Related papers: Mandelstam-Leibbrandt prescription
Dimensional regularization is arguably the most popular and efficient scheme for multi-loop calculations. Yet, when applied to chiral (gauge) theories like the Standard Model and its extensions, one is forced to deal with the infamous…
We present calculations of next-to-leading order QCD splitting functions, employing the light-cone gauge method of Curci, Furmanski, and Petronzio (CFP). In contrast to the `principal-value' prescription used in the original CFP paper for…
A Lorentz-covariant regularization scheme for effective field theories with an arbitrary number of propagating heavy and light particles is given. This regularization scheme leaves the low-energy analytic structure of Greens functions…
In this article, we provide sufficient conditions under which the controlled vector fields solution of optimal control problems formulated on continuity equations are Lipschitz regular in space. Our approach involves a novel combination of…
We show that typical implicit regularization assumptions for deep neural networks (for regression) do not hold for coordinate-MLPs, a family of MLPs that are now ubiquitous in computer vision for representing high-frequency signals. Lack of…
Through defining irreducible loop integrals (ILIs), a set of consistency conditions for the regularized (quadratically and logarithmically) divergent ILIs are obtained to maintain the generalized Ward identities of gauge invariance in…
We calculate field theory loop amplitudes by string methods, applied to half-maximal 4-point one-loop graviton amplitudes. Infrared divergences are regulated similarly to soft-collinear effective field theory (SCET): new mass scales are…
Estimating the unconstrained mean and covariance matrix is a popular topic in statistics. However, estimation of the parameters of $N_p(\mu,\Sigma)$ under joint constraints such as $\Sigma\mu = \mu$ has not received much attention. It can…
Three-dimensional cutoff regulators are frequently employed in multi-nucleon calculations, but they violate chiral symmetry and Lorentz invariance. A cutoff regularization scheme is proposed to compensate systematically at subleading orders…
Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known $\mathcal{S}$-lemma. However, the…
An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the…
We apply negative dimensional integration method (NDIM) to three outstanding gauges: Feynman, light-cone and Coulomb gauges. Our aim is to show that NDIM is a very suitable technique to deal with loop integrals, being them originated from…
We derive non-linear recursion equation for the leading infrared logarithms (LL) in four dimensional sigma-model with fields on an arbitrary Riemann manifold. The derived equation allows one to compute leading infrared logarithms to…
We derive Mandelstam formulae for two generalisations of the Wilson loop. In these generalisations path-ordering of Lie algebra generators is replaced by an anti-commuting one dimensional field theory along the loop. We extend the…
The multipole expansion for electromagnetic radiation, valid for all wave-lengths and all distances from bounded sources, is presented in Lorentz gauge, rather than the usual Coulomb gauge. This gauge is likely to be preferred in…
The consistency of loop regularization (LORE) method is explored in multiloop calculations. A key concept of the LORE method is the introduction of irreducible loop integrals (ILIs) which are evaluated from the Feynman diagrams by adopting…
To verify the conjecture that Yang-Mills theory in the infrared limit is equivalent to a spin system whose excitations are knot solitons, a numerical algorithm based on the inverse Monte Carlo method is proposed. To investigate the…
A local gauge invariant infrared regularization for the Yang-Mills theory is constructed on the basis of a higher derivative formulation of the model.
We derive the Leading Order DGLAP evolution of gluon distribution function in the target light cone gauge starting from its standard operator definition. The derivation is performed using the background field formalism also employed in the…
In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is…