arXiv subjects
Publications and source records attributed to C. V. Usenko.
A possible way for the consistent probability interpretation of the Klein-Gordon equation is proposed. It is assumed that some states of a scalar charged particle cannot be physically realized. The rest of quantum states are proven to have positive-definite probability distributions.
Spinor representation of group GL(4,R) on special spinor space is developed. Representation space has a structure of the fiber space with the space of diagonal metricses as the base and standard spinor space as typical fiber. Non-isometric motions of the space-time entail spinor transformations which are represented by translation over fibering base in addition to standard $Spin(4,C)$ representation.
We have examined the head-on collision of two electrons in approximation of coherent states. We have shown that the character of collision depends mainly on ratio of initial relative electron's momentum to momentum uncertainty of electrons. When this ratio becomes greater then 1, the Coulomb interaction does not practically influence the scattering.
Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of problems is band structure of energy spectrum for a relativistic particle. This corresponds to an internal degree of freedom, so-called charge variable. In physical problems we often deal with such of dynamical variables that do not depend on this degree of freedom. These are position, momentum, and any combination of them. Restricting our consideration to this kind of observables we propose the relativistic Weyl--Wigner--Moyal formalism that contains some surprising differences from its non-relativistic counterpart.
We consider relativistic coherent states for a spin-0 charged particle that satisfy the next additional requirements: (i) the expected values of the standard coordinate and momentum operators are uniquely related to the real and imaginary parts of the coherent state parameter; (ii) these states contain only one charge component. Three cases are considered: free particle, relativistic rotator, and particle in a constant homogeneous magnetic field. For the rotational motion of the two latter cases, such a description leads to the appearance of the so-called nonlinear coherent states.
A relativistic phase-space representation for a class of observables with matrix-valued Weyl symbols proportional to the identity matrix (charge-invariant observables)is proposed. We take into account the nontrivial charge structure of the position and momentum operators. The evolution equation coincides with its analog in relativistic quantum mechanics with nonlocal Hamiltonian under conditions where particle-pair creation does not take place (free particle and constant magnetic field). The differences in the equations are connected with peculiarities of the constraints on the initial conditions. An effective increase in coherence between eigenstates of the Hamiltonian is found and possibilities of its experimental observation are discussed.
Relativistic quantum effects on physical observables of scalar charged particles are studied. Possible peculiarities of their behavior that can be verified in an experiment can confirm several fundamental conceptions of quantum mechanics. For observables independent of charge variable, we propose relativistic Wigner function formalism that contains explicitly the measurement device frame. This approach can provide the description of charged particles gas (plasma). It differs from the traditional one but is consistent with the Copenhagen interpretation of quantum mechanics. The effects that are connected with this approach can be observed in astrophysical objects - neutron stars.
The relativistic phase-space representation by means of the usual position and momentum operators for a class of observables with Weyl symbols independent of charge variable (i.e. with any combination of position and momentum) is proposed. The dynamical equation coincides with its analogue in the non-local theory (generalization of the Newton-Wigner position operator approach) under conditions when particles creation is impossible. Differences reveal themselves in specific constraints on possible initial conditions.
A description of scalar charged particles, based on the Feshbach-Villars formalism, is proposed. Particles are described by an object that is a Wigner function in usual coordinates and momenta and a density matrix in the charge variable. It is possible to introduce the usual Wigner function for a large class of dynamical variables. Such an approach explicitly contains a measuring device frame. From our point of view it corresponds to the Copenhagen interpretation of quantum mechanics. It is shown how physical properties of such particles depend on the definition of the coordinate operator. The evolution equation for the Wigner function of a single-charge state in the classical limit coincides with the Liouville equation. Localization peculiarities manifest themselves in specific constraints on possible initial conditions.
Theoretical study of mutual orientation of fullerene $C_{60}$ molecule atom spins is presented in this work. Spin-spin interaction was described by Habbard's model. Existence of antiferromagnetic sturcture of spin sub-system in ground state is found.