The quasiclassical Green functions of the Dirac and Klein-Gordon equations in the external electric field are obtained with the first correction taken into account. The relevant potential is assumed to be localized, while its spherical symmetry is not required. Using these Green functions, the corresponding wave functions are found in the approximation similar to the Furry-Sommerfeld-Maue appro...

We discuss the renormalizability of the massless Thirring model in terms of the causal fermion Green functions and correlation functions of left–right fermion densities. We obtain the most general expressions for the causal two–point Green function and correlation function of left–right fermion densities with dynamical dimensions of fermion fields, parameterised by two parameters. The region of...

Since order parameter of the chiral symmetry breaking Green Functions are a useful link between the OPE expansion and χPT we perform a calculation to the NLO in αs, working in the chiral limit, for all the 2 and 3 point ones. These Green Functions have no perturbative term in the chiral limit and thence their main contribution comes from the ¯ qq operator.

We apply the coarea formula to obtain integrability of superharmonic functions and nonintegrability of subharmonic functions. The results involve the Green function. For a certain domain, say Lipschitz domain, we estimate the Green function and restate the results in terms of the distance from the boundary.

In these lecture notes we study the disordered two-dimensional electron gas in the presence of Rashba spin-orbit coupling, by using the Keldysh nonequilibrium Green function technique. We describe the effects of the spin-orbit coupling in terms of a SU(2) gauge field and derive a generalized Boltzmann equation for the charge and spin distribution functions. We then apply the formalism to discus...

We have considered resonant tunneling through a double tunnel junction where the central island has a mechanical degree of freedom controlling its position with respect to the electrodes. The effects of the coupling between mechanical vibrations of the dot and resonant tunneling of electrons have been studied under the assumption that there is only one available electronic state in the dot. By ...

We consider a 1 + 1 dimensional field theory constrained to a finite box of length L. Traditionally, calculations in a box are done by replacing the integrals over the spatial momenta by discrete sums and then evaluating sums and doing analytic continuations. We show that it is also possible to do such calculations using an analogy to finite temperature field theory. We develop a formalism that...

We consider higher-derivative corrections to quantum gravity and quantum field theories in curved space and investigate tools to calculate the short-distance expansions of Green functions and one-loop amplitudes. In the case of single higher-derivative insertions we derive a closed formula that relates the perturbed one-loop counterterms to the unperturbed Schwinger-DeWitt coefficients. In the ...