arXiv subjects

Marco Frasca

Publications and source records attributed to Marco Frasca.

At least 91 records · Page 5Linked to original sources

arXiv2013

Classical solutions of a massless Wess-Zumino model

We provide a current expansion for the classical equations of motion of the massles Wess-Zumino model. In the low-energy limit, there appears a massive behavior for bosonic degrees of freedom and, at small coupling, the fermion field shows the same mass and supersymmetry is overall preserved. In the limit of the coupling running to infinity, the fermion field displays a different equation of motion, a Nambu-Jona-Lasinio-like one, and we cannot draw an identical conclusion.

hep-th↗

arXiv2013

Revisiting the Higgs sector of the Standard Model

We analyze the Higgs sector of the Standard Model in the light of recently found exact solutions of its dynamical equation. We work in a conformal regime with zero mass term. It is seen that, provided self-interaction coupling is finite, the field acquires mass and behaves exactly as a vanilla Higgs field at the tree level. Changes are expected in the decay rates to vector bosons. We evaluate this with a quantitative analysis showing how difficult could be to observe higher excited states of the Higgs field presently. This field works like an impostor with respect to the Standard Model formulation.

hep-ph↗

arXiv2012

Beyond one-gluon exchange in the infrared limit of Yang-Mills theory

We analyze the Wilson loop for a pure Yang-Mills theory, using a decoupling solution in close agreement with lattice computations. At one-gluon exchange level it is seen that the potential cannot yield a linear rising contribution as expected for a confining theory. Next-to-leading order correction gives rise to a quartic term for momenta in the gluon propagator that, in agreement with Gribov's view, yields a linear confining term. This correction is due to a two-loop or sunrise integral that we need to evaluate in the low-momenta limit. In the infrared regime, the physical consistency of the theory is determined by a natural cut-off, arising from the integration of the classical equations of the theory, fixing in this way the regularization scheme.

hep-ph↗

arXiv2012

Chiral Wess-Zumino model and breaking of supersymmetry

We prove that the Wess-Zumino model breaks supersymmetry in the low-energy limit. The mechanism is identical to the breaking of chiral symmetry in quantum chromodynamics as the low-energy limit is a Nambu-Jona-Lasinio model and the gap equation has a solution. This happens at a critical coupling at lower momenta. Instanton liquid plays an essential role in the behavior of the theory in this limit.

hep-th↗

arXiv2012

Exact solution of Dyson-Schwinger equations for a scalar field theory

We exactly solve Dyson-Schwinger equations for a massless quartic scalar field theory. n-point functions are computed till n=4 and the exact propagator computed from the two-point function. The spectrum is so obtained, being the same of a harmonic oscillator. Callan-Symanzik equation for the two-point function gives the beta function. This gives the result that this theory has only trivial fixed points. In the low-energy limit the coupling goes to zero making the theory trivial and, at high energies, it reaches infinity. No Landau pole appears, rather this should be seen as a precursor, in a weak perturbation expansion, of the coupling reaching the trivial fixed point at infinity. Using a mapping theorem, recently proved, between massless quartic scalar field theory and gauge theories, we derive some properties of the latter.

hep-th↗

arXiv2012

Low-energy QCD from first principles

We show how, starting from QCD Lagrangian, a low-energy limit can be derived that is given by a non-local Nambu-Jona-Lasinio model with the form factor in close agreement with the one expected from an instanton liquid model but with all the parameters properly fixed. In the mean field approximation, the agreement with experimental data is excellent.

hep-ph↗

arXiv2012

Low energy limit of QCD and the emerging of confinement

After a derivation of low-energy limit of QCD, being this a non-local Nambu-Jona-Lasinio model, we are able to show that confinement emerges as a two-loop correction to the gluon propagator. One-gluon exchange is not enough as recently shown in literature about studies on the gluon propagator in the Landau gauge.

hep-ph↗

arXiv2012

Probabilistic Turing Machine and Landauer Limit

We show the equivalence between a probabilistic Turing machine and the time evolution of a one-dimensional Ising model, the Glauber model in one dimension, equilibrium positions representing the results of computations of the Turing machine. This equivalence permits to map a physical system on a computational system providing in this way an evaluation of the entropy at the end of computation. The result agrees with Landauer limit.

math-ph↗

arXiv2012

Condensates in the refined Gribov-Zwanziger scenario

Recent lattice computations showed how the approach dubbed "refined Gribov-Zwanziger scenario" is in very good agreement with data and the gluon propagator fits them very well. This propagator can be described as a finite sum of Yukawa propagators and can be obtained introducing some condensates representing the contribution of the vacuum of Yang-Mills theory. The values of the condensates are arbitrary and are obtained through lattice data. This kind of structure of the propagator is in agreement with the one we obtained using a different analytical approach but with the substantial difference that here all the physical parameters are properly fixed. We show that our approach can properly fix all the values of the condensates in the refined Gribov-Zwanziger scenario giving a complete validation to both techniques. This will provide an interesting view to the gluon propagator and a set of values to be experimentally determined.

