arXiv subjects

L. L. Salcedo

Publications and source records attributed to L. L. Salcedo.

At least 19 recordsLinked to original sources

arXiv2026

Localization of quantum states within subspaces from the Lebesgue decomposition

Relying on the Lebesgue-type decomposition of positive operators, this work introduces a rigorous notion of localization probability of a quantum state within a given subspace of its Hilbert space. A non-negative operator A is uniquely decomposed as A=B+C, where B is the maximal positive operator supported inside the chosen subspace and C has support disjoint from it. The localized component B can be expressed via the Schur complement and characterized through an A-dependent inner product and suitable trace inequalities. For quantum states, this yields a probability lambda that a state rho be completely contained in a subspace, which is strictly more restrictive than the usual overlap probability Tr(P rho) and enjoys concavity and super-additivity properties. The resulting framework admits natural interpretations in quantum information, including entropic aspects and a potential cryptographic masking scheme based on the uniqueness of the decomposition.

quant-ph↗

arXiv2025

Linearized renormalization

Using an infinitesimal approach, this work addresses the renormalization problem to deal with the ultraviolet divergences arising in quantum field theory. Under the assumption that the action has already been renormalized to yield an ultraviolet-finite effective action that satisfies a certain set of renormalization conditions, we analyze how the action must be adjusted to reproduce a first-order change in these renormalization conditions. The analysis then provides the change that is induced on the correlation functions of the theory. This program is successfully carried out in the case of super-renormalizable theories, namely, a scalar field with cubic interaction in four space-time dimensions and with quartic interaction in three space-time dimensions. Relying on existing results in the theory of perturbative renormalization, we derive explicit renormalized expressions for these theories, each of which involves only a finite number of graphs constructed with full propagators and full $n$-point vertices. The renormalizable case is analyzed as well; the derived expressions are ultraviolet finite as the regulator is removed but cannot be written without a regulator. In this sense, the renormalization is not fully explicit in the renormalizable case. Nevertheless, a perturbative solution of the equations starting from the free theory provides the renormalized Feynman graphs, similar to the BPHZ program. For compatibility with the preservation of the renormalization conditions, a projective renormalization scheme, as opposed to a minimal one, is also introduced. The ideas developed are extended to the study of the renormalization of composite operators and the Schwinger-Dyson equations.

hep-th↗

arXiv2025

Power corrections in the quark-antiquark potential at finite temperature

A recently proposed phenomenological model, which includes nonperturbative effects from dimension two gluon condensates, is applied to analyze the available lattice data for the heavy quark free energy in the deconfined phase of quenched QCD. For large $q\bar{q}$ separations, we recover previous results for the Polyakov loop, exhibiting unequivocal power corrections in the temperature. For the $q\bar{q}$ potential at finite temperature and finite separation, we find that a good overall description of the lattice data can be achieved once the condensate is properly accounted for. In addition, the model predicts a duality between the zero temperature potential as a function of the $q\bar{q}$ separation, on the one hand, and the quark selfenergy as a function of the temperature, on the other, which turns out to be satisfied to a high degree by the lattice data.

hep-ph↗

arXiv2024

Reduction of unitary operators, quantum graphs and quantum channels

Given a unitary operator in a finite dimensional complex Hilbert space, its unitary reduction to a subspace is defined. The application to quantum graphs is discussed. It is shown how the reduction allows to generate the scattering matrices of new quantum graphs from assembling of simpler graphs. The reduction of quantum channels is also defined. The implementation of the quantum gates corresponding to the reduced unitary operator is investigated, although no explicit construction is presented. The situation is different for the reduction of quantum channels for which explicit implementations are given.

quant-ph↗

arXiv2022

Non-minimal non-Abelian quantum vector fields in curved spacetime

The quantum effective action of non-minimal vector fields with Abelian or non-Abelian gauge degrees of freedom in curved spacetime is studied. The Proca or Yang-Mills fields are coupled to a local mass-like term acting in both coordinate and gauge spaces. Pathologies due to gauge invariance in the ultraviolet are avoided through the introduction of a non-Abelian version of the Stueckelberg field. It is found that the breaking of gauge invariance induced by the mass term affects only the tree level part of the effective action. The ultraviolet divergent part of the effective action to one loop is obtained using the method of covariant symbols and dimensional regularization. Formulas are given valid for any spacetime dimension and explicit results are shown for the two-dimensional case. As already happened for a single vector field, the ultraviolet divergences are local but not of polynomial type.

hep-th↗

arXiv2020

Quark-diquark string tension, excited baryonic resonances and thermal fluctuations

We study the baryonic fluctuations from second to eighth order involving electric charge, baryon number and strangeness below the quark-gluon plasma crossover and numerically known from lattice QCD calculations. By considering a particular realization of the Hadron Resonance Gas model, we provide evidence on the dominant role of quark-diquark degrees of freedom to describe excited baryonic resonances. After proving by means of suitable Polyakov loop correlators that the quark-diquark and the quark-antiquark forces coincide, $V_{\bar q q } (r) = V_{\bar q D } (r) + \textrm{const}$, we find that the corresponding susceptibilities can be saturated with excited baryonic states in a quark-diquark model picture.

hep-ph↗

arXiv2019

Quark-diquark models and baryonic fluctuations in QCD

We study the baryonic fluctuations of electric charge, baryon number and strangeness, by considering a realization of the Hadron Resonance Gas model in the light flavor sector of QCD. We elaborate on the idea that the susceptibilities can be saturated with excited baryonic states with a quark-diquark structure with a linearly confining interaction identical up to a constant to the quark-antiquark potential, $V_{qD}^\prime(r) = V_{q{\bar q}}^\prime(r)$. We obtain an overall good agreement with the spectrum obtained with other quark models and with lattice data for the fluctuations.

hep-ph↗

arXiv2019

Baryonic susceptibilities, quark-diquark models, and quark-hadron duality at finite temperature

Fluctuations of conserved charges such as baryon number, electric charge and strangeness may provide a test for completeness of states in lattice QCD for three light flavors. We elaborate on the idea that the corresponding susceptibilities can be saturated with excited baryonic states with an underlying quark-diquark structure with a linearly confining interaction. Using Polyakov-loop correlators we show that in the static limit, the quark-diquark potential coincides with the quark-antiquark potential in marked agreement with recent lattice studies. We thus study in a quark-diquark model the baryonic fluctuations of electric charge, baryon number and strangeness: $χ_{BQ}$, $χ_{BB}$ and $χ_{BS}$; by considering a realization of the hadron resonance gas model in the light flavor sector of QCD. These results have been obtained by using the baryon spectrum computed within a relativistic quark-diquark model, leading to an overall good agreement with the spectrum obtained with other quark models and with lattice data for the fluctuations.

hep-ph↗

arXiv2019

Renormalization of vector fields with mass-like coupling in curved spacetime

Using the method of covariant symbols we compute the divergent part of the effective action of the Proca field with non-minimal mass term. Specifically a quantum Abelian vector field with a non-derivative coupling to an external tensor field in curved spacetime in four dimensions is considered. Relatively explicit expressions are obtained which are manifestly local but non polynomial in the external fields. Our result is shown to reproduce existing ones in all particular cases considered. Internal consistency with Weyl invariance is also verified.

hep-th↗

arXiv2019

Fluctuations and correlations in thermal QCD

We study the equation of state, fluctuations and static correlators of electric charge, baryon number and strangeness, by considering a realization of the Hadron Resonance Gas model in the light flavor sector of QCD. We emphasize the importance of these observables to study, within this approach, the possible existence of exotic and missing states in the hadron spectrum. Some preliminary results for the baryon spectrum have been obtained within a relativistic quark-diquark model, leading to an overall good agreement with the spectrum obtained with other quark models. Finally, it is conjectured, within the Hadron Resonance Gas approach, the existence of a singularity in the correlators at zero temperature, which turns out to be analogous to the divergence of the partition function at the Hagedorn temperature.

hep-ph↗

arXiv2018

Positive representations of complex distributions on groups

A normalizable complex distribution $P(x)$ on a manifold $\mathcal{M}$ can be regarded as a complex weight, thereby allowing to define expectation values of observables $A(x)$ defined on $\mathcal{M}$. Straightforward importance sampling, $x\sim P$, is not available for non positive $P$, leading to the well-known sign (or phase) problem. A positive representation $ρ(z)$ of $P(x)$ is any normalizable positive distribution on the complexified manifold $\mathcal{M}^c$, such that, $\langle A(x)\rangle_P = \langle A(z) \rangle_ρ$ for a dense set of observables, where $A(z)$ stands for the analytically continued function on $\mathcal{M}^c$. Such representations allow to carry out Monte Carlo calculations to obtain estimates of $\langle A(x) \rangle_P$, through the sampling $z \sim ρ$. In the present work we tackle the problem of constructing positive representations for complex weights defined on manifolds of compact Lie groups, both Abelian and non Abelian, as required in lattice gauge field theories. Since the variance of the estimates increase for broad representations, special attention is put on the question of localization of the support of the representations.

hep-lat↗

arXiv2018

Thermal correlators in the hadron resonance gas: a dual Hagedorn distance

Fluctuations and correlations of conserved quantities in the confined phase of QCD are a viable way to characterize the existence of exotic and missing states with given quantum numbers in the hadronic spectrum. We study a realization of the Hadron Resonance Gas model in the light quark (uds) flavor sector of QCD to study the fluctuations and static correlators of electric charge, baryon number and strangeness. It is also conjectured an interesting duality between the correlators at zero temperature, and the fluctuations of integrated quantities at low temperatures, leading to the appearance of a dual Hagedorn distance for the former.

