Related papers: QCD Inequalities
These lectures on QCD stress the theoretical elements that underlie a wide range of phenomenological studies, particularly gauge invariance, renormalization, factorization and infrared safety. The three parts cover the basics of QCD, QCD at…
In this paper, we prove several Poincar\'e inequalities of fractional type on conformally flat manifolds with finite total Q-curvature. This shows a new aspect of the $Q$-curvature on noncompact complete manifolds.
We discuss the origin and size of potential uncertainties arising in the estimate of cross sections for the production of multiparticle final states induced by QCD instantons at the LHC.
Quantum field theory in curved spacetime may be defined either through a manifestly unitary canonical approach or via the manifestly covariant path integral formalism. For gauge theories, these two approaches have produced conflicting…
I review some recent progress and open problems in the calculation of heavy-quarkonium inclusive decay widths into light particles in the framework of QCD non-relativistic effective field theories.
These lectures on QCD stress the theoretical elements that underlie a wide range of phenomenological studies, particularly gauge invariance, renormalization, factorization and infrared safety. The three parts cover the basics of QCD, QCD at…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few…
We prove weighted $q$-variation inequalities with $2<q<\infty$ for differential and singular integral operators in higher dimensions. The vector-valued extensions of these inequalities are also given.
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
Using the Gell-Mann-Oakes-Renner (GOR) relation and semi-classical arguments, we show that the bulk quark spectrum in QCD exhibits a variety of regimes including the ergodic one described by random matrix theory. We analyze the quark…
Recent achievements in the heavy quark theory are critically reviewed. The emphasis is put on those aspects which either did not attract enough attention or cause heated debates in the current literature. Among other topics we discuss (i)…
We study the effects on length spaces imposed by quadratic inequalities on the six distances between the points in every quadruple.
A rigorous QED theory of the spectral line profiles is applied to transition probabilities in few-electron highly charged ions. Interelectron interaction corrections are included as well as radiative corrections. Parity nonconserving (PNC)…
In this paper, we propose a new approach to Cwikel estimates both for the Euclidean space and for the noncommutative Euclidean space.
Elements of the alternative approach to hard collisions of photons, proposed recently by the author, are reviewed, with particular attention to QCD analysis of $F^{\gamma}_2$. This approach is based on clear separation of genuine QCD…
A relativistic Coulomb-like resummation factor in QCD is suggested, based on the solution of the quasipotential equation.
Using stochastic quantization method we derive gauge-invariant equations, connecting multilocal vacuum correlators of nonperturbative field configurations immersed into the quantum background. Three alternative methods of stochastic…
The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a local uniqueness result. Moreover, we introduce a direct sampling method for quantitatively…
In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.