arXiv subjects

G. Leibbrandt

Publications and source records attributed to G. Leibbrandt.

4 recordsLinked to original sources

arXiv2000

Vector Supersymmetry and Finite Quantum Correction of Chern-Simons Theory in the Light-Cone Gauge

Vector supersymmetry is shown to exist also in light-cone gauge Chern-Simons theory. Using a gauge invariant regularization scheme, we demonstrate explicitly that the finite quantum correction to the coupling constant of Chern-Simons theory is intimately associated with the breaking of vector supersymmetry at the regularization level. The advantage of investigating such a quantum phenomenon in the light-cone gauge is emphasized and the BRST and vector supersymmetry invariance of quantum effective action is discussed.

hep-th↗

arXiv1999

Split dimensional regularization for the Coulomb gauge at two loops

We evaluate the coefficients of the leading poles of the complete two-loop quark self-energy Σ(p) in the Coulomb gauge. Working in the framework of split dimensional regularization, with complex regulating parameters σand n/2-σfor the energy and space components of the loop momentum, respectively, we find that split dimensional regularization leads to well-defined two-loop integrals, and that the overall coefficient of the leading pole term for Σ(p) is strictly local. Extensive tables showing the pole parts of one- and two-loop Coulomb integrals are given. We also comment on some general implications of split dimensional regularization, discussing in particular the limit σ\to 1/2 and the subleading terms in the epsilon-expansion of noncovariant integrals.

hep-th↗

arXiv1998

The Three-point Function in Split Dimensional Regularization in the Coulomb Gauge

We use a gauge-invariant regularization procedure, called ``split dimensional regularization'', to evaluate the quark self-energy $Σ(p)$ and quark-quark-gluon vertex function $Λ_μ(p^\prime,p)$ in the Coulomb gauge, $\vec{\bigtriangledown}\cdot\vec{A}^a = 0$. The technique of split dimensional regularization was designed to regulate Coulomb-gauge Feynman integrals in non-Abelian theories. The technique which is based on two complex regulating parameters, $ω$ and $σ$, is shown to generate a well-defined set of Coulomb-gauge integrals. A major component of this project deals with the evaluation of four-propagator and five-propagator Coulomb integrals, some of which are nonlocal. It is further argued that the standard one-loop BRST identity relating $Σ$ and $Λ_μ$, should by rights be replaced by a more general BRST identity which contains two additional contributions from ghost vertex diagrams. Despite the appearance of nonlocal Coulomb integrals, both $Σ$ and $Λ_μ$ are local functions which satisfy the appropriate BRST identity. Application of split dimensional regularization to two-loop energy integrals is briefly discussed.

hep-th↗

arXiv1998

The Pole Part of the 1PI Four-Point Function in Light-Cone Gauge Yang-Mills Theory

The complete UV-divergent contribution to the one-loop 1PI four-point function of Yang-Mills theory in the light-cone gauge is computed in this paper. The formidable UV-divergent contributions arising from each four-point Feynman diagram yield a succinct final result which contains nonlocal terms as expected. These nonlocal contributions are consistent with gauge symmetry, and correspond to a nonlocal renormalization of the wave function. Renormalization of Yang-Mills theory in the light-cone gauge is thus shown explicitly at the one-loop level.

hep-th↗