arXiv subjects

Alessio Maiezza

Publications and source records attributed to Alessio Maiezza.

At least 19 recordsLinked to original sources

arXiv2026

Universal Emergence of Bosonic and Fermionic Algebras in a Deterministic Proper-Time Framework

This work develops the deterministic, discrete proper-time framework introduced in our previous work, Eur.\ Phys.\ J.\ C \textbf{86} (2026) 829, in which quantum field theory emerges as an effective infrared description characterized by a running Planck constant. There, the effective quantization scale was inferred from the microscopic multiplicity unresolved by coarse-graining. Here, we provide its dynamical and operatorial realization and extend the construction to fermionic degrees of freedom. First, consistency under changes of macroscopic resolution leads to the structure of the Renormalization Group Equation, while the running Planck constant governs the crossover toward the deterministic regime. Second, we represent the reversible microscopic dynamics through finite-difference translations in field-configuration space. After coarse-graining, the resulting operator-valued canonical commutation relations reproduce the same quantization scale previously obtained from statistical microstate counting, thereby linking microscopic evolution to the emergent canonical algebra. Third, representing the same update within a Grassmann algebra yields the corresponding canonical anticommutation relations. The bosonic and fermionic sectors thus inherit a common effective Planck constant without introducing an independent fermionic update or quantization scale. Finally, we discuss possible implications for high-energy loop amplitudes and effective Hawking radiation.

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arXiv2026

Minimal Proper Time and Deterministic Microstates: Emergent Quantum Fields and Relativistic Spacetime

We develop a top-down counterpart of the minimal proper-time formulation of quantum field theory previously introduced as an effective bottom-up framework. Starting from a deterministic pre-geometric substrate of causally ordered events, we show how coarse-graining over microscopic histories leads, at low energies, to an effective Nambu-like quantum dynamics. The elementary deterministic update is identified with the minimal proper-time step, while the growth of coarse-grained equivalence classes controls both the ultraviolet dissipative correction and the scale dependence of the effective quantization strength, encoded in a running Planck constant. In this way, the proper-time cutoff kernel of the bottom-up formulation acquires a microscopic interpretation as the inverse growth of unresolved deterministic histories. In the infrared limit, the dissipative term vanishes and standard unitary quantum field theory is recovered. The same coarse-grained structure also provides a natural setting for an emergent relativistic spacetime geometry, compatible in the macroscopic limit with Einstein gravity. The resulting picture suggests a common deterministic origin for minimal-scale structure, quantum behavior, and relativistic spacetime.

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arXiv2026

Minimal Proper-time in Quantum Field Theory

We propose a generalization of quantum field theory within Schrodinger's functional representation, inspired by Nambu's proper-time formulation of quantum mechanics. The key motivation for this generalization is to incorporate a fundamental, Lorentz-invariant minimum scale, which in this formulation is played by a minimal proper time $\tau_{\min}$. The introduction of $\tau_{\min}$ leads to several significant effects at very high energies: it modifies the Heisenberg uncertainty principle, induces a controlled violation of unitarity, and suppresses high-energy modes. This minimal scale renders the theory asymptotically safe through a mechanism akin to dimensional reduction, while reproducing all the standard results at low energies, where quantum field theory emerges. Remarkably, the same framework can accommodate a deterministic regime at energies approaching the Planck scale. These features suggest that a minimal proper-time formulation renders the quantum field theory an effective but finite theory, superseded at trans-Planckian energies.

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arXiv2025

Quantum Field Theory on Multifractal Spacetime: Varying Dimension and Ultraviolet Completeness

Inspired by various quantum gravity approaches, we explore quantum field theory where spacetime exhibits scaling properties and dimensional reduction with changing energy scales, effectively behaving as a multifractal manifold. Working within canonical quantization, we demonstrate how to properly quantize fields in such a multifractal spacetime. Our analysis reveals that a non-differentiable nature of spacetime is not merely compatible with quantum field theory but significantly enhances its mathematical foundation. Most notably, this approach ensures perturbative UV finiteness and improved behavior of the series expansion and enables rigorous construction of the S-matrix in the interaction picture by breaking vacuum translational invariance. The multifractal structure tames dominant, large-order divergence sources in the perturbative series and resolves the Landau pole problem through asymptotic safety, substantially improving the theory's behavior in the deep ultraviolet regime. Our formulation preserves all established predictions of standard quantum field theory at low energies while offering novel physical behaviors at high energy scales.

