The geometry of a covariant expansion in chiral theories with nucleons

We deal with the geometrical foundations of a covariant scheme, which is developed to give a co-ordinate independent perturbation expansion ofSU(2)×SU(2) chiral theories with pions and nucleons. The pion fields play the role of local co-ordinates on a 3-D manifold with constant curvature in isospace. The presence of the nucleon isospinor field forces us to deal with the problem of endowing the manifold with a spin structure. In this way the nucleon isospinor is accommodated in the fiber space of the principal fiber bundle of the tangent bundle of the manifold.     

Renormalizability of leading order covariant chiral nucleon-nucleon interaction

In this work,we study the renormalization group invariance of the recently proposed covariant power counting in the case of nucleon-nucleon scattering [Chin.Phys.C 42(2018) 014103] at leading order.We show that unlike the Weinberg scheme,renormalizaion group invariance is satisfied in the ~3 P_0 channel.Another interesting feature is that the ~1 S_0 and ~3 P_1 channels are correlated.Fixing the relevant low energy constants by fitting to the ~1 S_O phase shifts at T_(lab).=10 and 25 MeV with cutoff values ∧=400-650 MeV,one can describe the ~3 p_1 phase shifts relatively well.In the limit of ∧→∞,the ~1 S_0 phase shifts become cutoff-independent,whereas the ~3 P_1 phase shifts do not.This is consistent with the Wigner bound and previous observations that the ~3 P_1 channel is best treated perturbatively.As for the ~1 P_1 and ~3 S_1-~3 D_1 channels,renormalization group invariance is satisfied.     

On the chiral covariant approach to ρρ scattering

We examine in detail a recent work(D. Gülmez, U. G. Mei?ner and J. A. Oller, Eur. Phys. J. C,77: 460(2017)), where improvements to make ρρ scattering relativistically covariant are made. The paper has the remarkable conclusion that the J =2 state disappears with a potential which is much more attractive than for J =0,where a bound state is found. We trace this abnormal conclusion to the fact that an "on-shell" factorization of the potential is done in a region where this potential is singular and develops a large discontinuous and unphysical imaginary part. A method is developed, evaluating the loops with full ρ propagators, and we show that they do not develop singularities and do not have an imaginary part below threshold. With this result for the loops we define an effective potential, which when used with the Bethe-Salpeter equation provides a state with J =2 around the energy of the f_2(1270). In addition, the coupling of the state to ρρ is evaluated and we find that this coupling and the T matrix around the energy of the bound state are remarkably similar to those obtained with a drastic approximation used previously, in which the q~2 terms of the propagators of the exchanged ρ mesons are dropped, once the cut-off in the ρρ loop function is tuned to reproduce the bound state at the same energy.     

The chiral ring and the periods of the resolvent

The strongly coupled vacua of an supersymmetric gauge theory can be described by imposing quantization conditions on the periods of the gauge theory resolvent, or equivalently by imposing factorization conditions on the associated Seiberg–Witten curve (the so-called strong-coupling approach). We show that these conditions are equivalent to the existence of certain relations in the chiral ring, which themselves follow from the fact that the gauge group has a finite rank. This provides a conceptually very simple explanation of why and how the strongly coupled physics of theories, including fractional instanton effects, chiral symmetry breaking and confinement, can be derived from purely semi-classical calculations involving instantons only.     

Recent development in SU(3) covariant baryon chiral perturbation theory

Baryon chiral perturbation theory (BChPT), as an effective field theory of low-energy quantum chromodynamics (QCD), has played and is still playing an important role in our understanding of non-perturbative strong-interaction phenomena. In the past two decades, inspired by the rapid progress in lattice QCD simulations and the new experimental campaign to study the strangeness sector of low-energy QCD, many efforts have been made to develop a fully covariant BChPT and to test its validity in all scenarios. These new endeavours have not only deepened our understanding of some long-standing problems, such as the power-counting-breaking problem and the convergence problem, but also resulted in theoretical tools that can be confidently applied to make robust predictions. Particularly, the manifestly covariant BChPT supplemented with the extended-on-mass-shell (EOMS) renormalization scheme has been shown to satisfy all analyticity and symmetry constraints and converge relatively faster compared to its non-relativistic and infrared counterparts. In this article, we provide a brief review of the fully covariant BChPT and its latest applications in the u, d, and s three-flavor sector.     

The covariant perturbative string spectrum

We provide generating functions for the perturbative massive string spectrum which are covariant with respect to the SO(9)$\mathit{SO}(9)$ little group, and which contain all the representation theoretic content of the spectrum. Generating functions for perturbative bosonic, Type II, Heterotic and Type I string theories are presented, and generalizations are discussed.     

