Electrodynamics in e⁻ linacs

We report a new calculation of electron beam acceleration along linac using fundamental electrodynamics as basis. Following laws are considered: increasing of work equals multiplication of force to elementary interval; power equals work growth over time interval; force acting on charge equals charge value multiplied to electric field value. Using electrodynamic characteristic, series impedance, equaled a square of electric eld value divided by power, and also taking into account laws mentioned above, an equation for the electric field radiated by the beam is calculated. A transient process of electric field radiated by beam is considered.Рассмотрен расчет ускорения сгустков в линейных ускорителях электронов, основанный на постулатах электродинамики. Перечислены основные постулаты: увеличение работы равно произведению силы на элемент пройденного расстояния; мгновенная мощность равна отношению прироста работы на отрезок времени; сила, действующая на заряд, равна величине заряда, умноженного на напряженность электрического поля. Используя электродинамическую характеристику, последовательное сопротивление круглого диафрагмированного волновода, равное отношению квадрата напряженности электрического поля к мгновенной мощности, и выше названные постулаты электродинамики, получено выражение для электрического поля излучения. Рассмотрен переходный процесс поля излучения цуга сгустков.Розглянуто розрахунок прискорення згусткiв у лiнiйних прискорювачах електронiв, оснований на постулатах електродинамiки. Перелiченi основнi постулати: збiльшення роботи дорiвнює здобутку сили на елемент пройденої вiдстанi; миттєва потужнiсть дорiвнює вiдношенню приросту роботи на вiдрiзок часу; сила, дiюча на заряд, рiвна величинi заряду, помноженого на напруженiсть электричного поля. Використовуючи електродинамiчну характеристику, послiдовний опiр круглого дiафрагмованого хвильопровода, який дорiвнює вiдношеннию квадрата напруженостi електричного поля на миттєву потужнiсть, та перелiченi вище постулати електродинамiки, отриманоно вираз для електричного поля випромiнювання. Розглянуто перехiдний процес поля випромiнювання цуга сгусткiв

Translational invariance of the Einstein-Cartan action in any dimension

We demonstrate that from the first order formulation of the Einstein-Cartan action it is possible to derive the basic differential identity that leads to translational invariance of the action in the tangent space. The transformations of fields is written explicitly for both the first and second order formulations and the group properties of transformations are studied. This, combined with the preliminary results from the Hamiltonian formulation (arXiv:0907.1553 [gr-qc]), allows us to conclude that without any modification, the Einstein-Cartan action in any dimension higher than two possesses not only rotational invariance but also a form of \textit{translational invariance in the tangent space}. We argue that \textit{not} only a complete Hamiltonian analysis can unambiguously give an answer to the question of what a gauge symmetry is, but also the pure Lagrangian methods allow us to find the same gauge symmetry from the \textit{basic} differential identities.Comment: 25 pages, new Section on group properties of transformations is added, references are added. This version will appear in General Relativity and Gravitatio

Measurement of ϕ\phi(1020) meson leptonic width with CMD-2 detector at VEPP-2M Collider

The $\phi$(1020) meson leptonic width has been determined from the combined analysis of 4 major decay modes of the resonance ($\phi\to K^+ K^-,K^0_LK^0_S,\pi^+\pi^-\pi^0,\eta\gamma$) studied with the CMD-2 detector at the VEPP-2M $e^+e^-$ collider. The following value has been obtained: $\Gamma(\phi\to e^+e^-) = 1.235\pm 0.006\pm 0.022$ keV. The $\phi(1020)$ meson parameters in four main decay channels have been also recalculated: $B(\phi\to K^+K^-) = 0.493\pm 0.003\pm 0.007$, $B(\phi\to K_LK_S) = 0.336\pm 0.002\pm 0.006$, $B(\phi\to\pi^+\pi^-\pi^0) = 0.155\pm 0.002\pm 0.005$, $B(\phi\to\eta\gamma) = 0.0138\pm 0.0002\pm 0.0002$.Comment: 14 pages, 3 figure

Darboux coordinates for the Hamiltonian of first order Einstein-Cartan gravity

Based on preliminary analysis of the Hamiltonian formulation of the first order Einstein-Cartan action (arXiv:0902.0856 [gr-qc] and arXiv:0907.1553 [gr-qc]) we derive the Darboux coordinates, which are a unique and uniform change of variables preserving equivalence with the original action in all spacetime dimensions higher than two. Considerable simplification of the Hamiltonian formulation using the Darboux coordinates, compared with direct analysis, is explicitly demonstrated. Even an incomplete Hamiltonian analysis in combination with known symmetries of the Einstein-Cartan action and the equivalence of Hamiltonian and Lagrangian formulations allows us to unambiguously conclude that the \textit{unique} \textit{gauge} invariances generated by the first class constraints of the Einstein-Cartan action and the corresponding Hamiltonian are \textit{translation and rotation in the tangent space}. Diffeomorphism invariance, though a manifest invariance of the action, is not generated by the first class constraints of the theory.Comment: 44 pages, references are added, organization of material is slightly modified (additional section is introduced), more details of calculation of the Dirac bracket between translational and rotational constraints are provide

