Quantization of electrodynamics in curved space-time in the Lorenz gauge and with arbitrary gauge parameter makes it necessary to study Green functions of non-minimal operators with variable coefficients. Starting from the integral representation of photon Green functions, we link them to the evaluation of integrals involving Γ-functions. Eventually, the full asymptotic expansion of the Feynman...

The study of biharmonic functions under the ordinary (Euclidean) Laplace operator on the open unit disk D in C arises in connection with plate theory, and in particular, with the biharmonic Green functions which measure, subject to various boundary conditions, the deflection at one point due to a load placed at another point. A homogeneous tree T is widely considered as a discrete analogue of t...

The fermion propagator and the 4-fermion Green function in the massless QED2 are explicitly found with topological effects taken into account. The corrections due to instanton sectors k = ±1, contributing to the propagator, are shown to be just the homogenous terms admitted by the Dyson-Schwinger equation for S. In the case of the 4-fermion function also sectors k = ±2 are included into conside...

Generalizing the ’t Hooft and Veltman method of unitary regulators, we demonstrate for the first time the existence of local, Lorentz-invariant, physically motivated Lagrangians of quantum-electrodynamic phenomena such that: (i) Feynman diagrams are finite and equal the diagrams of QED but with regularized propagators. (ii) N-point Green functions are C-, P-, and Tinvariant up to a phase factor...

The aim of this article is twofold. First we examine from a new angle the question of the recovery of time in quantum cosmology. We construct Green functions for matter fields from the solutions of the Wheeler De Witt equation. For simplicity we work in a mini-superspace context. By evaluating these Green functions in a first order development of the energy increment induced by matrix elements ...

Lattice Green functions appear in lattice gauge theories, in lattice models of statistical physics and in random walks. Here, space coordinates are treated as parameters and series expansions in the mass are obtained. The singular points in arbitrary dimensions are found. For odd dimensions these are branch points with half odd-integer exponents, while for even dimensions they are of the logari...

The thermal expectation values of all possible bosonic generalised retarded functions evaluated at zero energy are studied. The relationship of such functions to calculational schemes, technical problems and physical applications is outlined. It is then shown that all generalised retarded functions constructed from any one set of bosonic fields are equal at zero energy. This is done completely ...

In this paper, we restudy the Green function expressions of field equations. We derive the explicit form of the Green functions for the Klein-Gordon equation and Dirac equation, and then estimate the decay rate of the solution to the linear equations. The main motivation of this paper is to show that: (1). The formal solutions of field equations expressed by Green function can be elevated as a ...

It is proved that calculations of three-point diagrams using the Real-Time Formalism of nite temperature eld theory produce the time-ordered Green functions while the Imaginary-Time Formalism calculate retarded and advanced Green functions. A non-trivial relation between these Green functions is found. Similarly, a spectral representation for the real-time three-point function is found. The hig...

A general approach for derivation of the spectral relations for the multitime correlation functions is presented. A special attention is paid to the consideration of the non-ergodic (conserving) contributions and it is shown that such contributions can be treated in a rigorous way using multitime temperature Green functions. Representation of the multitime Green functions in terms of the spectr...