Joannis Papavassiliou

The pinch technique and its applications to non-Abelian gauge theories

Introduction 1. The Pinch Technique at one loop 2. Advanced pinch technique - still one loop 3. Pinch technique to all orders 4. The pinch technique in the Batalin-Vilkovisky framework 5. The gauge technique 6. Schwinger-Dyson equations in the pinch technique framework 7. Non-perturbative gluon mass and quantum solitons 8. Nexuses, sphalerons, and fractional topological charge 9. A brief summary of d=3 NAGTs 10. The pinch technique for electroweak theory 11. Other applications of the pinch technique Appendix Index.

Gauge-independent transverse and longitudinal self-energies and vertices via the pinch technique

In the context of the standard model we show how to apply the pinch technique to four-fermion amplitudes with nonconserved external charged currents, in order to construct to one-loop order gauge-independent self-energies and vertices. We discuss the technical difficulties arising due to the presence of longitudinal contributions from the [ital W] and Goldstone boson ([phi]) propagators, and derive gauge-independent [ital WW], [phi][ital W], and [phi][phi] effective self-energies and vertices. The quantities so constructed satisfy a set of Ward identities, whose validity enforces the gauge invariance of the physical amplitude considered; their derivation does not require knowledge of the explicit closed form of the gauge-independent self-energies and vertices. Use of these Ward identities enables the decomposition of the amplitude in manifestly gauge-independent transverse and longitudinal structures with distinct kinematic properties. Explicit one-loop calculations are carried out, and several applications of the results are briefly discussed.

Gauge-invariant resummation formalism for two-point correlation functions

The consistent description of unstable particles, renormalons, or other Schwinger-Dyson-type solutions within the framework of perturbative gauge field theories necessitates the definition and resummation of off-shell Green{close_quote}s functions, which must respect several crucial physical requirements. A formalism is presented for resummation of off-shell two-point correlation functions, which is mainly based on arguments of analyticity, unitarity, gauge invariance, and renormalizability. The analytic results obtained with various methods, including the background field gauges and the pinch technique, are confronted with the physical requirements imposed; to one-loop order the pinch technique approach satisfies all of them. Using renormalization group arguments, we discuss the issues of the uniqueness of the resummation procedure related to the latter method. {copyright} {ital 1996 The American Physical Society.}

Process-independent strong running coupling

We unify two widely different approaches to understanding the infrared behaviour of quantum chromodynamics (QCD), one essentially phenomenological, based on data, and the other computational, realised via quantum field equations in the continuum theory. Using the latter, we explain and calculate a process-independent running-coupling for QCD, a new type of effective charge that is an analogue of the Gell-Mann--Low effective coupling in quantum electrodynamics. The result is almost identical to the process-dependent effective charge defined via the Bjorken sum rule, which provides one of the most basic constraints on our knowledge of nucleon spin structure. This reveals the Bjorken sum to be a near direct means by which to gain empirical insight into QCDs Gell-Mann--Low effective charge.

Symmetry preserving truncations of the gap and Bethe-Salpeter equations

Ward-Green-Takahashi (WGT) identities play a crucial role in hadron physics, e.g. imposing stringent relationships between the kernels of the one- and two-body problems, which must be preserved in any veracious treatment of mesons as bound-states. In this connection, one may view the dressed gluon-quark vertex,

Gluon mass generation in the presence of dynamical quarks

\Gamma_\mu^a

Chiral fermions and gauge fixing in five-dimensional theories

, as fundamental. We use a novel representation of

Gauge-invariant three-boson vertices and their Ward identities in the standard model.

\Gamma_\mu^a

CP violation through particle mixing and the H-A lineshape

, in terms of the gluon-quark scattering matrix, to develop a method capable of elucidating the unique quark-antiquark Bethe-Salpeter kernel,

Universal extra dimensions and Z ---> b anti-b

K