arXiv subjects

M. I. Shirokov

Publications and source records attributed to M. I. Shirokov.

7 recordsLinked to original sources

arXiv2009

Packet Spreading and Einstein Retardation

According to the classical special theory of relativity any nonstationary system moving with velocity $v$ must evolve (e.g., decay) $1/γ$ times slower than the system at rest, $γ=(1-v^2)^{-1/2}$ (the Einstein retardation ER). Quantum mechanics allows one to calculate the evolution of both systems separately and to compare them thus verifying ER. It is shown here that ER is not valid for a simple system: the spreading packet of the free spinless particle. Earlier it was shown that ER does not hold for some other systems. So one may state that ER is not a universal kinematic law in quantum mechanics.

quant-ph↗

arXiv2008

Moving system with speeded-up evolution

In the classical (non-quantum) relativity theory the course of the moving clock is dilated as compared to the course of the clock at rest (the Einstein dilation). Any unstable system may be regarded as a clock. The time evolution (e.g., the decay) of a uniformly moving physical system is considered using the relativistic quantum theory. The example of a moving system is given whose evolution turns out to be speeded-up instead of being dilated. A discussion of this paradoxical result is presented.

quant-ph↗

arXiv2007

Wave packets in quantum theory of collisions

Two methodological troubles of the quantum theory of collisions are considered. The first is the undesirable interference of the incident and scattered waves in the stationary approach to scattering. The second concerns the nonstationary approach to the theory of collisions of the type $a+b\to c+d$. In order to calculate the cross section one uses the matrix element $ $ of the $S$-matrix. The element is proportional to $δ$-function expressing the energy conservation. The corresponding probability $|< cd|S|ab>|^2$ contains $δ^2$ which is mathematically senseless. The known regular way to overcome the difficulty seems to be unsatisfactory. In this paper, both the troubles are resolved using wave packets of incident particles.

quant-ph↗

arXiv2007

"Dressing" and Haag's theorem

It is demonstrated that the "dressed particle" approach to relativistic local quantum field theories does not contradict Haag's theorem. On the contrary, "dressing" is the way to overcome the difficulties revealed by Haag's theorem.

math-ph↗

arXiv2006

Evolution in Time of Moving Unstable Systems

Relativistic quantum theory shows that the known Einstein time dilation (ED) approximately holds for the decay law of the unstable particle having definite momentum p (DP). I use a different definition of the moving particle as the state with definite velocity v (DV). It is shown that in this case the decay law is not dilated. On the contrary, it is contracted as compared with the decay law of the particle at rest. It is demonstrated that ED fails in both DP and DV cases for time evolution of the simple unstable system of the kind of oscillating neutrino. Experiments are known which show that ED holds for mesons. The used theory may explain the fact by supposing that the measured mesons are in DP state.

quant-ph↗

arXiv2004

Interpretation of Uncertainty Relations for Three or More Observables

Conventional quantum uncertainty relations (URs) contain dispersions of two observables. Generalized URs are known which contain three or more dispersions. They are derived here starting with suitable generalized Cauchy inequalities. It is shown what new information the generalized URs provide. Similar interpretation is given to generalized Cauchy inequalities.

quant-ph↗

arXiv2001

Unitary Transformations in Quantum Field Theory and Bound States

Finding the eigenstates of the total Hamiltonian H or its diagonalization is the important problem of quantum physics. However, in relativistic quantum field theory (RQFT) its complete and exact solution is possible for a few simple models only. Unitary transformations (UT's) considered in this survey do not diagonalize H, but convert H into a form which enables us to find approximately some H eigenstates. During the last years there have appeared many papers devoted to physical applications of such UT's. Our aim is to present a systematic and self-sufficient exposition of the UT method. The two general kinds of UT's are pointed out, distinct variations of each kind being possible. We consider in detail the problem of finding the simplest H eigenstates for interacting mesons and nucleons using the so-called ``clothing'' UT and Okubo's UT. These UT's allow us to suggest definite approaches to the problem of two-particle (deuteron-like) bound states in RQFT. The approaches are shown to yield the same two-nucleon quasipotentials in the first nonvanishing approximation. We demonstrate how the particle mass renormalization can be fulfilled in the framework of the ``clothing'' procedure. Besides the UT of the Hamiltonian we discuss the accompanying UT of the Lorentz boost generators.

nucl-th↗