Hadrons as QCD Bound States

Bound state perturbation theory is well established for QED atoms. Today the hyperfine splitting of Positronium is known to 𝒪 (α7 log α). Whereas standard expansions of scattering amplitudes start from free states, bound states are expanded around eigenstates of the Hamiltonian including a binding potential. The eigenstate wave functions have all powers of α, requiring a choice in the ordering of the perturbative expansion. Temporal (A0 = 0) gauge permits an expansion starting from valence Fock states, bound by their instantaneous gauge field. This formulation is applicable in any frame and seems promising even for hadrons in QCD. The 𝒪(αs0) confining potential is determined (up to a universal scale) by a homogeneous solution of Gauss’ law.

Ontology of a Wavefunction from the Perspective of an Invariant Proper Time

All the arguments of a wavefunction are defined at the same instant, implying the notion of simultaneity. In a somewhat related matter, certain phenomena in quantum mechanics seem to have non-local causal relations. Both concepts contradict the special relativity. We propose defining the wavefunction with respect to the invariant proper time of special relativity instead of the standard time. Moreover, we shall adopt the original idea of Schrodinger, suggesting that the wavefunction represents an ontological cloud-like object that we shall call “individual fabric” that has a finite density amplitude vanishing at infinity. Consequently, the action of measurement can be assimilated to the introduction of a confining potential that triggers an inherent nonlocal mechanism within the individual fabric. This mechanism is formalised by multiplying the wavefunction with a localising Gaussian, as in the GRW theory, but in a deterministic manner.

Work fluctuations in the active Ornstein–Uhlenbeck particle model

We study the large deviations of the power injected by the active force for an active Ornstein–Uhlenbeck particle (AOUP), free or in a confining potential. For the free-particle case, we compute the rate function analytically in d-dimensions from a saddle-point expansion, and numerically in two dimensions by (a) direct sampling of the active work in numerical solutions of the AOUP equations and (b) Legendre–Fenchel transform of the scaled cumulant generating function obtained via a cloning algorithm. The rate function presents asymptotically linear branches on both sides and it is independent of the system’s dimensionality, apart from a multiplicative factor. For the confining potential case, we focus on two-dimensional systems and obtain the rate function numerically using both methods (a) and (b). We find a different scenario for harmonic and anharmonic potentials: in the former case, the phenomenology of fluctuations is analogous to that of a free particle, but the rate function might be non-analytic; in the latter case the rate functions are analytic, but fluctuations are realised by entirely different means, which rely strongly on the particle-potential interaction. Finally, we check the validity of a fluctuation relation for the active work distribution. In the free-particle case, the relation is satisfied with a slope proportional to the bath temperature. The same slope is found for the harmonic potential, regardless of activity, and for an anharmonic potential with low activity. In the anharmonic case with high activity, instead, we find a different slope which is equal to an effective temperature obtained from the fluctuation–dissipation theorem.

Electronegativity under Confinement

The electronegativity concept was first formulated by Pauling in the first half of the 20th century to explain quantitatively the properties of chemical bonds between different types of atoms. Today, it is widely known that, in high-pressure regimes, the reactivity properties of atoms can change, and, thus, the bond patterns in molecules and solids are affected. In this work, we studied the effects of high pressure modeled by a confining potential on different definitions of electronegativity and, additionally, tested the accuracy of first-order perturbation theory in the context of density functional theory for confined atoms of the second row at the Hartree–Fock level. As expected, the electronegativity of atoms at high confinement is very different than that of their free counterparts since it depends on the electronic configuration of the atom, and, thus, its periodicity is modified at higher pressures.

Contact interactions: the two-dimensional case

We prove that in two dimensions the contact interaction of two wave functions is represented by a self-adjoint operator. Together with a confining potential, this provides a stable condensate of two-particle systems. Recall that in three dimensions one has a condensate of four wave functions in contact interaction (the Bose–Einstein condensate).

Neutron interactions with electromagnetic fields and single-neutron solitons

We address the bound-state dynamics of a neutron with anomalous magnetic dipole moment in the presence of electromagnetic (EM) fields described by a generalized Dirac–Pauli equation. This generalization consists of including appropriate couplings between Lorentz scalar and pseudoscalar fields with EM fields in the Lagrangian of the system. We exactly solve two single-particle problems: first, a Hydrogen-like system; second, a relativistic Schrödinger-like equation for a linear confining potential. We comment on the relevance of this approach to explore fermion (e.g. neutron) self-interactions as solitonic models of the neutron.

An Effective Model for Glueballs and Dual Superconductivity at Finite Temperature

The glueballs lead to gluon and QCD monopole condensations as by-products of color confinement. A color dielectric function G ∣ ϕ ∣ coupled with a Abelian gauge field is properly defined to mediate the glueball interactions at confining regime after spontaneous symmetry breaking (SSB) of the gauge symmetry. The particles are expected to form through the quark-gluon plasma (QGP) hadronization phase where the free quarks and gluons start clamping together to form hadrons. The QCD-like vacuum η 2 m η 2 F μ ν F μ ν , confining potential V c r , string tension σ , penetration depth λ , superconducting and normal monopole densities ( n s n n ), and the effective masses ( m η 2 and m A 2 ) will be investigated at finite temperature T . We also calculate the strong “running” coupling α s and subsequently the QCD β -function. The dual superconducting nature of the QCD vacuum will be investigated based on monopole condensation.