Related papers: Reparameterization Invariant Operator Basis for NR…
We discuss the renormalization of the lattice formulation of the Heavy Quark Effective Theory (LHQET). In addition to wave function and composite operator renormalizations, on the lattice the classical velocity is also renormalized. The…
The heavy quark effective field theory Lagrangian is renormalized to order 1/m^2. Our technique eliminates operators that vanish by the equation of motion by continuously redefining the heavy quark fields during renormalization. It is…
Using the virial theorem of the heavy-quark effective theory, we show that the mixing of the operator for the heavy-quark kinetic energy with the identity operator is forbidden at the one-loop order by Lorentz invariance. This explains why…
We proposed a new formulation for heavy quark effective theory (HQET), whose Lagrangian is hermitian and has a manifest reparameterization invariance. As an application, we calculated the semileptonic and nonleptonic inclusive heavy hadron…
We propose a novel parametrization of the four-point vertex function in the one-loop one-particle irreducible renormalization group (RG) scheme for fermions. It is based on a decomposition of the effective two-fermion interaction into…
One approach to multivariate operator theory involves concepts and techniques from algebraic and complex geometry and is formulated in terms of Hilbert modules. In these notes we provide an introduction to this approach including many…
We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regularization, but existence of solutions of the regularized…
This work establishes a systematic framework for operator construction in the non-relativistic effective field theory, incorporating both the three dimensional Euclidean symmetry and the internal symmetries. By employing double cover of the…
HQET lagrangian up to $1/m^3$ terms is discussed. Consequences of reparameterization invariance are considered. Results for the chromomagnetic interaction coefficient at two loops, and in all orders in the large--$\beta_1$ approximation,…
The algebraic structure of the 1D Hubbard model is studied by means of the fermionic R-operator approach. This approach treats the fermion models directly in the framework of the quantum inverse scattering method. Compared with the graded…
The renormalization properties of two local BRST invariant composite operators, $(O,V_\mu)$, corresponding respectively to the gauge invariant description of the Higgs particle and of the massive gauge vector boson, are scrutinized in the…
We examine the constraints imposed by reparametrization invariance on heavy-baryon chiral perturbation theory (HBChPT). We study the case of 3 flavors and consider both the strong and weak ($|\Delta S| =1$) interaction sector. Some of the…
A relativistic quantum mechanics is formulated in which all of the interactions are in the four-momentum operator and Lorentz transformations are kinematic. Interactions are introduced through vertices, which are bilinear in fermion and…
In this paper we introduce a Hilbert series approach to build the operator basis for a N = 1 supersymmetry theory with chiral superfields. We give explicitly the form of the corrections that remove redundancies due to the equations of…
The construction of heavy quark effective field theory (HqEFT) is extended to arbitrary order in both expansion parameters $\alpha_s$ and $1/m_q$. Matching conditions are discussed for the general case, and it is verified that this approach…
The reparametrization transformation between ultrametrically organised states of replicated disordered systems is explicitly defined. The invariance of the longitudinal free energy under this transformation, i.e. reparametrization…
An operator basis of an effective theory with a heavy particle, subject to external gauge fields, is spanned by a particular kind of neutral scalar primary of the nonrelativistic conformal group. We calculate the characters that can be used…
We discuss Poincare' invariance in the context of non-relativistic effective field theories of QCD. We show, in the cases of the HQET and pNRQCD, that the algebra of the generators of the Poincare' transformations imposes precise…
Effective Field Theory technique is one of the most elegant ways to capture the impact of high scale theory, if any, at some low energy by incorporating higher mass dimensional ($\geq 5$) effective operators ($\mathcal{O}_i$). The low…
We consider properties of connected diagrams with fermion-photon interaction and such fermion and photon propagators and vertex function that the values of these diagrams are finite. We establish the properties of these propagators and…