Related papers: Quantum tomography for Dirac spinors
Recent progress to construct Dirac operators and spinors on compact quantum groups is discussed. The case $SU_q(2)$ is studied carefully and the relationship between known approaches is explained. New examples are given.
Dirac matrices, also known as gamma matrices, are defined only up to a similarity transformation. Usually, some explicit representation of these matrices is assumed in order to deal with them. In this article, we show how it is possible to…
We construct an explicit example of dimensional reduction of the free massless Dirac operator with an internal SU(3) symmetry, defined on a twelve-dimensional manifold that is the total space of a principal SU(3)-bundle over a…
Starting with a new theory of symmetries generated by isometries in field theories with spin, one finds the generators of the spinor representation in backgrounds with a given symmetry. In this manner one obtains a collection of conserved…
A possibility of describing two-level atom states in terms of positive probability distributions (analog to the symplectic tomography scheme) is considered. As a result the basis of the irreducible representation of a rotation group can be…
Several dynamical symmetries of the Dirac Hamiltonian are reviewed in a systematic manner and the conditions under which such symmetries hold. These include relativistic spin and orbital angular momentum symmetries, SO(4)\times…
We explore new aspects of internal fermionic shifting symmetries, present in physical systems such as free Dirac spinors and p-form tensor-spinor fields. We propose a novel procedure to gauge these global symmetries, which also introduces a…
It is shown that the Dirac equation with the Coulomb potential can be solved using the algebra of the three spinor invariants of the Dirac equation without the involvement of the methods of supersymmetric quantum mechanics. The Dirac…
We show that the Dirac equation can be rewritten as a relation describing the fundamental symmetry group of special topological manifold corresponding to the Dirac wave field. It leads to unification of the time-space and internal…
We compare the way one of us got spinors out of fields, which are a priori antisymmetric tensor fields, to the Dirac-K\"ahler rewriting. Since using our Grassmann formulation is simple it may be useful in describing the Dirac-K\"ahler…
Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.
Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2,2) gauge transformations acting on the spinor index of the wave functions. This…
In this paper the problem of tomographic reconstruction of states is investigated within the so-called Schwinger's picture of Quantum Mechanics in which a groupoid is associated with every quantum system. The attention is focused on spin…
By requiring unambiguous symmetric quantization leading to the Dirac equation in a curved space, we obtain a special representation of the spin connections in terms of the Dirac gamma matrices and their space-time derivatives. We also…
Definition of Dirac operators on the quantum group $SU_{q}(2)$ and the quantum sphere $S^{2}_{q \mu}$ are discussed. In both cases similar $SU_{q}(2)$-invariant form is obtained. It is connected with corresponding Laplace operators.
We perform a deformation quantization of the classical isotropic rigid rotator. The resulting quantum system is not invariant under the usual $SU(2)\times SU(2)$ chiral symmetry, but instead $SU_{q^{-1}}(2) \times SU_q(2)$.
The article is a natural continuation of our paper {\em Quantum scalar field in FRW Universe with constant electromagnetic background}, Int. J. Mod. Phys. {\bf A12}, 4837 (1997). We generalize the latter consideration to the case of massive…
In "Part I: Vector Analysis of Spinors", the author studied the geometry of two component spinors as points on the Riemann sphere in the geometric algebra of three dimensional Euclidean space. Here, these ideas are generalized to apply to…
We study various noncommutative geometric aspects of the compact quantum group SU_q(2) for positive q (not equal to 1), following the suggestion of Connes and his coauthors [CL, CD] for considering the so-called true Dirac operator.…
A generalized description of entanglement and quantum correlation properties constraining internal degrees of freedom of Dirac(-like) structures driven by arbitrary Poincar\'e classes of external field potentials is proposed. The role of…