Related papers: Extending the Universal One-Loop Effective Action …
It has been found that residual networks are an Euler discretization of solutions to Ordinary Differential Equations (ODEs). In this paper, we explore a deeper relationship between Transformer and numerical methods of ODEs. We show that a…
Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many…
A unified and systematic scheme for constraction of differential opreator realization of any irreducible representation of $sl(n)$ is developed. The $q$-analogue of this unified scheme is used to constract $q$-difference operator…
We present the universal one-loop effective action up to dimension eight after integrating out heavy fermion(s) using the Heat-Kernel method. We have discussed how the Dirac operator being a weak elliptic operator, the fermionic operator…
We present the complete one-loop effective action up to dimension eight after integrating out degenerate scalars using the Heat-Kernel method. The result is provided without assuming any specific form of either UV or low energy theories,…
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators,…
We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point…
In this note we discuss some formal properties of universal linearization operator, relate this to brackets of non-linear differential operators and discuss application to the calculus of auxiliary integrals, used in compatibility…
The exact renormalization group (ERG) is a powerful tool for understanding the formal properties of field theories. By adapting generalized ERG schemes to the flow of wavefunctionals, we obtain a large class of continuous unitary networks,…
Two program packages are presented for evaluating one-loop amplitudes. They can work either in dimensional regularization or in constrained differential renormalization. The latter method is found at the one-loop level to be equivalent to…
Training Neural Ordinary Differential Equations (ODEs) is often computationally expensive. Indeed, computing the forward pass of such models involves solving an ODE which can become arbitrarily complex during training. Recent works have…
The RG expansions for renormalized coupling constants g_6 and g_8 of the 3D n-vector model are calculated in the 4-loop and 3-loop approximations respectively. Resummation of the RG series for g_6 by the Pade-Borel-Leroy technique results…
It may be possible to use operator regularization with Feynman diagrams, which would greatly simplify its use as it has so far been limited to the more complicated Schwinger approach. Operator regularization, unlike $\zeta$-function…
Renormalization is a well-known technique to get rid of ultraviolet (UV) singularities. When relying on Dimensional Regularization (DREG), these become manifest as $\epsilon$-poles, allowing to define counter-terms with useful recursive…
We introduce an unsupervised domain adaption (UDA) strategy that combines multiple image translations, ensemble learning and self-supervised learning in one coherent approach. We focus on one of the standard tasks of UDA in which a semantic…
Motivated by the study of quantum fields in a Friedman-Robertson-Walker (FRW) spacetime, the one-loop effective action for a scalar field defined in the ultrastatic manifold $R\times H^3/\Gamma$, $H^3/\Gamma$ being the finite volume,…
Fierz transformations for four-fermion operators are generalized to the one-loop level. A general renormalization scheme is used to compute QCD and QED corrections to the tree-level relations, which result from Fierz-evanescent operators.…
We offer a guide to dimensional reduction (DRED) in theories with anomaly mediated supersymmetry breaking. Evanescent operators proportional to epsilon arise in the bare Lagrangian when it is reduced from d=4 to d= (4-2 epsilon) dimensions.…
We consider the most general loop integral that appears in non-relativistic effective field theories with no light particles. The divergences of this integral are in correspondence with simple poles in the space of complex space-time…
We derive a new class of one-loop non-renormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop…