Effects of Background Fields on Some Physical Processes.
We computed the operator product expansion of the scalar, spinor and the vector (in a specific gauge) propagator in an arbitrary background gauge field. The Schwinger background field formalism--as developed by DeWitt and others--is a very suitable tool for this purpose. The analysis is used to verify, at the tree level, the conjecture put forward by Shifman et al., that a smooth background field does not modify the coefficient functions of a perturbative operator product expansion. The expansion was done using the "heat kernel" method with the proper time variable as the expansion parameter; and in the momentum space the successive coefficients of the composite operators have an inverse power structure. The phase factor P exp-(INT) Adz, emerging naturally in the expansion scheme, preserves the gauge covariance of the scalar and spinor propagator. The formalism may be used to find the background field effects in various Green's functions. The vector field propagator in an instanton field has an infrared divergent piece D(,(alpha))(1/D('2))('2) D(,(beta)), but is also amenable to a similar expansion scheme. From the expansion it follows that the divergences in the momentum space, except for the inverse power structure, are of the type (delta)('(4)) (p) or derivatives thereof. It is also evident that only for the vector is it possible to ascribe a non-perturbative vacuum expectation value to the composite operators. We used these results to find the leading instanton effect for the spin-independent structure functions. The process chosen as a model is the deep inelastic scattering of an electromagnetic current off a single quark state. One can calculate the diagonal matrix elements between single quark states of twist-2 operators at the lowest order in the strong coupling constant. They describe the moments of the structure functions, and inverting the moment relations, we can obtain the instanton generated structure functions. A systematic expansion in the parameter m(rho), where m is the constituent quark mass, and (rho) is the average instanton size, is available. However, our results are negative --up to the order (m(rho))('2). When the finite wave function renormalization constant Z(,2) for the quark legs are taken into account, the matrix element of all the twist-2 operators reduces to their free field values. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author.) UMI.
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- Physics: Elementary Particles and High Energy