hep-ph↗

arXiv2017

Representation of complex probabilities and complex Gibbs sampling

Complex weights appear in Physics which are beyond a straightforward importance sampling treatment, as required in Monte Carlo calculations. This is the well-known sign problem. The complex Langevin approach amounts to effectively construct a posi\-tive distribution on the complexified manifold reproducing the expectation values of the observables through their analytical extension. Here we discuss the direct construction of such positive distributions paying attention to their localization on the complexified manifold. Explicit localized repre\-sentations are obtained for complex probabilities defined on Abelian and non Abelian groups. The viability and performance of a complex version of the heat bath method, based on such representations, is analyzed.

hep-lat↗

arXiv2017

Workshop on Excited Hyperons in QCD Thermodynamics at Freeze-Out (YSTAR2016) Mini-Proceedings

This Workshop brought top experts, researchers, postdocs, and students from high-energy heavy ion interactions, lattice QCD and hadronic physics communities together. YSTAR2016 discussed the impact of "missing" hyperon resonances on QCD thermodynamics, on freeze-out in heavy ion collisions, on the evolution of early universe, and on the spectroscopy of strange particles. Recent studies that compared lattice QCD predictions of thermodynamic properties of quark-gluon plasma at freeze-out with calculations based on statistical hadron resonance gas models as well as experimentally measured ratios between yields of different hadron species in heavy ion collisions provide indirect evidence for the presence of "missing" resonances in all of these contexts. The aim of the YSTAR2016 Workshop was to sharpen these comparisons and advance our understanding of the formation of strange hadrons from quarks and gluons microseconds after the Big Bang and in todays experiments at LHC and RHIC as well as at future facilities like FAIR, J-PARC and KL at JLab. It was concluded that the new initiative to create a secondary beam of neutral kaons at JLab will make a bridge between the hardron spectroscopy, heavy-ion experiments and lattice QCD studies addressing some major issues related to thermodynamics of the early universe and cosmology in general.

hep-ph↗

arXiv2017

Canonical bracket in quantum-classical hybrid systems

We study compound systems with a classical sector and a quantum sector. Among other consistency conditions we require a canonical structure, that is, a Lie bracket for the dynamical evolution of hybrid observables in the Heisenberg picture, interpolating between the Poisson bracket and the commutator. Weak and strong postulates are proposed. We explicitly construct one such hybrid bracket when the Hilbert space of the quantum sector is finite dimensional and show that it is unique if the strong postulates are enforced. The adjoint bracket for the Schrodinger picture version of the dynamics is also obtained. Unfortunately, preservation of the positivity of the density matrix under the evolution is not guaranteed. The case of a particle with classical position and momentum and quantum spin-$\frac{1}{2}$ is discussed and the spin-orbit dynamics is worked out.

quant-ph↗

arXiv2016

Does the complex Langevin method give unbiased results?

We investigate whether the stationary solution of the Fokker-Planck equation of the complex Langevin algorithm reproduces the correct expectation values. When the complex Langevin algorithm for an action $S(x)$ is convergent, it produces an equivalent complex probability distribution $P(x)$ which ideally would coincide with $e^{-S(x)}$. We show that the projected Fokker-Planck equation fulfilled by $P(x)$ may contain an anomalous term whose form is made explicit. Such term spoils the relation $P(x)=e^{-S(x)}$, introducing a bias in the expectation values. Through the analysis of several periodic and non-periodic one-dimensional problems, using either exact or numerical solutions of the Fokker-Planck equation on the complex plane, it is shown that the anomaly is present quite generally. In fact, an anomaly is expected whenever the Langevin walker needs only a finite time to go to infinity and come back, and this is the case for typical actions. We conjecture that the anomaly is the rule rather than the exception in the one-dimensional case, however, this could change as the number of variables involved increases.

hep-lat↗

arXiv2016

Heavy quark-antiquark free energy and thermodynamics of string-hadron avoided crossings

The correlation function between two Polyakov loops encodes the free-energy shift due to a pair of separated colour conjugated sources in the hot QCD medium. This is analyzed in terms of a novel Källén-Lehmann spectral representation for the separating distance, implying an increasing and concave free-energy at all temperatures. We express the heavy $\bar{Q} Q$ free-energy shift below the phase transition in QCD in terms of colour neutral purely hadronic states with no explicit reference to quarks and gluons. Good agreement with lattice data is achieved when considering the avoided crossing mechanism underlying string breaking and with standard quenched values of the string tension known from charmonium and bottomonium phenomenology. We also address the role of the corresponding entropy shift and its renormalization group properties.

hep-ph↗

arXiv2016

Gibbs sampling of complex valued distributions

A new technique is explored for the Monte Carlo sampling of complex-valued distributions. The method is based on a heat bath approach where the conditional probability is replaced by a positive representation of it on the complex plane. Efficient ways to construct such representations are also introduced. The performance of the algorithm is tested on small and large lattices with a $λϕ^4$ theory with quadratic nearest-neighbor complex coupling. The method works for moderate complex couplings, reproducing reweighting and complex Langevin results and fulfilling various Schwinger-Dyson relations.

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