The Hamiltonian of Einstein affine-metric formulation of General Relativity

It is shown that the Hamiltonian of the Einstein affine-metric (first order) formulation of General Relativity (GR) leads to a constraint structure that allows the restoration of its unique gauge invariance, four-diffeomorphism, without the need of any field dependent redefinition of gauge parameters as is the case for the second order formulation. In the second order formulation of ADM gravity the need for such a redefinition is the result of the non-canonical change of variables [arXiv: 0809.0097]. For the first order formulation, the necessity of such a redefinition "to correspond to diffeomorphism invariance" (reported by Ghalati [arXiv: 0901.3344]) is just an artifact of using the Henneaux-Teitelboim-Zanelli ansatz [Nucl. Phys. B 332 (1990) 169], which is sensitive to the choice of linear combination of tertiary constraints. This ansatz cannot be used as an algorithm for finding a gauge invariance, which is a unique property of a physical system, and it should not be affected by different choices of linear combinations of non-primary first class constraints. The algorithm of Castellani [Ann. Phys. 143 (1982) 357] is free from such a deficiency and it leads directly to four-diffeomorphism invariance for first, as well as for second order Hamiltonian formulations of GR. The distinct role of primary first class constraints, the effect of considering different linear combinations of constraints, the canonical transformations of phase-space variables, and their interplay are discussed in some detail for Hamiltonians of the second and first order formulations of metric GR. The first order formulation of Einstein-Cartan theory, which is the classical background of Loop Quantum Gravity, is also discussed.Comment: 74 page

Study of the radiative decay ϕ→ηγ\phi \to \eta \gamma with CMD-2 detector

Using the $1.9 pb^{-1}$ of data collected with the CMD-2 detector at VEPP-2M the decay mode $\phi \to \eta \gamma$, $\eta \to \pi^+\pi^-\pi^0$ has been studied. The obtained branching ratio is B($\phi \to \eta \gamma) = (1.18 \pm 0.03 \pm 0.06)$.Comment: 13 pages, 5 figures, LaTex2e, to be published in Phys. Lett.

Observation of KS0K_S^0 semileptonic decays with CMD-2 detector

The decay $K_S^0 \to \pi e \nu$ has been observed by the CMD-2 detector at the e^+e^- collider VEPP-2M at Novosibirsk. Of 6 million produced $K_L^0K_S^0$ pairs, $75 \pm 13$ events of the $K_S^0 \to \pi e \nu$ decay were selected. The corresponding branching ratio is $B(K_S^0 \to \pi e \nu)=(7.2 \pm 1.4)\times10^{-4}$. This result is consistent with the evaluation of $B(K_S^0 \to \pi e \nu)$ from the $K_L^0$ semileptonic rate and $K_S^0$ lifetime assuming $\Delta S=\Delta Q$ .Comment: 7 pages, 6 figures, LaTex2e. Submitted to Phys.Lett.

Measurement of omega meson parameters in pi^+pi^-pi^0 decay mode with CMD-2

About 11 200 e^+e^- -> omega -> pi^+pi^-pi^0 events selected in the center of mass energy range from 760 to 810 MeV were used for the measurement of the \omega meson parameters. The following results have been obtained: sigma _{0}=(1457 \pm 23 \pm 19)nb, m_{\omega}=(782.71 \pm 0.07 \pm 0.04) MeV/c^{2}, \Gamma_{\omega}=(8.68 \pm 0.23 \pm 0.10) MeV, \Gamma_{e^+e^-}\cdot Br (\omega -> pi^+pi^-pi^0)= (0.528 \pm 0.012 \pm 0.007) \cdot 10^{-3} MeV.Comment: 8 pages, 4 figure

Study of the process e+e- to pi+pi-pi+pi-pi0 with CMD-2 detector

The process e+e- to pi+ pi- pi+ pi- pi0 has been studied in the center of mass energy range 1280 -- 1380 MeV using 3.0 1/pb of data collected with the CMD-2 detector in Novosibirsk. Analysis shows that the cross section of the five pion production is dominated by the contributions of the eta pi+pi- and omega pi+pi- intermediate states.Comment: 8 pages, 3 figure. Submitted to Phys. Lett.

High-statistics measurement of the pion form factor in the rho-meson energy range with the CMD-2 detector

We present a measurement of the pion form factor based on e+e- annihilation data from the CMD-2 detector in the energy range 0.6<sqrt(s)<1.0 GeV with a systematic uncertainty of 0.8%. A data sample is five times larger than that used in our previous measurement.Comment: 18 pages, 10 figures. Added comparison with KLOE measurement, minor updates. Accepted by PL