A numerical algorithm for efficiently obtaining a Feynman parameter representation of one-gluon loop QCD Feynman diagrams for a large number of external gluons

A numerical program is presented which facilitates a computation pertaining to the full set of one-gluon loop diagrams (including ghost loop contributions), with M attached external gluon lines in all possible ways. The feasibility of such a task rests on a suitably defined master formula, which is expressed in terms of a set of Grassmann and a set of Feynman parameters. The program carries out the Grassmann integration and performs the Lorentz trace on the involved functions, expressing the result as a compact sum of parametric integrals. The computation is based on tracing the structure of the final result, thus avoiding all intermediate unnecessary calculations and directly writing the output. Similar terms entering the final result are grouped together. The running time of the program demonstrates its effectiveness, especially for large M.Comment: 32 pages, 5 figures. in press Computer Physics Communication

A space-time approach to multigluon computations in QCD: An application to effective action terms

The applicability of the space-time formulation of the gluonic sector of QCD in terms of the Polyakov worldline path integral, via the use of the background field gauge fixing method, is extended to multi-gluon loop configurations. Relevant master formulas are derived for the computation of effective action terms.Comment: 10 page

Zig Zag symmetry in AdS/CFT duality

The validity of the Bianchi identity, which is intimately connected with the zig zag symmetry, is established, for piecewise continuous contours, in the context of Polakov's gauge field-string connection in the large 'tHooft coupling limit, according to which the chromoelectric `string' propagates in five dimensions with its ends attached on a Wilson loop in four dimensions. An explicit check in the wavy line approximation is presented.Comment: 24 pages version to appear in EPJ

Pion production from a critical QCD phase

A theoretical scheme which relates multiparticle states generated in ultrarelativistic nuclear collisions to a QCD phase transition is considered in the framework of the universality class provided by the 3-D Ising model. Two different evolution scenarios for the QGP system are examined. The statistical mechanics of the critical state is accounted for in terms of (critical) cluster formation consistent with suitably cast effective action functionals, one for each considered type of expansion. Fractal properties associated with these clusters, characterizing the density fluctuations near the QCD critical point, are determined. Monte-Carlo simulations are employed to generate events, pertaining to the total system, which correspond to signals associated with unconventional sources of pion production

Worldline approach to Sudakov-type form factors in non-Abelian gauge theories

We calculate Sudakov-type form factors for isolated spin-1/2 particles (fermions) entering non-Abelian gauge-field systems. We consider both the on- and the off-mass-shell case using a methodology which rests on a worldline casting of field theories. The simplicity and utility of our approach derives from the fact that we are in a position to make, a priori, a more transparent separation (factorization), with respect to a given scale, between short- and long-distance physics than diagramatic methods.Comment: 18 pages. RevTex is used. No figure

Isotopic Grand Unification with the Inclusion of Gravity (revised version)

We introduce a dual lifting of unified gauge theories, the first characterized by the isotopies, which are axiom- preserving maps into broader structures with positive-definite generalized units used for the representation of matter under the isotopies of the Poincare' symmetry, and the second characterized by the isodualities, which are anti-isomorphic maps with negative-definite generalized units used for the representation of antimatter under the isodualities of the Poincare' symmetry. We then submit, apparently for the first time, a novel grand unification with the inclusion of gravity for matter embedded in the generalized positive-definite units of unified gauge theories while gravity for antimatter is embedded in the isodual isounit. We then show that the proposed grand unification provides realistic possibilities for a resolution of the axiomatic incompatibilities between gravitation and electroweak interactions due to curvature, antimatter and the fundamental space-time symmetries.Comment: 20 pages, Latex, revised in various details and with added reference

Renormalizability aspects of massive Yang-Mills field models

We confront the problem concerning the renormalizability of massive Yang-Mills theories in which the mass term for the vector fields has been inserted by hand. Explicitly, our starting Lagrangians are of the type studied in the past by Veltman and Boulware and found to be nonrenormalizable. We rely heavily on Boulware's analysis in which the basic point of view is to split the massive Yang-Mills fields into transverse and longitudinal components. The latter carry all the nonrenormalizability pathologies which manifest themselves in terms of certain nonpolynomial factors involving the longitudinal fields. The fact that these factors cannot be removed via a redefinition of the longitudinal fields leads to the conclusion of nonrenormalizability. We call the problem on hand, namely the removal of the bad nonpolynomial terms, Boulware's problem. We study this problem closely, within the context of the adjoint representation of the gauge group [we restrict ourselves to SU(2) for the most part] employing the language of differential geometry. We prove a theorem according to which a necessary condition for solving Boulware's problem is the introduction of extra fields. In the case of SU(2) we find an explicit solution which requires the introduction of a triplet of scalar fields belonging to the adjoint representation of SU(2). We interpret the additional fields as ghost, or superfluous fields-most probably corresponding to the ghost fields of spontaneously broken gauge theories in the R gauge. Here we note a basic difference between our program and that of Cornwall et al. First of all, our interpretation of the fields which combine with the longitudinal ones in order to remove the nonpolynomial factors as ghost fields is not evident in the treatment of Cornwall et al. Finally, unlike the case in Cornwall et al., we do not just show the existence of the transformation which removes the undesirable terms but also give the explicit conditions which bring about this result in the case of SU(2). A proposition relating the models under consideration to spontaneously broken gauge ones is also presented. We argue, without explicit proof, that the combination of this proposition with our main theorem corresponds to building a spontaneously broken gauge theory in the R gauge, having started from a non-Abelian theory with mass inserted by hand. © 1976 The American Physical Society

Diagonalizability of the longitudinal sector of the functional integral in massive SU (2) Yang-Mills theories via topological contributions

The problem of longitudinal sector diagonalizability of the functional integral in massive SU (2) Yang-Mills theories is revisited. A new decomposition law of a massive SU (2) vector field into transverse and longitudinal parts is proposed which takes into account the more recently discovered topological properties of SU (2) gauge theories. After establishing the credibility of this decomposition law, it is shown how it leads to the diagonalizability of the longitudinal sector of the functional integral. This result is related to the problem of the existence of the zero-mass limit in massive SU (2) Yang-Mills theories. © 1981 American Institute of Physics

A geometric realization of Van Hove's quantization prescription

We consider, on one hand, Segal's geometric quantization scheme which is formulated on a non-linear configuration-space manifold M and, on other, Van Hove's solution of the quantization mapping with an inherent phase space content. We furnish geometrical interpretations for Van Hove's solution with respect to both M and its cotangent bundle T*(M) (phase space). In the latter case, we are able to introduce commutation relations which extend Segal's scheme in the direction suggested by Van Hove's mapping. © 1992

Worldline casting of the stochastic vacuum model and nonperturbative properties of QCD: General formalism and applications

The stochastic vacuum model for QCD, proposed by Dosch and Simonov, is fused with a worldline casting of the underlying theory, i.e. QCD. Important nonperturbative features of the model are studied. In particular, contributions associated with the spin-field interaction are calculated, and the validity of both the loop equations and of the Bianchi identity is explicitly demonstrated. As an application, a simulated meson-meson scattering problem is studied in the Regge kinematical regime. The process is modeled in terms of the helicoidal Wilson contour along the lines introduced by Janik and Peschanski in a related study based on an AdS/CFT-type approach. Working strictly in the framework of the stochastic vacuum model and in a semiclassical approximation scheme, the Regge behavior for the scattering amplitude is demonstrated. Going beyond this approximation, the contribution resulting from boundary fluctuations of the Wilson loop contour is also estimated. © 2009 The American Physical Society