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Marco Frasca

Publications and source records attributed to Marco Frasca.

At least 109 records · Page 6Linked to original sources
arXiv2010

Infrared behavior of the running coupling in scalar field theory

We compute the Green function of the massless scalar field theory in the infrared till the next-to-leading order, providing a fully covariant strong coupling expansion. Applying Callan-Symanzik equation we obtain the exact running coupling for this case by computing the beta function. This result is applied using a recently proved mapping theorem between a massless scalar field theory and Yang-Mills theory. This beta function gives a running coupling going to zero as $p^4$ in agreement with lattice results presented in Boucaud et al. [JHEP 0304 (2003) 005] and showing that the right definition of the running coupling for a Yang-Mills theory in the infrared is given in a MOM scheme. The emerging scenario is supporting a quantum field theory based on instantons.

hep-th↗
arXiv2010

Glueball spectrum and hadronic processes in low-energy QCD

Low-energy limit of quantum chromodynamics (QCD) is obtained using a mapping theorem recently proved. This theorem states that, classically, solutions of a massless quartic scalar field theory are approximate solutions of Yang-Mills equations in the limit of the gauge coupling going to infinity. Low-energy QCD is described by a Yukawa theory further reducible to a Nambu-Jona-Lasinio model. At the leading order one can compute glue-quark interactions and one is able to calculate the properties of the $σ$ and $η-η'$ mesons. Finally, it is seen that all the physics of strong interactions, both in the infrared and ultraviolet limit, is described by a single constant $Λ$ arising in the ultraviolet by dimensional transmutation and in the infrared as an integration constant.

hep-ph↗
arXiv2010

Low-energy QCD

We derive a low-energy quantum field theory from quantum chromodynamics (QCD) that holds in the limit of a very large coupling. All the parameters of the bare theory are fixed through QCD. Low-energy limit is obtained through a mapping theorem between massless quartic scalar field theory and Yang-Mills theory. One gets a Yukawa theory that, in the same limit of strong coupling, reduces to a Nambu-Jona-Lasinio model with a current-current coupling with scalar-like excitations arising from Yang-Mills degrees of freedom. A current-current expansion in the strong coupling limit yields a fully integrated generating functional that, neglecting quark-quark current coupling, describes all processes involving glue excitations and quark. Some processes are analyzed and we are able to show consistency of Narison-Veneziano sum rules. Width of the $σ$ resonance is computed. The decay $η'\toη+π^++π^-$ is discussed in this approximation and analyzed through the more elementary processes $η'\toη+σ$ and $σ\toπ^++π^-$. In this way we get an estimation of the mass of the $σ$ resonance and the value of the $η$ decay constant. This $η'$ decay appears a possible source of study for the $σ$ resonance.

hep-ph↗
arXiv2009

Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case

We analyze a recent proposal to map a massless scalar field theory onto a Yang-Mills theory at classical level. It is seen that this mapping exists at a perturbative level when the expansion is a gradient expansion. In this limit the theories share the spectrum, at the leading order, that is the one of an harmonic oscillator. Gradient expansion is exploited maintaining Lorentz covariance by introducing a fifth coordinate and turning the theory to Euclidean space. These expansions give common solutions to scalar and Yang-Mills field equations that are so proved to exist by construction, confirming that the selected components of the Yang-Mills field are indeed an extremum of the corresponding action functional.

math-ph↗
arXiv2009

Dual Lindstedt series and KAM theorem

We prove that exists a Lindstedt series that holds when a Hamiltonian is driven by a perturbation going to infinity. This series appears to be dual to a standard Lindstedt series as it can be obtained by interchanging the role of the perturbation and the unperturbed system. The existence of this dual series implies that a dual KAM theorem holds and, when a leading order Hamiltonian exists that is non degenerate, the effect of tori reforming can be observed with a system passing from regular motion to fully developed chaos and back to regular motion with the reappearance of invariant tori. We apply these results to a perturbed harmonic oscillator proving numerically the appearance of tori reforming. Tori reforming appears as an effect limiting chaotic behavior to a finite range of parameter space of some Hamiltonian systems. Dual KAM theorem, as proved here, applies when the perturbation, combined with a kinetic term, provides again an integrable system.

math-ph↗
arXiv2009

Observability of glueball spectrum in QCD and the width of $σ$ resonance

We prove a theorem in QCD stating that in the limit of strong coupling, $g\to\infty$, the observed spectrum of glueballs in QCD is the same of a pure Yang-Mills theory, being mixing effects due to the next-to-leading order. A full effective theory for QCD is obtained and the width of the $σ$ resonance decay is straightforwardly computed. This appears as the lowest glueball state. Vacuum gluon condensate is computed that consistently support studies on the identification of this meson as a glueball.

