Related papers: Worldline Green Functions for Arbitrary Feynman Di…
The free energy of a multi-component scalar field theory is considered as a functional W[G,J] of the free correlation function G and an external current J. It obeys non-linear functional differential equations which are turned into…
The long-standing problem of representing the general massive one-loop Feynman integral as a meromorphic function of the space-time dimension $d$ has been solved for the basis of scalar one- to four-point functions with indices one. In 2003…
A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…
Solutions of the classical $\phi^4$-theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree…
1D lattice summations of the 3D Green's function are needed in many applications such as photonic crystals, antenna arrays, and so on. Such summations are usually divided into two cases, depending on the location of the observer: Out of the…
A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…
We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and…
We construct, using fermionic functional integrals, thermodynamic Green's functions for a weakly coupled fermion gas whose Fermi energy lies in a gap. Estimates on the Green's functions are obtained that are characteristic of the size of…
The thermal Wightman functions for free, massless particles of spin 0, 1/2, 1, 3/2, and 2 are computed directly in coordinate space by solving the appropriate differential equation and imposing the Kubo-Martin-Schwinger condition. The…
The linear Boltzmann equation with constant coefficients in the three-dimensional infinite space is revisited. It is known that the Green's function can be calculated via the Fourier transform in the case of isotropic scattering. In this…
With a super-high-efficient numerical algorithm, we are able to self-consistently calculate the Green's function in the renormalized-ring-diagram approximation for a two-dimensional electron system with long-range Coulomb interactions. The…
When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the standard functional-integral tools such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes.…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
The worldline formalism provides an alternative to Feynman diagrams that has been found particularly useful for external-field calculations in quantum electrodynamics. Here I summarize its present range of applications, which includes…
The single-particle Green's function of an interacting Fermi system with dominant forward scattering is calculated by decoupling the interaction by means of a Hubbard-Stratonowich transformation involving a bosonic auxiliary field…
We summarize recent progress in applying the worldline formalism to the analytic calculation of one-loop N-point amplitudes. This string-inspired approach is well-adapted to avoiding some of the calculational inefficiencies of the standard…
Lusztig's algorithm of computing generalized Green functions of reductive groups involves an ambiguity of certain scalars. In this paper, for reductive groups of classical type with arbitrary characteristic, we determine those scalars…
In this work we present a three step procedure for generating a closed form expression of the Green's function on both closed and open finite quantum graphs with general self-adjoint matching conditions. We first generalize and simplify the…
This paper presents a full-spectrum Green function methodology (which is valid, in particular, at and around Wood-anomaly frequencies) for evaluation of scattering by periodic arrays of cylinders of arbitrary cross section-with application…
New methods for obtaining functional equations for Feynman integrals are presented. Application of these methods for finding functional equations for various one- and two- loop integrals described in detail. It is shown that with the aid of…