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Marco Frasca

Publications and source records attributed to Marco Frasca.

At least 37 records · Page 2Linked to original sources

Effective potential in non-perturbative gauge theories

We consider a formalism to describe the false-vacuum decay of a scalar field in gauge theories in non-perturbative regimes. We find that the larger the gauge coupling with respect to the self-coupling of the scalar, the shallower the local minimum of the unstable vacuum, to the point where it disappears. This offers the possibility to obtain a consistent picture of early universe cosmology: at high temperatures, a false-vacuum decay is strongly favoured and the universe naturally evolves towards a stable state.

hep-th↗

Fate of False Vacuum in Non-perturbative Regimes

We use some exact results in the scalar field theory to revise the analysis by Coleman and Callan about the false vacuum decay and propose a simple non-perturbative formalism. We introduce exact Green's function which incorporates non-perturbative corrections in the strong coupling regimes of the theory. The solution of the scalar field theory involves Jacobi elliptical function and has been used to calculate the effective potential for any arbitrary coupling values. We demonstrate the use of this formalism in a simple $λϕ^4$ theory and show that the effective potential exhibits a false minimum at the origin. We then calculate the false vacuum decay rate and suggest simple analytic formulas which may be useful for the analysis for the first order phase transition beyond the perturbative regime. In our methodology, we show that the standard results obtained in perturbation theory are reproduced by taking the coupling values very small.

hep-th↗

Non-perturbative Lee-Wick gauge theory: Towards Confinement and RGE with strong couplings

We consider a non-Abelian Lee--Wick gauge theory and discuss Becchi-Rouet-Stora-Tyutin (BRST) invariance. It contains fourth-order derivative as extensions of the kinetic term, leading to massive ghosts in the theory upon quantization. We particularly provide essential clues towards confinement conditions in strongly-coupled regimes, using the Kugo-Ojima approach, and obtain the $β-$functions in the non-perturbative regimes. This is achieved using a set of exact solutions of the corresponding local theory in terms of Jacobi elliptical functions. We obtain a similar $β-$function just as for the ordinary Yang-Mills theory but the main differences are that now, the cut-off arises naturally from the Lee-Wick heavy mass scales (M). We show that the fate of the ghosts is fixed in these regimes: they are no more the propagating degrees of freedom in the infrared (IR)-limit. As it also happens for the ordinary case, confinement is due to the non-Abelian nature of the theory. In the limit $M\rightarrow\infty $, one recovers the standard results for the local non-Abelian Yang-Mills theory.

hep-ph↗

Confinement in QCD and generic Yang-Mills theories with matter representations

We derive the low-energy limit of quantum chromodynamics (QCD) and provide evidence that in the 't Hooft limit, i.e. for a very large number of colors and increasing 't Hooft coupling, quark confinement is recovered. The low energy limit of the theory turns out to be a non-local Nambu-Jona-Lasinio (NJL) model. The effect of non-locality, arising from a gluon propagator that fits quite well to the profile of an instanton liquid, is to produce a phase transition from a chiral condensate to an instanton liquid, as the coupling increases with lower momentum. This phase transition suffices to move the poles of the quark propagator to the complex plane. As a consequence, free quarks are no longer physical states in the spectrum of the theory.

hep-ph↗

Confining complex ghost degrees of freedom

We show a theorem proving that a non-local bosonic field upon a covariant interaction with a confining gauge field undergoes the confinement of its degrees of freedom present in the free theory changing completely the physical mass spectrum following Kugo-Ojima criterion. This is applicable to an infinite number of excitations of the bosonic field including ghosts whereas we pay special attention to the modes with the complex conjugate masses, states appearing in the string field theory motivated infinite-derivative models. The same recipe will obviously work for the Lee-Wick models.

hep-th↗

A Critical Analysis of Classifier Selection in Learned Bloom Filters

Learned Bloom Filters, i.e., models induced from data via machine learning techniques and solving the approximate set membership problem, have recently been introduced with the aim of enhancing the performance of standard Bloom Filters, with special focus on space occupancy. Unlike in the classical case, the "complexity" of the data used to build the filter might heavily impact on its performance. Therefore, here we propose the first in-depth analysis, to the best of our knowledge, for the performance assessment of a given Learned Bloom Filter, in conjunction with a given classifier, on a dataset of a given classification complexity. Indeed, we propose a novel methodology, supported by software, for designing, analyzing and implementing Learned Bloom Filters in function of specific constraints on their multi-criteria nature (that is, constraints involving space efficiency, false positive rate, and reject time). Our experiments show that the proposed methodology and the supporting software are valid and useful: we find out that only two classifiers have desirable properties in relation to problems with different data complexity, and, interestingly, none of them has been considered so far in the literature. We also experimentally show that the Sandwiched variant of Learned Bloom filters is the most robust to data complexity and classifier performance variability, as well as those usually having smaller reject times. The software can be readily used to test new Learned Bloom Filter proposals, which can be compared with the best ones identified here.