hep-ph↗

arXiv2012

Consistency of the adiabatic theorem and perturbation theory

We present an analysis of the adiabatic approximation to understand when it applies, in view of the recent criticisms and studies for the validity of the adiabatic theorem. We point out that this approximation is just the leading order of a perturbation series, that holds in a regime of a perturbation going to infinity, and so the conditions for its validity can be only obtained going to higher orders in the expansion and removing secular terms, that is terms that runs to infinity as the time increases. In this way, it is always possible to get the exact criteria for the approximation to hold.

quant-ph↗

arXiv2012

Parameters of NJL models for a generic representation of the gauge group

We generalize a non-local Nambu-Jona-Lasinio model to a generic representation of the gauge group. The critical temperature is given in a closed form as a function of the parameters of the theory and the cut-off. This result is generally useful in the understanding of QCD-like theories and their thermodynamical behavior.

hep-ph↗

arXiv2012

Quantum mechanics is the square root of a stochastic process

We prove a theorem showing that quantum mechanics is not directly a stochastic process characterizing Brownian motion but rather its square root. This implies that a complex-valued stochastic process is involved. Schrödinger equation is immediately derived without further assumptions using Itō integrals that are properly generalized. Fluctuations in space arise from a Brownian motion and the combined effect of a stochastic process with a symmetric Bernoulli distribution typical of tossing a coin.

math-ph↗

arXiv2011

Chiral symmetry in the low-energy limit of QCD at finite temperature

We derive a non-local Nambu-Jona-Lasinio model from QCD with a form factor exactly obtained in the infrared limit. With this model, having all the parameters properly fixed through those of QCD, we consider the case of finite temperature and compute the solution of the gap equation at small temperature and small momenta and zero chemical potential. Taking the quark masses to be zero, it is proved that the theory undergoes a phase transition with a critical temperature exactly determined. These results prove unequivocally that the picture of the vacuum of QCD as a liquid of instantons is a very good approximation.

hep-ph↗

arXiv2011

Low-energy limit of QCD at finite temperature

We are able to show, in the low-energy limit of quantum chromodynamics, that the theory has a critical point. In this limit, QCD becomes a non-local Nambu-Jona-Lasinio model. The critical temperature is also obtained in agreement with lattice computations.

hep-ph↗

arXiv2011

Magnetic Susceptibility of the Quark Condensate and Polarization from Chiral Models

We compute the magnetic susceptibility of the quark condensate and the polarization of quarks at zero temperature and in a uniform magnetic background. Our theoretical framework consists of two chiral models that allow to treat self-consistently the spontaneous breaking of chiral symmetry: the linear $σ-$model coupled to quarks, dubbed quark-meson model, and the Nambu-Jona-Lasinio model. We also perform analytic estimates of the same quantities within the renormalized quark-meson model, both in the regimes of weak and strong fields. Our numerical results are in agreement with the recent literature; moreover, we confirm previous Lattice findings, related to the saturation of the polarization at large fields.

hep-ph↗

arXiv2011

Mapping theorem and Green functions in Yang-Mills theory

It is shown how, starting from a mapping theorem recently proved between massless quartic scalar field theory and Yang-Mills theory, both two-point functions and spectrum of the Yang-Mills theory can be obtained. These results compare very well with respect to lattice computations.

hep-th↗

arXiv2010

Mass generation and supersymmetry

Using a recent understanding of mass generation for Yang-Mills theory and a quartic massless scalar field theory mapping each other, we show that when such a scalar field theory is coupled to a gauge field and Dirac spinors, all fields become massive at a classical level with all the properties of supersymmetry fulfilled, when the self-interaction of the scalar field is taken infinitely large. Assuming that the mechanism for mass generation must be the same in QCD as in the Standard Model, this implies that Higgs particle must be supersymmetric.

hep-th↗

arXiv2010

Exact solutions of classical scalar field equations

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wave-like behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term renormalized in the dispersion relation through a term depending on the coupling and an integration constant. When spontaneous breaking of symmetry is considered, such wave-like solutions show how a mass term with the wrong sign and the nonlinearity give rise to a proper dispersion relation. These latter solutions do not change the sign maintaining the property of the selected value of the equilibrium state. Then, we use these solutions to obtain a quantum field theory for the case of a quartic massless field. We get the propagator from a first order correction showing that is consistent in the limit of a very large coupling. The spectrum of a massless quartic scalar field theory is then provided. From this we can conclude that, for an infinite countable number of exact classical solutions, there exist an infinite number of equivalent quantum field theories that are trivial in the limit of the coupling going to infinity.

math-ph↗