Integral equation for gauge invariant quark Green’s function
نویسنده
چکیده
We consider gauge invariant quark two-point Green’s functions in which the gluonic phase factor follows a skew-polygonal line. Using a particular representation for the quark propagator in the presence of an external gluon field, functional relations between Green’s functions with different numbers of segments of the polygonal lines are established. An integral equation is obtained for the Green’s function having a phase factor along a single straight line. The related kernels involve Wilson loops with skew-polygonal contours and with functional derivatives along the sides of the contours. PACS numbers: 12.38.Aw, 12.38.Lg.
منابع مشابه
Salpeter amplitudes in a Wilson-loop context
The bound state problem for a gauge invariant quark-antiquark system is considered in the instantaneous rest frame. Focus here is on the long range non-perturbative interaction. A two-time Green’s function is constructed for Salpeter amplitudes. The corresponding Schrödinger equation is found to be in the Salpeter form with a Wilson-loop term as the instantaneous kernel.
متن کاملA Gribov equation for the photon Green’s function
We present a derivation of the Gribov equation for the gluon/photon Green’s function D(q). Our derivation is based on the second derivative of the gauge-invariant quantity Tr lnD(q), which we interpret as the gauge-boson ‘self-loop’. By considering the higher-order corrections to this quantity, we are able to obtain a Gribov equation which sums the logarithmically enhanced corrections. By solvi...
متن کاملPath integral of the hydrogen atom, the Jacobi’s principle of least action and one-dimensional quantum gravity
A path integral evaluation of the Green’s function for the hydrogen atom initiated by Duru and Kleinert is studied by recognizing it as a special case of the general treatment of the separable Hamiltonian of Liouville-type. The basic dynamical principle involved is identified as the Jacobi’s principle of least action for given energy which is reparametrization invariant, and thus the appearance...
متن کاملPerturbative Approach to Calculating the Correlation Function of bi-isotropic Metamaterials
A bi-isotropic magneto-electric metamaterials is modeled by two independent reservoirs. The reservoirs contain a continuum of three dimensional harmonic oscillators, which describe polarizability and magnetizability of the medium. The paper aimed to investigate the effect of electromagnetic field on bi-isotropic. Starting with a total Lagrangian and using Euler-Lagrange equation, researcher cou...
متن کاملPath Integral for Separable Hamiltonians of Liouville-type
A general path integral analysis of the separable Hamiltonian of Liouville-type is reviewed. The basic dynamical principle used is the Jacobi’s principle of least action for given energy which is reparametrization invariant, and thus the gauge freedom naturally appears. The choice of gauge in path integral corresponds to the separation of variables in operator formalism. The gauge independence ...
متن کامل