Pion-pion phase shifts from covariant perturbation theory for a chiral invariant field theoretic model

The Lehmann model for pion -pion scattering consists of a low-energy expansion of the scattering amplitude to fourth order in the momenta on the basis of the chiral-invariant pion-nucleon Lagrangian. Because of the non-renormalizability of the pion Lagrangian two parameters remain undetermined in the pion-loop contribution. Using covariant perturbation theory and superpropagator methods, we calculate these two parameters independently of the choice of the pion field coordinates. The resulting phase shifts are shown to be in very good agreement with the data.     

The interacting gauge covariant bosonic string

The interaction of the gauge covariant open bosonic string is presented in oscillator form, and in functional form. In the latter form, the string is described by commuting and anticommuting coordinates. The interaction is essentially the condition that the strings should overlap.     

The synchronization problem in covariant relativistic dynamics

In the classical Stueckelberg-Horwitz-Piron relativistic Hamiltonian mechanics, a significant aspect of evolution of the classical n-body particle system with mutual interaction is the method by which events along distinct particle world lines are put into correspondence as a dynamical state. Approaches to this procedure are discussed in connection with active and passive symmetry principles.     

The enveloping algebra of a covariant system

In an earlier work, Doplicher, Kastler and Robinson have examined a mathematical structure consisting of a pair (A, G), whereA is aC*-algebra andG is a locally compact automorphism group ofA. We call such a structure a covariant system. The enveloping von Neumann algebraA(A, G) of (A, G) is defined as a *-algebra of operator valued functions (called options) on the space of covariant representations of (A, G). The system (A, G) is canonically embedded in, and in fact generates, the von Neumann algebraA(A, G). Further we show there is a natural one-to-one correspondence between the normal *-representations ofA(A, G) and the proper covariant representations of (A, G). The relation ofA(A, G) to the covarainceC*-algebraC*(A, G) is also examined.     

K-essential covariant holography

Braneworld models may yield interesting effects ranging from high-energy physics to cosmology, or even some low-energy physics. Their mode structure modifies standard results in these physical realms that can be tested and used, for example, to set bounds on the models parameters. Now, to define braneworld deviations from standard 4D physics, a notion of matter and gravity localization on the brane is crucial. In this work we investigate the localization of universal massive scalar fields in a de Sitter thick tachyonic braneworld generated by gravity coupled to a tachyonic bulk scalar field. This braneworld possesses a 4D de Sitter induced metric and is asymptotically flat despite the presence of a negative bulk cosmological constant, a novel and interesting peculiarity that contrasts with previously known models. It turns out that universal scalar fields can be localized in this expanding braneworld if their bulk mass obeys an upper bound, otherwise the scalar fields delocalize: The dynamics of the scalar field is governed by a Schrödinger equation with an analog quantum mechanical potential of modified Pöschl–Teller type. This potential depends on the bulk curvature of the braneworld system as well as on the value of the bulk scalar field mass. For masses satisfying a certain upper bound, the potential displays a negative minimum and possesses a single massless bound state separated from the Kaluza–Klein (KK) massive modes by a mass gap defined by the Hubble (expansion scale) parameter of the 3-brane. As the bulk scalar field mass increases, the minimum of the quantum mechanical potential approaches a null value and, when the bulk mass reaches certain upper bound, it becomes positive (eventually transforming into a potential barrier), leading to delocalization of the bulk scalar field from the brane. We present analytical expressions for the general solution of the Schrödinger equation. Thus, the KK massive modes are given in terms of general Heun functions as well as the expression for the massless zero mode, giving rise to a new application of these special functions.     

The Fubini-Furlan-Rosetti sum rule and related aspects in light of covariant baryon chiral perturbation theory<Superscript>⋆</Superscript>

We analyze the Fubini-Furlan-Rosetti sum rule in the framework of covariant baryon chiral perturbation theory to leading one-loop accuracy and including next-to-leading-order polynomial contributions. We discuss the relation between the subtraction constants in the invariant amplitudes and certain low-energy constants employed in earlier chiral perturbation theory studies of threshold neutral pion photoproduction off nucleons. In particular, we consider the corrections to the sum rule due to the finite pion mass and show that below the threshold they agree well with determinations based on fixed-t dispersion relations. We also discuss the energy dependence of the electric dipole amplitude E₀₊.     

The method of covariant symbols in curved space-time

Diagonal matrix elements of pseudodifferential operators are needed in order to compute effective Lagrangians and currents. For this purpose the method of symbols is often used, which however lacks manifest covariance. In this work the method of covariant symbols, introduced by Pletnev and Banin, is extended to curved space-time with arbitrary gauge and coordinate connections. For the Riemannian connection we compute the covariant symbols corresponding to external fields, the covariant derivative and the Laplacian, to fourth order in a covariant derivative expansion. This allows one to obtain the covariant symbol of general operators to the same order. The procedure is illustrated by computing the diagonal matrix element of a nontrivial operator to second order. Applications of the method are discussed. PACS 04.62.+v; 11.15.-q; 11.15.Tk