered as describing class of special solutions of the membrane. An appropriate set of variables is find, in which the light-cone quantization turns out to be possible. It is shown that anomaly terms in the algebra of the light-cone Poincare generators are absent for the case D=27.Comment: 14 pages, LaTex file, Minor correction

Quantum mechanics on noncommutative plane and sphere from constrained systems

It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints presented in the models. It leads, in particular, to a possibility of quantization in terms of the initial NC variables. For a two-dimensional plane we present two Lagrangian actions, one of which admits addition of an arbitrary potential. Quantization leads to quantum mechanics with ordinary product replaced by the Moyal product. For a three-dimensional case we present Lagrangian formulations for a particle on NC sphere as well as for a particle on commutative sphere with a magnetic monopole at the center, the latter is shown to be equivalent to the model of usual rotor. There are several natural possibilities to choose physical variables, which lead either to commutative or to NC brackets for space variables. In the NC representation all information on the space variable dynamics is encoded in the NC geometry. Potential of special form can be added, which leads to an example of quantum mechanics on the NC sphere.Comment: 18 pages, LaTex file, Extended versio

On zero modes of the eleven dimensional superstring

It is shown that recently pointed out by Berkovits on-shell degrees of freedom of the D=11 superstring do not make contributions into the quantum states spectrum of the theory. As a consequence, the spectrum coincides with that of the D=10 type IIA superstring.Comment: 7 pages, LaTex fil