Related papers: Integral equation for gauge invariant quark Green'…
Homogeneous and inhomogeneous biharmonic equation are considered on the $n$-dimensional unit sphere. The Green function is given as a series of Gegenbauer polynomials. In the paper, explicit representations of the Green function are found…
We study semi-martingale obliquely reflected Brownian motion with drift in the first quadrant of the plane in the transient case. Our main result determines a general explicit integral expression for the moment generating function of…
In an SU(N) gauge field theory, the n-point Green functions, namely, propagators and vertices, transform under the simultaneous local gauge variations of the gluon vector potential and the quark matter field in such a manner that the…
We show that cluster algorithms for quantum models have a meaning independent of the basis chosen to construct them. Using this idea, we propose a new method for measuring with little effort a whole class of Green's functions, once a…
We study a model of fermions interacting with a gauge field and calculate gauge-invariant two-particle Green's functions or response functions. The leading singular contributions from the self-energy correction are found to be cancelled by…
We construct a quark target model (QTM) to incorporate intrinsic glue into effective low-energy models of QCD, which often contain only quark degrees of freedom. This method guarantees the gauge invariance of observables order-by-order in…
We construct Green's function for the quantum degenerate parametric oscillator in terms of standard solutions of Ince's equation in a framework of a general approach to harmonic oscillators. Exact time-dependent wave functions and their…
We explore the analytic structure of the gluon and quark propagators of Landau gauge QCD from numerical solutions of the coupled system of renormalized Dyson--Schwinger equations and from fits to lattice data. We find sizable negative norm…
We provide explicit representations of Green's functions for general linear fractional differential operators with {\it variable coefficients} and Riemann-Liouvilles derivatives. We assume that all their coefficients are continuous in $[0,…
We compute the full non-perturbative ghost and gluon two-point Green functions by using gauge field configurations with $\nf=2$ and $\nf=2+1+1$ twisted-mass quark flavours. We use simulations with several different light quark masses, heavy…
Wilson loop averages are evaluated for large contours and in the large N limit by means of minimal surfaces. This allows the study of the quark-antiquark gauge invariant Green function through its dependence on Wilson loops. A covariant…
The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for…
One- and two-dimensional operators which originate from the asymptotic form of the three-body Coulomb wave equation in parabolic coordinates are treated within the context of square integrable basis set. The matrix representations of…
We derive a relation between four-fermion QED Green functions of different covariant gauges which defines the gauge dependence completely. We use the derived gauge dependence to check the gauge invariance of atom-like bound state…
In this paper, a quantum mechanical Green's function $G_{qo}(y_b,t_b;$ $y_a,t_a)$ for the quartic oscillator is presented. This result is built upon two previous papers: first [1], detailing the linearization of the quartic oscillator…
We derive formulas for the matrix elements of the two dimensional square lattice Green function along the diagonal, and along the coordinate axes. We also give an asymptotic formula for the diagonal elements.
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…
By separating the gluon field into physical and pure-gauge components, the usual Poincar\'e subalgebra for an interacting system can be reconciled with gauge-invariance when decomposing the total rotation and translation generators of QCD…
Higher Green functions are real-valued functions of two variables on the upper half plane which are bi-invariant under the action of a congruence subgroup, have logarithmic singularity along the diagonal, but instead of the usual equation…
In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational…