arXiv subjects
Publications and source records attributed to Y. Gabellini.
About twelve years ago the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green's functions of $QCD$. This non-perturbative phenomenon is dubbed Effective Locality. In a much simpler way than in $QCD$, the most remarkable and intriguing aspects of Effective Locality are presented here, in the Yang--Mills theory on Minkowski spacetime.
Using previously described functional techniques for some non-perturbative, gauge invariant, renormalized QCD processes, a simplified version of the amplitudes - in which forms akin to Pomerons naturally appear - provides fits to ISR and LHC-TOTEM pp elastic scattering data. Those amplitudes rely on a specific function $ϕ(b)$ which describes the fluctuations of the transverse position of quarks inside hadrons.
Using previously described functional techniques for some non--perturbative, gauge invariant, renormalized QCD processes, a simplified version of the amplitudes --- in which forms akin to Pomerons naturally appear --- provides fits to ISR and LHC--TOTEM $pp$ elastic scattering data. Those amplitudes rely on a specific function $φ(\vec b)$ which describes the fluctuations of the transverse position of quarks inside hadrons.
This letter is meant to be a brief survey of several recent publications providing a simple, sequential explanation of Dark Energy, Inflation and Dark Matter, which leads to a simple picture of the why and the how of the Big Bang, and thence to a possible understanding of the birth and death of a Universe.
A new non-perturbative, gauge-invariant model QCD renormalization is applied to high energy elastic pp-scattering. The differential cross-section deduced from this model displays a diffraction dip that resembles those of experiments. Comparison with ISR and LHC data is currently underway.
A particular choice of renormalization, within the simplifications provided by the non-perturbative property of Effective Locality, leads to a completely finite, renormalized theory of QCD, in which all correlation functions can, in principle, be defined and calculated. In this Model of renormalization, only the Bundle chain-Graphs of the cluster expansion are non-zero. All Bundle graphs connecting to closed quark loops of whatever complexity, and attached to a single quark line, provided no 'self-energy' to that quark line, and hence no effective renormalization. However, the exchange of momentum between one quark line and another, involves only the cluster-expansion's chain graphs, and yields a set of contributions which can be summed and provide a finite color-charge renormalization that can be incorporated into all other QCD processes. An application to high energy elastic pp scattering is now underway.
A QED-based model of a new version of Vacuum Energy has recently been suggested, which leads to a simple, finite, one parameter representation of Dark Energy. An elementary, obvious, but perhaps radical generalization is then able to describe both Dark Energy and Inflation in the same framework of Vacuum Energy. One further, obvious generalization then leads to a relation between Inflation and the Big Bang, to the automatic inclusion of Dark Matter, and to a possible understanding of the birth (and death) of a Universe.
A QED--based "bootstrap" mechanism is suggested as an explanation for the vacuum energy that furnished the initial impulse for Inflation, and continues on to provide present day Dark Energy. Virtual vacuum fluctuations are assumed to generate effective electromagnetic fields whose average value corresponds to an effective c--number $A_μ^{\rm vac}(x)$, which is itself equal to the vacuum expectation value of the operator $A_μ(x)$ in the presence of that $A_μ^{\rm vac}(x)$. Lorentz invariance is manifest, as every observer would measure the same electric field in his or her own reference frame. The model has one arbitrary parameter $ξ$, and fits the energy density of present day Dark Energy for $ξ\sim O(1)$.
A QED-based symmetry breaking/bootstrap mechanism, appearing at sufficiently small space-time distances, is suggested as an explanation for the vacuum energy that furnished the initial impulse for Inflation, and continues on, to the present day, to provide the "Dark Energy" which is apparently forcing our Universe apart. Very high frequency virtual vacuum currents are assumed to generate weak, effective electromagnetic fields, corresponding to the appearance of an effective 4-potential A_vac (x), which is itself equal to the vacuum expectation value of the operator A(x) in the presence of that A_vac (x). Lorentz invariance is manifest, as every observer would measure the same electric field in his or her own reference frame. Such an effective vacuum field would have no relevance to the motion of ordinary charged particules until particle energies on the order of 10^5 TeV are possible. The model is sufficiently constrained so that one parameter is needed to fit the vacuum energy densities and relevant times for the onset and end of Inflation, as well as those parameters of present day Dark Energy.
Removal of the quenched approximation in the mechanism which produced an analytic estimate of quark-binding potentials, along with a reasonable conjecture of the color structure of the nucleon formed by such a binding potential, is shown to generate an effective, nucleon scattering and binding potential. The mass-scale factor on the order of the pion mass, previously introduced to define transverse imprecision of quark coordinates, is again used, while the strength of the potential is proportional to the square of a renormalized QCD coupling constant. The potential so derived does not include corrections due to spin, angular momentum, nucleon structure, and electroweak interactions; rather, it is qualitative in nature, showing how Nuclear Physics can arise from fundamental QCD.
