ar X iv : h ep - p h / 03 10 14 9 v 1 1 3 O ct 2 00 3 1 BRST - driven cancellations and gauge invariant Green ’ s functions

We study a fundamental, all order cancellation operating between graphs of distinct kinematic nature, which allows for the construction of gauge-independent effective self-energies, vertices, and boxes at arbitrary order. When quantizing gauge theories in the continuum one must invariably resort to an appropriate gauge-fixing procedure in order to remove redundant (non-dynamical) degrees of freedom originating from the gauge invariance of the theory. Thus, one adds to the gauge invariant (classical) Lagrangian L I a gauge-fixing term L GF , which allows for the consistent derivation of Feynman rules. At this point a new type of redundancy makes its appearance, this time at the level of the building blocks defining the perturbative expansion. In particular, individual off-shell Green's functions (n-point functions) carry a great deal of unphysical information, which disappears when physical observables are formed. S-matrix elements , for example, are independent of the gauge-fixing scheme and parameters chosen to quan-tize the theory, they are gauge-invariant (in the sense of current conservation), they are unitary (in the sense of conservation of probability), and well behaved at high energies. On the other hand Green's functions depend explicitly (and generally non-trivially) on the gauge-fixing parameter entering in the definition of L GF , they grow much faster than physical amplitudes at high energies and display unphysical thresholds. Last but not least, in the context of the standard path-integral quantization by means of the Faddeev-Popov Ansatz, Green's functions satisfy complicated Slavnov-Taylor identities (STIs) [1] involving ghost fields, instead of the usual Ward identities generally associated with the original gauge invariance. The above observations imply that in going from unphysical Green's functions to physical amplitudes , subtle field theoretical mechanisms are at work, implementing vast cancellations among the various Green's functions. Interestingly enough, these cancellations may be exploited in a very particular way by the Pinch Technique (PT) [2,3]: a given physical amplitude is reorganized into sub-amplitudes, which have the same kine-matic properties as conventional n-point functions (self-energies, vertices, boxes) but, in addition , they are endowed with important physical properties [4]. The basic observation, which essentially defines the PT, is that there exists a fundamental cancellation, driven by the underlying Becchi-Rouet-Stora-Tyutin (BRST) symmetry [5], which takes place between sets of diagrams with different kinematic properties, such as self-energy, vertex, and box diagrams. This cancellations are activated when longitudinal momenta circulating inside vertex and box diagrams, generate (by " pinching " out internal fermion lines) …