cs.LG↗

Quintessence Dark Energy from strongly-coupled Higgs mass gap: Local and Non-local higher-derivative non-perturbative scenarios

We entertain the possibility that dark energy arises from the Higgs field of quintessence type in the non-perturbative regimes. For this purpose we utilize a set of exact solutions of Higgs field theory recently devised, in terms of Jacobi elliptical function for a massless quartic scalar field, that satisfy a massive dispersion relation. In certain regions of the parameter space, determined by the quartic coupling value, we show that such solutions have the property to give the correct behavior for the equation of state of the dark energy depending on the initial $θ$ value of periodicity of the Jacobi elliptical function solution. It is seen that on a time scale determined by the Hubble constant and the strength of the self-interaction of the scalar field, when conformal invariance is restored, the equation of state for the dark energy becomes manifest. Further we investigate scenarios within standard field theory framework and also extending to higher-derivative theories, namely infinite-derivative theory, motivated from p-adic string field theory, and Lee-Wick theories and in all cases, we find suitable choices of the parameter space leads to dark energy behavior of the Higgs field, which we compare.

hep-th↗

Quark confinement in QCD in the 't Hooft limit

We treat quantum chromodynamics (QCD) using a set of Dyson-Schwinger equations derived, in differential form, with the Bender-Milton-Savage technique. In this way, we are able to derive the low energy limit that assumes the form of a non-local Nambu-Jona-Lasinio model. The corresponding gap equation is then studied to show that such a model has no free quarks in the low-energy limit.

hep-ph↗

On a novel evalutation of the hadronic contribution to the muon's $g-2$ from QCD

We evaluate the hadronic contribution to the $g-2$ of the muon by deriving the low-energy limit of quantum chromodynamics (QCD) and computing in this way the hadronic vacuum polarization. The low-energy limit is a non-local Nambu--Jona-Lasinio (NJL) model that has all the parameters fixed from QCD, and the only experimental input used is the confinement scale that is known from measurements of hadronic physics. Our estimations provide a novel analytical alternative to the current lattice computations and we find that our result is close to the similar computation performed from experimental data. We also comment on how this analytical approach technique, in general, may provide prospective estimates for hadronic computations from dark sectors and its implication in BSM model-building in future.

hep-ph↗

On the Choice of General Purpose Classifiers in Learned Bloom Filters: An Initial Analysis Within Basic Filters

Bloom Filters are a fundamental and pervasive data structure. Within the growing area of Learned Data Structures, several Learned versions of Bloom Filters have been considered, yielding advantages over classic Filters. Each of them uses a classifier, which is the Learned part of the data structure. Although it has a central role in those new filters, and its space footprint as well as classification time may affect the performance of the Learned Filter, no systematic study of which specific classifier to use in which circumstances is available. We report progress in this area here, providing also initial guidelines on which classifier to choose among five classic classification paradigms.

cs.LG↗

Casimir effect in Yang-Mills theories

We study both massless scalar and Yang-Mills field theories in the deep infrared in presence of a simple boundary. We can show, with the help of the recent scenario emerging from studies on the propagators, that the presence of a mass gap makes the Casimir contribution exponentially small as should be expected. We obtain our result from the solution of the Dyson-Schwinger set of equations obtained in form of partial differential equations. Our results agree fairly well with recent lattice computations.

hep-ph↗

Nambu-Jona-Lasinio model correlation functions from QCD

We treat quantum chromodynamics (QCD) using a set of Dyson-Schwinger equations derived, in differential form, with the Bender-Milton-Savage technique. In this way, we are able to derive the low energy limit that assumes the form of a non-local Nambu-Jona-Lasinio model with all the parameters properly fixed by the QCD Lagrangian and the determination of the mass gap of the gluon sector.

hep-ph↗

Compact representations of convolutional neural networks via weight pruning and quantization