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arXiv2024

Uncovering Hidden Patterns: Approximate Resurgent Resummation from Truncated Series

We analyze truncated series generated as divergent formal solutions of non-linear ordinary differential equations. Motivating the study is a specific non-linear, first-order differential equation, which is the basis of the resurgent formulation of renormalized perturbation theory in quantum field theory. We use the Borel-Pad\'e approximant and classical analysis to determine the analytic structure of the solution using the first few terms of its asymptotic series. Afterward, we build an approximant, consistent with the resurgent properties of the equation. The procedure gives an approximate expression for the Borel-Ecalle resummation of the solution useful for practical applications. Connections with other physical applications are also discussed.

math-ph↗

arXiv2024

Renormalization group flows and emergent symmetries

We discuss the following proposition: Renormalization Group flow of quantum theory with a biased symmetry exhibits a fixed hypersurface at which the symmetry is exact. Such emergent symmetries may have important phenomenological implications, including supersymmetric models, gauge theories, and massive gravity. Most interesting example is an emergent supersymmetry in non-abelian gauge theories with appropriate field content, in the IR limit i.e. strong coupling regime.

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arXiv2024

Gluon Mass Generation from Renormalons and Resurgence

We establish a link between the concepts of infrared renormalons, infrared fixed point, and dynamical nonperturbative mass generation of gluons in pure Yang-Mills theories. By utilizing recent results in the resurgent analysis of renormalons through non-linear ordinary differential equations, we develop a new description for the gluon propagator, thereby realizing the Schwinger mechanism. Specifically, this approach leads to a nonperturbative, dynamic mass generation for Yang-Mills gauge bosons in the deep infrared region, a phenomenon closely associated with color confinement. Furthermore, we present arguments about the limit of applicability of the Borel-Ecalle resummation of the renormalons by comparing it with the Kallen-Lehman representation of the gluon propagator.

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arXiv2023

Resurgence and self-completion in renormalized gauge theories

Under certain assumptions and independent of the instantons, we show that the logarithm expansion of dimensional regularization in quantum field theory needs a nonperturbative completion to have a renormalization-group flow valid at all energies. Then, we show that such nonperturbative completion has the analytic properties of the renormalons, which we find with only a marginal reference to diagrammatic calculations. We demonstrate that renormalon corrections necessarily lead to analyzable functions, namely, resurgent transseries. A detailed analysis of the resurgent properties of the renormalons is provided. The self-consistency of the theory requires these nonperturbative contributions to render the running coupling well-defined at any energy, thus with no Landau pole. We illustrate the point within the case of QED. This way, we explicitly realize the correspondence between the nonperturbative Landau pole scale and the renormalons. What is seen as a Landau pole in perturbation theory is cured by the nonperturbative, resurgent contributions.

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arXiv2023

Neutrinoless double beta decay: neutrino mass versus new physics

Neutrinoless double beta decay is the textbook example of lepton number violation, often claimed to be a probe of neutrino Majorana mass. However, it could be triggered by new physics; after all, neutrino Majorana mass requires physics beyond the Standard Model. If at least one electron were right-handed, it would automatically signify new physics rather than neutrino mass. In case both electrons were left-handed, the situation would become rather complicated, and additional effort would be needed to untangle the source for this process. We offer a comprehensive study of this issue from both the effective operator approach and the possible UV completions, including the Pati-Salam quark-lepton unification. While neutrino exchange is natural and physically preferred, our findings show that new physics can still be responsible for the neutrinoless double beta decay. In particular, the Pati-Salam theory can do the job, consistently with all the phenomenological and unification constraints, as long as the unification scale lies above 10^12 GeV, albeit at the price of fine-tuning of some scalar masses.

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arXiv2022

A consistent quantum field theory from dimensional reduction

We incorporate the concept of dimensional reduction at high energies within the perturbative formulation of quantum field theory. In this new framework, space and momentum integrations are modified by a weighting function incorporating an effective mass energy associated with the dimensional reduction scale. We quantize the theory within canonical formalism. We then show that it can be made finite in perturbation theory, free of renormalon ambiguities, and with better analytic behavior for infinitesimal coupling constant compared to standard quantum field theory. The new approach reproduces the known results at low energies. One key feature of this class of models is that the coupling constant always reaches a fixed point in the ultraviolet region, making the models ultra-violet complete.

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arXiv2022

The QCD Adler function and the muon $g-2$ anomaly from renormalons

We describe the Adler function in Quantum Chromodynamics using a transseries representation within a resurgent framework. The approach is based on a Borel-Ecalle resummation of the infrared renormalons combined with an effective running for the strong coupling. The new approach is flexible enough to give values in agreement with the current Adler function determinations. We then apply our finding to the muon's anomalous magnetic moment studying the possibility of saturating, solely in terms of the vacuum polarization function, the current discrepancy between the best Standard Model value for the muon's anomalous magnetic moment and the experimental value obtained by the most recent muon g-2 collaboration. The latter shows that the Adler function's new representation can also be consistent with recent lattice determinations.

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arXiv2022

Parity from gauge symmetry

We argue that Left-Right parity symmetry $\mathcal{P}$ can arise as a discrete remnant of a unified gauge symmetry. The high-energy unification necessarily includes the gauging of the Lorentz symmetry, bringing into the game gravitational interactions, and leading to a gravi-GUT scheme. Parity emerges unbroken below the Planck scale, and can be broken spontaneously at lower energies making contact with the Standard Model. This framework motivates the spontaneous origin of parity violation as in Left-Right symmetric theories with $\mathcal{P}$. The possible unifying gauge groups are identified as SO(1,7) for gravitational and weak interactions, or SO(7,7) for a complete unification.

