arXiv subjects
Publications and source records attributed to T. Grandou.
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.
Both at formal and philosophical levels, decades of efforts have been devoted to a deciphering of the `quantum enigma', the `crazy way quantum objects behave', to quote R.P. Feynman's words. We posit that the enigma cannot recede without resorting to a thorough questioning of the quantum ontology. In the current paper this questioning is introduced through a revisitation of the famous Schr\"odinger's cat paradox, and of the main attempts at solving it. Our proposal thereof, is that the quantum world enjoys a sound physical reality (complying, in particular, with the scientifc requirement of experimental reproducibility), but also, that this physical reality calls for an enlarged, and however precise notion of `what is real', such that what is real and actual can be distinguished from what is real but potential
The most successful "Standard Model" allows one to define the so-called "Elementary Particles". Now from another point of view, philosophical, how can we think of them? Which kind of a status can be attributed to Elementary Particles and their associated quantised fields? Beyond the unprecedented efficiency and reach of quantum field theories the current paper attempts at understanding the nature of what we talk about, the enigmatic reality of the quantum world.
The most debated status of the wave function of Quantum Mechanics is discussed in the light of the epistemological vs ontological opposition.
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.
In eikonal and quenched approximation, it is argued that the strong coupling fermionic QCD Green's functions and related amplitudes depart from a sole dependence on the SUc(3) quadratic Casimir operator, C2f, evaluated over the fundamental gauge group representation. Noticed in non-relativistic Quark Models and in a non-perturbative generalization of the Schwinger mechanism, an additional dependence on the cubic Casimir operator shows up, in contradistinction with perturbation theory and other non-perturbative approaches. However, it accounts for the full algebraic content of the rank-2 Lie algebra of SUc(3). Though numerically sub-leading effects, cubic Casimir dependences, here and elsewhere, appear to be a signature of the non-perturbative fermonic sector of QCD.
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.
In eikonal and quenched approximations at least, it is argued that the strong coupling fermionic QCD amplitudes obtained with the help of the newly discovered effective locality property, depart from a dependence on the sole $SU_c(3)$ quadratic Casimir operator, evaluated over the fundamental gauge group representation. This result, in contradistinction with Perturbation Theory, but also with a number of non-perturbative approaches such as the MIT Bag, the Stochastic Vacuum Models, and Lattice simulations, accounts, instead, for the full algebraic content of the rank-2 $SU_c(3)$-Lie algebra
Even though approximated, strong coupling non-perturbative QCD amplitudes remain very difficult to obtain. In this article, in eikonal and quenched approximations, physical insights are presented that rely on the newly-discovered property of Effective Locality.
Following a previous calculation of quark scattering in eikonal approximation, this paper presents a new, analytic and rigorous approach to the calculation of QCD phenomena. In this formulation a basic distinction between the conventional "idealistic" description of QCD and a more "realistic" description is brought into focus by a non-perturbative, gauge-invariant evaluation of the Schwinger solution for the QCD generating functional in terms of the exact Fradkin representations of the Green's functional and the vacuum functional. Because quarks exist asymptotically only in bound states, their transverse coordinates can never be measured with arbitrary precision; the non-perturbative neglect of this statement leads to obstructions that are easily corrected by invoking in the basic Lagrangian a probability amplitude which describes such transverse imprecision. The second result of this non-perturbative analysis is the appearance of a new and simplifying output called "Effective Locality", in which the interactions between quarks by the exchange of a "gluon bundle" - which "bundle" contains an infinite number of gluons, including cubic and quartic gluon interactions - display an exact locality property that reduces the several functional integrals of the formulation down to a set of ordinary integrals. It should be emphasized that "non-perturbative" here refers to the effective summation of all gluons between a pair of quark lines, but does not (yet) include a summation over all closed-quark loops which are tied by gluon-bundle exchange to the rest of the "Bundle Diagram". As an example of the power of these methods we offer as a first analytic calculation the quark-antiquark binding potential of a pion, and the corresponding three-quark binding potential of a nucleon, obtained in a simple way from relevant eikonal scattering approximations.
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 basic distinction, long overlooked, between the conventional, "idealistic" formulation of QCD, and a more "realistic" formulation is brought into focus by a rigorous, non-perturbative, gauge-invariant evaluation of the Schwinger solution for the QCD generating functional in terms of exact Fradkin representations for the Green's functional $\mathbf{G}_{c}(x,y|A)$ and the vacuum functional $\mathbf{L}[A]$. The quanta of all (Abelian) quantized fields may be expected to obey standard quantum-mechanical measurement properties, perfect position dependence at the cost of unknown momenta, and vice-versa, but this is impossible for quarks since they always appear asymptotically in bound states, and their transverse position or momenta can never, in principle, be exactly measured. Violation of this principle produces an absurdity in the exact evaluation of each and every QCD amplitude. We here suggest a phenomenological change in the basic QCD Lagrangian, such that a limitation of transverse precision is automatically contained in the now "realistic" theory, with the function essential to quark binding into hadrons appearing in the new Lagrangian. All absurdities in estimates of all "realistic" QCD amplitudes are then removed, and one obtains the possibility of hadron formation by appropriate quark binding potentials, and nucleon scattering and binding by effective, Yukawa-type potentials; the first of these potentials are constructed, in detail, in the following paper.
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 long standing issue known as the hot QCD collinear singularity problem has been proven to rely on an incorrect sequence of two mathematical operations. Here, the original derivation of this problem is entirely revisited within the correct sequence, bringing to light new and unexpected conclusions.
In a recent paper it was shown how quark scattering in a quenched, eikonal model led to a momentum-transfer dependent amplitude expressed in terms of Halpern's functional integral; and how the requirement of manifest gauge invariance converted that functional integral into a local integral, capable of being evaluated with precision by a finite set of numerical integrations. We here prove that this property of "effective locality" holds true for all quark processes, without approximation and without exception.
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.