# A new approach to analytic, non-perturbative and gauge-invariant QCD

## Abstract

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 Green's functional G{sub c}(x,y|A) and the vacuum functional L[A]. 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 summationmore »

- Authors:

- Physics Department, Brown University, Providence, RI 02912 (United States)
- Universite de Nice-Sophia Antipolis, Institut Non Lineaire de Nice, UMR 6618 CNRS, 06560 Valbonne (France)

- Publication Date:

- OSTI Identifier:
- 22157007

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics (New York)

- Additional Journal Information:
- Journal Volume: 327; Journal Issue: 11; Other Information: Copyright (c) 2012 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUND STATE; DEUTERONS; EIKONAL APPROXIMATION; GAUGE INVARIANCE; GLUONS; GREEN FUNCTION; LAGRANGIAN FUNCTION; MATHEMATICAL SOLUTIONS; PIONS; POTENTIALS; QUANTUM CHROMODYNAMICS; QUARKS; SCHWINGER FUNCTIONAL EQUATIONS; SELF-ENERGY

### Citation Formats

```
Fried, H.M., Grandou, T., and Sheu, Y.-M., E-mail: ymsheu@alumni.brown.edu.
```*A new approach to analytic, non-perturbative and gauge-invariant QCD*. United States: N. p., 2012.
Web. doi:10.1016/J.AOP.2012.07.008.

```
Fried, H.M., Grandou, T., & Sheu, Y.-M., E-mail: ymsheu@alumni.brown.edu.
```*A new approach to analytic, non-perturbative and gauge-invariant QCD*. United States. doi:10.1016/J.AOP.2012.07.008.

```
Fried, H.M., Grandou, T., and Sheu, Y.-M., E-mail: ymsheu@alumni.brown.edu. Thu .
"A new approach to analytic, non-perturbative and gauge-invariant QCD". United States. doi:10.1016/J.AOP.2012.07.008.
```

```
@article{osti_22157007,
```

title = {A new approach to analytic, non-perturbative and gauge-invariant QCD},

author = {Fried, H.M. and Grandou, T. and Sheu, Y.-M., E-mail: ymsheu@alumni.brown.edu},

abstractNote = {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 Green's functional G{sub c}(x,y|A) and the vacuum functional L[A]. 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-which may be the same quark line, as in a self-energy graph-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. A second calculation, analytic, non-perturbative and gauge-invariant, of a nucleon-nucleon binding potential to form a model deuteron, will appear separately. - Highlights: Black-Right-Pointing-Pointer An analytic, non-perturbative and gauge-invariant formulation for QCD processes. Black-Right-Pointing-Pointer A new property called Effective Locality appears in the QCD fermionic amplitudes. Black-Right-Pointing-Pointer An effective quark-antiquark and 3-quark binding potential is obtained. Black-Right-Pointing-Pointer A single 'gluon bundle' replaces the sum of an infinite number of Feynman graphs.},

doi = {10.1016/J.AOP.2012.07.008},

journal = {Annals of Physics (New York)},

issn = {0003-4916},

number = 11,

volume = 327,

place = {United States},

year = {2012},

month = {11}

}