A functional method to achieve the summation of all Feynman graphs relevant to a particular Field Theory process is suggested, and applied to QED, demonstrating manifestly gauge invariant calculations of the dressed photon propagator in approximations of increas- ing complexity. These lead in a natural way to the extraction of the leading logarithmic divergences of every perturbative order, and to a demonstration of the possible cancellation of all such divergences in the calculation of the (inverse of the) photon's wavefunction renormalization constant Z3. This analysis provides a qualitative understanding of why the measured value of the renormalized fine structure constant is, approximately, 1/137.
This paper applies the analytic forms of a recent non-perturbative, manifestly gauge- and Lorentz-invariant description (of the exchange of all possible virtual gluons between quarks ($Q$) and/or anti-quarks ($\bar{Q}$) in a quenched, eikonal approximation) to extract analytic forms for the binding potentials generating a model $Q$-$\bar{Q}$ "pion", and a model $QQQ$ "nucleon". Other, more complicated $Q$, $\bar{Q}$ contributions to such color-singlet states may also be identified analytically. An elementary minimization technique, relevant to the ground states of such bound systems, is adopted to approximate the solutions to a more proper, but far more complicated Schroedinger/Dirac equation; the existence of possible contributions to the pion and nucleon masses due to spin, angular momentum, and "deformation" degrees of freedom is noted but not pursued. Neglecting electromagnetic and weak interactions, this analysis illustrates how the one new parameter making its appearance in this exact, realistic formalism may be evaluated, along with a qualitative estimate of the lowest quark mass and the energy contributions to the ground states of the gluon fields, from a knowledge of the pion and (ground state) nucleon masses.
The interpretation of virtual gluons as ghosts in the non-linear gluonic structure of QCD permits the formulation and realization of a manifestly gauge-invariant and Lorentz covariant theory of interacting quarks/anti-quarks, for all values of coupling. The simplest example of quark/anti-quark scattering in a high-energy, quenched, eikonal model at large coupling is shown to be expressible as a set of finite, local integrals which may be evaluated numerically; and before evaluation, it is clear that the result will be dependent only on, and is damped by increasing momentum transfer, while displaying physically-reasonable color dependence in a manner underlying the MIT Bag Model and an effective, asymptotic freedom. A similar but more complicated integral will result from all possible gluonic-radiative corrections to this simplest eikonal model. Our results are compatible with an earlier, field-strength analysis of Reinhardt et al.
It is suggested that charged tachyons of extremely large mass M could not only contribute to the dark matter needed to fit astrophysical observations, but could also provide an explanation for gamma ray bursts and ulta high energy cosmic rays. The present paper defines a quantum field theory of tachyons, particles similar to ordinary leptons, but with momenta larger than energy. The theory is invariant under the full CPT transformation, but separately violates P and T invariance. Micro causality is broken for space-time intervals smaller than 1/M, but is effectively preserved for larger separations. Charged fermionic, rather than charged scalar tachyons are considered in order to minimize the probability of Cerenkov-like radiation by the tachyon, thereby permitting a high energy tachyon to retain its energy over galactic distances. Topics treated include the choice and Schwinger Action Principle variations of an appropriate Lagrangian, spinorial wave functions, relevant Green's functions, a functional description of an S-Matrix and generating functional, and a variety of interesting kinematical processes, including photon emission and reabsorption, and relevant annihilation and scattering effects. A version of Ehrenfest's theorem is developed, in order to provide a foundation for a classical description of charged tachyons in an external electromagnetic field. Applications are then made to three outstanding astrophysical puzzles : dark matter, gamma ray bursts and ultra high energy cosmic rays.
It is suggested that charged tachyons of extremely large mass M could not only contribute to the dark matter needed to fit astrophysical observations, but could also provide an explanation for gamma ray bursts and ultra high energy cosmic rays. The present paper defines a quantum field theory of tachyons, the latter similar to ordinary leptons, but with momenta larger than energy.
A physically reasonable model is introduced in order to estimate, in a functional way, the vast number of distinct graphs which are conventionally neglected in eikonal scattering models that lead to total cross sections increasing with energy in the form of the Froissart bound.
We present new, non trivial generalizations of the recent Tomaras, Tsamis and Woodard extension of the original Schwinger formula for charged pair production in a constant field.
We critically examine recently published results on the thermal production of massive vector bosons in a quark-gluon plasma. We claim the production rate is a collinear safe observable.