2000 Mathematics Suject Classification. Primary 30F10, 30F50; Secondary 14H15, 20H10. Abstract. In this work we prove that the hyperelliptic branch locus of orientable Klein surfaces of genus g with one boundary component is connected and in the case of non-orientable Klein surfaces it has g+1 2 components, if g is odd, and g+2 2 components for even g. We notice that, for non-orientable Klein s...

We study the scattering theory for charged Klein-Gordon equations:  (∂t − iv(x))2φ(t, x) + (x,Dx)φ(t, x) = 0, φ(0, x) = f0, i−1∂tφ(0, x) = f1, where: (x,Dx) = − ∑ 1≤j,k≤n ( ∂xj − ibj(x) ) a(x) (∂xk − ibk(x)) +m (x), describing a Klein-Gordon field minimally coupled to an external electromagnetic field described by the electric potential v(x) and magnetic potential ~b(x). The flow of the Kle...

Laplace operators on metric graphs give rise to Klein-Gordon and wave operators. Solutions of the Klein-Gordon equation and the wave equation are studied and finite propagation speed is established. Massive, free quantum fields are then constructed, whose commutator function is just the Klein-Gordon kernel. As a consequence of finite propagation speed Einstein causality (local commutativity) ho...

In this note we present additional arguments in favour of Kaluza and Klein picture of the world. In fact, we show that formula (1) provided by Kaluza-Klein approach with the fundamental scale early calculated [1] gives an excellent description for the mass spectrum of three-pion system. In our previous papers [1, 2] we have presented the arguments in favour of that the Kaluza-Klein picture of t...

It is proved that no Hamiltonian exists for the real Klein-Gordon field used in the Yukawa interaction. It is also shown that a real Klein-Gordon particle can be neither in a free isolated state nor in a bound state having an angular momentum l > 0. The experimental data support these conclusions. This outcome is in a complete agreement with Dirac's negative opinion on the Klein-Gordon equation.

We investigate the behavior of small perturbations around the Kaluza-Klein monopole in the five dimensional space-time. We find that the even parity gravitational wave does not propagate in the five dimensional space-time with Kaluza-Klein monopole provided that the gravitational wave is constant in the fifth direction. We conclude that a gravitational wave and a U(1) magnetic monopole do not c...

The full Klein-Nishina cross section for the inverse Compton scattering interactions of electrons implies a significant reduction of the electron energy loss rate compared to the Thomson limit when the electron energy exceeds the critical Klein-Nishina energy E K = γ K m e c 2 = 0.27m 2 e c 2 /(k B T), where T denotes the temperature of the photon graybody distribution. As a consequence the tot...

In this paper, we shall determine the complete list of irreducible quadrangulations of the Klein bottle. By this result, we can easily list all the minorminimal 2-representative graphs on the Klein bottle. Moreover, we shall show that any two bipartite quadrangulations of the Klein bottle with at least 10 vertices are transformed into each other by a sequence of diagonal slides and a sequence o...