КОГЕРЕНТНЫЕ СОСТОЯНИЯ НА ОРИСФЕРЕ ТРЕХМЕРНОГО ПРОСТРАНСТВА ЛОБАЧЕВСКОГО

The separation of variables in the Laplace–Beltrami operator (Hamiltonian for a free quantum mechanical particle) of three-dimensional Lobachevsky space in the horospherical and quasi Cartesian coordinates provides an opportunity to introduce standard (conventional) coherent states. We consider problems, (oscillator, quantum mechanical particle in the uniform magnetic field) for which introduced coherent states are the adequate method of investigation.Показано, что благодаря разделению переменных в операторе Лапласа–Бельтрами (гамильтониане свободной квантовомеханической частицы) в орисферических и квазидекартовых координатах трехмерного пространства Лобачевского возможно введение стандартных когерентных состояний. Рассмотрены некоторые задачи (осциллятор на орисфере, заряженная частица в аналоге постоянного однородного магнитного поля, определенного в вышеупомянутых системах координат), введение когерентных состояний, для решения которых является особенно адекватным методом

Simulation of the ECAL Trigger System of the COMET Experiment

New high precision experimental search for the violation of the lepton quantum number at the charge lepton sector (the COMET experiment) will start soon. The COMET PhaseI experiment is seeking to measure the coherent neutrinoless conversion of a muon to an electron (µ − e conversion) in the field of an aluminium nucleus, with a single event sensitivity of 3 ×10−15. The simple model of the electron calorimeter (ECAL) of the COMET experiment has been created using GEANT4. There were created and compared a few algorithms for the signal event reconstruction by the ECAL trigger system

Simulation of the ECAL Trigger System of the COMET Experiment

New high precision experimental search for the violation of the lepton quantum number at the charge lepton sector (the COMET experiment) will start soon. The COMET PhaseI experiment is seeking to measure the coherent neutrinoless conversion of a muon to an electron (µ − e conversion) in the field of an aluminium nucleus, with a single event sensitivity of 3 ×10−15. The simple model of the electron calorimeter (ECAL) of the COMET experiment has been created using GEANT4. There were created and compared a few algorithms for the signal event reconstruction by the ECAL trigger system

On Separation of Variables into Relative and Center of Mass Motion for Two-Body System in Three–Dimensional Spaces of Constant Curvature

Expressions for variables of the center of mass and relative motions for two-body system with different and equal masses in three–dimensional spaces of constant curvature are introduced in the terms of biquaternions. The problem of separation of the center mass and relative motion variables for action of two particles into biquaternionic form is formulated. We showed that the algebraic nature of these nonseparable variables follows from the fact that the algebra of biquaternions is noncommutative. Some special cases of separation of the center mass and relative motion variables are considered

On Separation of Variables into Relative and Center of Mass Motion for Two-Body System in Three–Dimensional Spaces of Constant Curvature

Expressions for variables of the center of mass and relative motions for two-body system with different and equal masses in three–dimensional spaces of constant curvature are introduced in the terms of biquaternions. The problem of separation of the center mass and relative motion variables for action of two particles into biquaternionic form is formulated. We showed that the algebraic nature of these nonseparable variables follows from the fact that the algebra of biquaternions is noncommutative. Some special cases of separation of the center mass and relative motion variables are considered

Lepton Pair Production in Hadronic Collisions by Two Photon Exchange in Weizsäcker-Williams Approximation.

We calculate the lepton pair production in hadron collisions a rather exactly. Then we compare numerical results with Tevatron experimental data and receive satisfactory agreement. This means the equivalent photon approximation or the Weizsäcker-Williams method is applicable in hadron collisions. Our final formula for elastic part of photon density distribution can be used for the description of future elastic events at the Large Hadron Collider