We propose a non-perturbative approach to calculate bound state energies and wave functions for quantum field theoretical models. It is based on the direct diagonalization of the corresponding quantum field theoretical Hamiltonian in an effectively truncated and discretized Hilbert space. We illustrate this approach for a Yukawa-like interaction between fermions and bosons in one spatial dimension and show where it agrees with the traditional method based on the potential picture and where it deviates due to recoil and radiative corrections. This method permits us also to obtain some first insight into the spatial characteristics of the distribution of the fermions in the ground state, such as the bremsstrahlung-induced widening. † (x) γ 0 Ψ d (x)] φ(x), where the parameter λ is the coupling strength, Ψ b and Ψ d are the two-component Dirac field operators for the fermions and φ denotes the scalar boson operator. For the special case of m=0 this model could also be used to study simplified QED interactions, where the "photon" has spin zero. The three field operators can be expanded in terms of annihilation and creation operators that fulfill the usual anti-commutator and commutator relationships [b(p), b † (p')] + = [d(p), d † (p')] + = [a(p), a † (p')]-= 3 8/15/2016 δ(p-p'). For couplings λ that are not exceedingly large, fermionic pair-creation processes are not important. The terms in the Hamiltonian that would couple the first fermion to its own antiparticle are proportional to b † (p+k) B † (p) [a † (-2p-k)+a(2p+k)] and b(p+k) B(p)[a † (2p+k)+a(-2p-k)]. Here the anti-particle operators B and B † fulfill the anticommutator relationships [b(p), B † (p')] + = 0 and [B(p), B † (p')] + = δ(p-p'). Similar terms characterize also the second fermion. As very energetic bosons are required in these interactions and the corresponding coupling function decreases rapidly with the boson momentum, we therefore neglect anti-fermions. This leads to the Hamiltonian of

We investigated the effect due to perpendicular magnetic field on quantum wires where spinorbit interaction (SOI) of electrons is not neglected. Based on the calculated energy dispersion, the nonlinear ballistic conductance (G) and electron-diffusion thermoelectric power (S d ) are calculated as functions of electron density, temperature and applied bias voltage. A low-temperature half-step feature in G, which was observed experimentally by Quay et al. [see Nature Physics 6, 336 (2010)], as well as a new peak in S d are reproduced here in the low density regime. These phenomena are related to the occurrence of the Zeeman splitting and SOI induced saddle point in the band structure, where the channel chemical potential lies within an anticrossing gap between the saddle point of the lower subband and the bottom of the upper subband. Additionally, side peaks in G far away from the zero bias for the nonlinear transport, as well as a quadratic bias-voltage dependence of G near zero voltage, are predicted and discussed.