Related papers: Relativistic Quantization and Improved Equation fo…
By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric…
Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…
The first quantized theory of N=2, D=3 massive superparticles with arbitrary fixed central charge and (half)integer or fractional superspin is constructed. The quantum states are realized on the fields carrying a finite dimensional, or a…
In 1971 Feynman, Kislinger and Ravndal [1] proposed Lorentz-invariant differential equation capable to describe relativistic particle with mass and internal space-time structure. By making use of new variables that differentiate between…
In the free case, it is possible to define quantum fields which describe particles with integer or half-integer spin larger than one. It is shown that particles with integer spin must have Bose statistic and particles with half-integer-spin…
The sixteen real coordinates of two-twistor space are transformed by a nonlinear mapping into an enlarged space-time framework. The standard relativistic phase space of coordinates $(X_\mu, P_\mu)$ is supplemented by a six-parameter spin…
The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e. a map from (space-time)^N to a spin space. This concept was originally proposed by Dirac as the…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…
A Lagrangian treatment of the quantization of first class Hamiltonian systems with constraints and Hamiltonian linear and quadratic in the momenta respectively is performed. The ``first reduce and then quantize'' and the ``first quantize…
Spin of elementary particles is the only kinematic degree of freedom not having classical corre- spondence. It arises when seeking for the finite-dimensional representations of the Lorentz group, which is the only symmetry group of…
We build the fully relativistic quantum field theory related to the asymmetric Dirac fields. These fields are solutions of the asymmetric Dirac equation, a Lorentz covariant Dirac-like equation whose positive and "negative" frequency plane…
Scattering transform is a well known powerful tool for quantisation of field theories in (1+1) dimensions. Conventionally only those models whose classical counterparts admit a Lax pair (origin of which is always mysterious) have been…
On the basis of the relativistic symmetry of Minkowski space, we derive a Lorentz invariant equation for a spread electron. This equation slightly differs from the Dirac equation and includes additional terms originating from the spread of…
By investigating the canonical commutation rules for gravitating quantized particles in a 2+1 dimensional world it is found that these particles live on a space-time lattice. The space-time lattice points can be characterized by three…
We describe relativistic particles with spin as points moving in phase space $X=T^* R^{1,3}\times C^2_L\times C^2_R$, where $T^* R^{1,3}=R^{1,3}\times R^{1,3}$ is the space of coordinates and momenta, and $C^2_L$ and $C^2_R$ are the spaces…
The effect of the relativistic spin rotation, conditioned by the setting of the spin in the rest frame of a particle and by the noncommutativity of the Lorentz transformations along noncolinear directions, is discussed. In connection with…
A manifestly relativistic-invariant Lellouch-L\"uscher formalism for the three-particle decays is proposed. Similarly to ref.[1], the formalism is based on the use of the non-relativistic effective Lagrangians. Manifest Lorentz invariance…
The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of…
A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics with its instantaneous Wigner 3-spaces and with its description of the particle world-lines by means of derived…
Does the measurement of a quantum system necessarily break Lorentz invariance? We present a simple model of a detector that measures the spacetime localization of a relativistic particle in a Lorentz invariant manner. The detector does not…