hep-ph↗
arXiv2009

Exact Massive Solutions of Classical Massless Field Theories

We give the exact solution of classical equation of motion of a quartic scalar massless field theory showing that this is massive and is represented by a superposition of free particle solutions with a discrete spectrum. Then we show that this is also a solution of the classical Yang-Mills field theory that is so proved acquiring mass by dynamical evolution with a corresponding discrete mass spectrum. Finally we develop quantum field theory starting with this solution.

hep-th↗
arXiv2008

Infrared Gluon and Ghost Propagators

We derive the form of the infrared gluon propagator by proving a mapping in the infrared of the quantum Yang-Mills and $λϕ^4$ theories. The equivalence is complete at a classical level. But while at a quantum level, the correspondence is spoiled by quantum fluctuations in the ultraviolet limit, we prove that it holds in the infrared where the coupling constant happens to be very large. The infrared propagator is then obtained from the quantum field theory of the scalar field producing a full spectrum. The results are in fully agreement with recent lattice computations. We get a finite propagator at zero momentum, the ghost propagator going to infinity as $1/p^{2+2κ}$ with $κ=0$.

hep-th↗
arXiv2008

Localization in a strongly disordered system: A perturbation approach

We prove that a strongly disordered two-dimensional system localizes with a localization length given analytically. We get a scaling law with a critical exponent is $ν=1$ in agreement with the Chayes criterion $ν\ge 1$. The case we are considering is for off-diagonal disorder. The method we use is a perturbation approach holding in the limit of an infinitely large perturbation as recently devised and the Anderson model is considered with a Gaussian distribution of disorder. The localization length diverges when energy goes to zero with a scaling law in agreement to numerical and theoretical expectations.

cond-mat.dis-nn↗
arXiv2008

Yang-Mills Propagators and QCD

We present a strong coupling expansion that permits to develop analysis of quantum field theory in the infrared limit. Application to a quartic massless scalar field gives a massive spectrum and the propagator in this regime. We extend the approach to a pure Yang-Mills theory obtaining analogous results. The gluon propagator is compared satisfactorily with lattice results and similarly for the spectrum. Comparison with experimental low energy spectrum of QCD supports the view that $σ$ resonance is indeed a glueball. The gluon propagator we obtained is finally used to formulate a low energy Lagrangian for QCD that reduces to a Nambu-Jona-Lasinio model with all the parameters fixed by those of the full theory.

hep-ph↗
arXiv2008

Infrared QCD

We prove that Nambu-Jona-Lasinio model is an exact description of infrared QCD deriving it from QCD Lagrangian. The model we obtain is renormalizable and confining but, taking very small momenta fixes completely all the parameters of the Nambu-Jona-Lasinio model through those of QCD. The choice of the infrared propagator is done consistently with recent numerical results from lattice and Dyson-Schwinger equations for Yang-Mills theory. The model we get coincides, once the ultraviolet contribution is removed, with the one proposed by Langfeld, Kettner and Reinhardt [Nucl. Phys. A {\bf 608}, 331 (1996)].

hep-th↗
arXiv2008

Källen-Lehman Representation and the Gluon Propagator

We exploit the Kallen-Lehman representation of the two-point Green function to prove that the gluon propagator cannot go to zero in the infrared limit. We are able to derive also the functional form of it. This means that current results on the lattice can be used to derive the scalar glueball spectrum to be compared both with experiments and different aimed lattice computations.

hep-th↗
arXiv2007

Green functions and nonlinear systems: Short time expansion

We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with numerical results. The relevance of these results relies on the possibility of fully exploiting a gradient expansion in both classical and quantum field theory granting the existence of a strong coupling expansion. Having a Green function in this regime in quantum field theory amounts to obtain the corresponding spectrum of the theory.

hep-th↗
arXiv2007

Spectrum in the broken phase of a $λϕ^4$ theory

We derive the spectrum in the broken phase of a $λϕ^4$ theory, in the limit $λ\to\infty$, showing that this goes as even integers of a renormalized mass in agreement with recent lattice computations.

hep-th↗
arXiv2007

Spectrum of Yang-Mills Theory in D=3+1

We give a comparison of the spectrum of Yang-Mills theory in $D=3+1$, recently derived with a strong coupling expansion, with lattice data. We verify excellent agreement also for 2$^{++}$ glueball. A deep analogy with the $D=2+1$ case is obtained and a full quantum theory of this approach is also given.

hep-th↗
arXiv2007

A strongly perturbed quantum system is a semiclassical system

We show that a strongly perturbed quantum system, being a semiclassical system characterized by the Wigner-Kirkwood expansion for the propagator, has the same expansion for the eigenvalues as for the WKB series. The perturbation series is rederived by the duality principle in perturbation theory.

hep-th↗
arXiv2007

Green Function Method for Nonlinear Systems

We show that a Green function solution can be given for a class of non-homogeneous nonlinear systems having relevance in quantum field theory. This in turn means that a quantum field theory in the strong coupling limit can be formulated and the spectrum obtained.

hep-th↗