The state-of-the-art performance for several real-world problems is currently reached by convolutional neural networks (CNN). Such learning models exploit recent results in the field of deep learning, typically leading to highly performing, yet very large neural networks with (at least) millions of parameters. As a result, the deployment of such models is not possible when only small amounts of RAM are available, or in general within resource-limited platforms, and strategies to compress CNNs became thus of paramount importance. In this paper we propose a novel lossless storage format for CNNs based on source coding and leveraging both weight pruning and quantization. We theoretically derive the space upper bounds for the proposed structures, showing their relationship with both sparsity and quantization levels of the weight matrices. Both compression rates and excution times have been tested against reference methods for matrix compression, and an empirical evaluation of state-of-the-art quantization schemes based on weight sharing is also discussed, to assess their impact on the performance when applied to both convolutional and fully connected layers. On four benchmarks for classification and regression problems and comparing to the baseline pre-trained uncompressed network, we achieved a reduction of space occupancy up to 0.6% on fully connected layers and 5.44% on the whole network, while performing at least as competitive as the baseline.

cs.LG↗

Mass Gap in Infinite Derivative Non-local Higgs: Dyson-Schwinger Approach

We investigate the non-perturbative degrees of freedom in the class of non-local Higgs theories that have been proposed as an ultraviolet completion 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher derivatives inspired by string field theory. At the perturbative level, the degrees of freedom of non-local Higgs are the same of the local theory. We prove that, at the non-perturbative level, the physical spectrum of the Higgs mass is actually corrected from the "infinite number of derivatives" present in the action. The technique we use permits to derive the set of Dyson-Schwinger equations in differential form. This proves essentially useful when exact solutions to the local equations are known. We show that all the formalism of the local theory involving the Dyson-Schwinger approach extends quite naturally to the non-local case. Using these methods, the spectrum of non-local theories become accessible and predictable in the non-perturbative regimes. We calculate the N-point correlation functions and predict the mass-gap in the spectrum arising purely from the self-interaction and the non-local scale M. The mass gap generated gets damped in the UV and it reaches conformal limit. We discuss some implications of our result in particle physics and cosmology.

hep-th↗

Strongly Coupled String-inspired Infinite Derivative Non-local Yang-Mills: Diluted Mass Gap

We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the 'infinite number of derivatives' present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV reaching asymptotically the conformal limit. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios. We end with some comments on the infinite-derivative non-local gravity which is quantum gravity approach to ghost-free, re-normalizable theories of gravity valid upto infinte ebergy scales in the UV.

hep-th↗

Confinement and Renormalization Group Equations in String-inspired Non-local Gauge Theories

As an extension of the weak perturbation theory obtained in recent analysis on infinite-derivative non-local non-Abelian gauge theories motivated from p-adic string field theory, and postulated as direction of UV-completion in 4-D Quantum Field Theory (QFT), here we investigate the confinement conditions and $β-$function in the strong coupling regime. We extend the confinement criterion, previously obtained by Kugo and Ojima for the local theory based on the Becchi-Rouet-Stora-Tyutin (BRST) invariance, to the non-local theory, by using a set of exact solutions of the corresponding local theory. We show that the infinite-derivatives which are active in the UV provides finite contributions also in the infrared (IR) limit and provide a proof of confinement, granted by the absence of the Landau pole. The main difference with the local case is that the IR fixed point is moved to infinity. We also show that in the limit of the energy scale of non-locality $M \rightarrow \infty$ we reproduce the local theory results and see how asymptotic freedom is properly recovered.

hep-th↗

Quantized Noncommutative Riemann Manifolds and Stochastic Processes: The theoretical foundations of the square root of Brownian motion

We lay the theoretical and mathematical foundations of the square root of Browniam motion and we prove the existence of such a process. In doing so, we consider Brownian motion on quantized noncommutative Riemannian manifolds and show how a set of stochastic processes on sets of complex numbers can be devised. This class of stochastic processes are shown to yield at the outset a Chapman-Kolmogorov equation with a complex diffusion coefficient that can be straightforwardly reduced to the Schrödinger equation. The existence of these processes has been recently shown numerically. In this work we provide an analogous support for the existence of the Chapman-Kolmogorov-Schrödinger equation for them, performing a Monte Carlo study. It is numerically seen as a Wick rotation can turn the heat kernel into the Schrödinger one, mapping such kernels through the corresponding stochastic processes. In this way, we introduce a new kind of improper complex stochastic process. This permits a reformulation of quantum mechanics using purely geometrical concepts that are strongly linked to stochastic processes. Applications to economics are also entailed.

quant-ph↗

Warping effects in strongly perturbed metrics

A technique devised some years ago permits to study a theory in a regime of strong perturbations. This translates into a gradient expansion that, at the leading order, can recover the BKL solution in general relativity. We solve exactly the leading order Einstein equations in a spherical symmetric case, assuming a Schwarzschild metric under the effect of a time-dependent perturbation, and we show that the 4-velocity in such a case is multiplied by an exponential warp factor when the perturbation is properly applied. This factor is always greater than one. We will give a closed form solution of this factor for a simple case. Some numerical examples are also given.

gr-qc↗