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arXiv2021

On Haag's theorem and renormalization ambiguities

We revisit the implications of Haag's theorem in the light of the renormalization group. There is still some lack of discussion in the literature about the possible impact of the theorem on the standard (as opposite of axiomatic) quantum field theory, and we try to shed light in this direction. Our discussion then deals with the interplay between Haag's theorem and renormalization. While we clarify how perturbative renormalization (for the sub-class of interactions that are renormalizable) marginalizes the its impact when the coupling is formally small, we argue that a non-perturbative and non-ambiguous renormalization cannot be built if there is any reference to the interaction picture with free fields. In other words, Haag's theorem should be regarded as a no-go theorem for the existence of a non-ambiguous analytic continuation from perturbative to non-perturbative QFT.

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arXiv2021

Resurgence of the QCD Adler function

We study the QCD Adler function in the energy region $\approx 0.7-2.5$ GeV, in which the non-perturbative effects become dominant. Our analysis is a renormalon-based evaluation using transseries within the resurgence of the Renormalization-Group-Equation and does not require the Operator-Product-Expansion.

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arXiv2020

Quark mixing with soft breaking of the parity in the minimal Left-Right model

We study the possibility of soft breaking effects of the generalized parity within the minimal Left-Right model. One aim of the paper is to elaborate on the potentiality, the limit, and the predictivity of a restored parity at high scale. While revisiting the issue of strong CP in the Left-Right theories, we motivate the possibility of explicit-parity-breaking, that we then parameterize in the right-handed quark mixing matrix. The strong CP parameter $\barθ$ is also parameterized in terms of the breaking. We discuss some possible phenomenological consequences in this scenario. In particular, the constraint provided by $\barθ$ enables us to quantify the maximal deviation of the right-handed quark mixings from the standard case with exact parity in term of a single parameter. This deviation has a direct impact on flavor physics.

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arXiv2020

Non-Wilsonian ultraviolet completion via transseries

We study some of the implications for the perturbative renormalization program when augmented with the Borel-Ecalle resummation. We show the emergence of a new kind of non-perturbative fixed point for the scalar $ϕ^4$ model, representing an ultraviolet self-completion by transseries. We argue that this completion is purely non-Wilsonian and it depends on one arbitrary constant stemming from the transseries solution of the renormalization group equation. On the other hand, if no fixed points are demanded through the adjustment of this arbitrary constant, we end up with an effective theory in which the scalar mass is quadratically-sensitive to the cut-off, even working in dimensional regularization. Complete decoupling of the scalar mass to this energy scale can be used to determine a physical prescription for the Borel-Laplace resummation of the renormalons in non-asymptotically free models. We also comment on possible orthogonal scenarios available in the literature that might play a role when no fixed points exist.

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arXiv2020

Kaon CP violation and neutron EDM in the minimal left-right symmetric model

Within the minimal Left-Right (LR) symmetric model we revisit the predictions for the kaon CP violating observables $\varepsilon$ and $\varepsilon'$ in correlation with the neutron electric dipole moment. We perform a complete study of the cross constraints on the model parameters, phases and the $M_{W_R}$ scale, considering the two cases of extended parity or charge conjugation as LR discrete symmetries, together with the possible presence of a Peccei-Quinn symmetry. We discuss in particular two scenarios: whether the Standard Model saturates the experimental value of $\varepsilon'/\varepsilon$ or whether new physics is needed, still an open issue after the recent lattice results on the QCD penguin matrix elements. Within the first scenario, we find no constraints on the LR scale in the charge-conjugation case while in the parity case we show that $M_{W_R}$ can be as low as 13 TeV. On the other side, the request that new physics contributes dominantly to $\varepsilon'$ implies strong correlations among the model parameters, with an upper bound of $M_{W_R}< 8-100$ TeV depending on $\tanβ$ in the case of charge conjugation and a range of $M_{W_R}\simeq 7-45$ TeV in the parity setup. Both scenarios may be probed directly at future colliders and only indirectly at the LHC.

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arXiv2020

Resurgence of the Renormalization Group Equation

We show how the renormalons emerge from the renormalization group equation with a priori no reference to any Feynman diagrams. The proof is rather given by recasting the renormalization group equation as a resurgent equation studied in the mathematical literature, which describes a function with an infinite number of singularities in the positive axis of the Borel plane. Consistency requires a one-to-one correspondence between the existence of such kind of equation and the actual (generalized) Borel resummation of the renormalons through a one-parameter transseries. Our finding suggests how non-perturbative contributions can affect the running couplings. We also discuss these concepts within the context of gauge theories, making use of the large number of flavor expansion.

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