Finitely additive states and completeness of inner product spaces

For any unit vector in an inner product space S, we define a mapping on the system of all -closed subspaces of S, F(S), whose restriction on the system of all splitting subspaces of S, E(S), is always a finitely additive state. We show that S is complete iff at least one such mapping is a finitely additive state on F(S). Moreover, we give a completeness criterion via the existence of a regular finitely additive state on appropriate systems of subspaces. Finally, the result will be generalized to general inner product spaces.     

Radiative kinks and fermionic zero modes in a (λφ6)1+1 model

We consider bidimensional scalar models including kink solutions _k (x). Using the hidden supersymmetric properties of the Dirac equation, we describe a general method to find normalizable fermionic zero modes. In particular, we apply the technique to a ( ⁶)₁₊₁ model. Going to the one-loop order of the effective potential, the emergence of a radiative kink provides an interesting scalar background in order to discuss the Dirac equation.     

QCD perturbation theory in the temporal gauge

In this paper we present a non-trivial check of the consistency of the quantization of a gauge theory with fermions (QCD) in the temporal gauge. We use the approach based on the finite time Feynman propagation kernel, in which the Gauss law is imposed as a constraint on the states by means of a functional integration over all the time independent gauge transformations acting on the boundary values of the fields. We spell out in detail the “Feynman rules” when fermions are present and we compute, as an example, the gauge invariant correlation function $$\begin{gathered} G(t) = \left\langle {\bar \psi (0,t)(\gamma _5 \gamma _0 )\frac{{1 - \gamma _0 }}{2}P} \right. \hfill \\ \left. { \cdot \exp \left( {ig\int\limits_0^t {A_0 (0,t')dt'} } \right)(\gamma _5 \gamma _0 )^ + (0,0)} \right\rangle \hfill \\ \end{gathered} $$ up to orderg ², obtaining the expected result.     

Inclusive\bar K^{0*} (892) andK 0*(892) production on silicon by 200 GeVK − andπ −

The production of the neutralK ^? (892) resonances by 200 GeVK ^? andπ ^? has been studied over the kinematic range 0.0<x _f<1.0 andp _t ² <5.0 GeV². Longitudinal and transverse momentum distributions are presented. In addition the decay angular distributions inK ^? fragmentation to \(\bar K^{0*} \) have been investigated.     

Taylor expansion of effective Hamiltonians by Monte Carlo simulations with fixed block spins

Monte Carlo simulations with fixed block spins allow the computation of Taylor expansion kernels for effective Hamiltonians. The expansion can be performed around arbitrary block spin configurations \(\bar \phi\) and does not suffer from truncation errors. Monte Carlo calculation of the Taylor kernels offers a ready possibility to check whether the effective Hamiltonian has good locality properties in the neighborhood of a given configuration \(\bar \phi\) . The method is applied in a renormalization group study of the 2-dimensional critical Ising model. The results show that one has to deal with a “large field problem”, as had been expected from rigorous renormalization group studies.     

Plane logarithmic spiral with peripheral excitation

Conclusion In a planar logarithmic spiral excited at its periphery there simultaneously exist surface, quasieffluent, and radiated waves; the phase velocities of surface and quasieffluent waves are identical and depend on the reduced radius k, which defines the regions of normal and anomalous dispersion; in the region kn the surface wave transforms to a radiated one by means of the quasieffluent; the directional pattern differs little from that for central excitation, with ellipticity coefficient of a spiral open at the center varying from 0.7 to 0.9 over a 1:2 frequency range; the input impedance depends weakly on the presence of reflection at the center of the spiral, is of an oscillating character, and changes more intensely than for central excitation.Khar'kov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 33, No. 1, pp. 78–84, January, 1990.