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Title: Infrared problems in gauge theories
Author: Alvarez-Coque, Arturo Garcia
ISNI:       0000 0001 3488 3698
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 1977
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After introductory remarks on the question of colour confinement in non-Abelian gauge theories of the strong interactions, Chapter 1 presents a brief review of the infrared (IR) phenomena in QED, with a comparative discussion of the non-Abelian case. In Chapter 2, the singularities arising in a purely massless process (Compton scattering in massless QED) are studied in perturbation theory. The IR and mass singularities from soft and hard bremsstrahlung are computed, and the cancellation implied by the Kinoshita-Lee-Nauenberg theorem is verified. The appearance of mass singularities in the renormalization process is discussed in the context of dimensional regularization. The first sections of Chapter 3 are devoted to the examination of general features of the IR divergence cancellation in the Yang-Mills theory. By making use of the Ward identities for on-shell amplitudes, soft virtual corrections and emission of soft and hard Yang-Mills quanta (gluons) are analyzed. In Section 3.4, the interest of considering a purely massless process in order to bring out characteristic features of the non-Abelian theory is emphasized, and gluon scattering in a colourless external potential is discussed Soft and hard gluon emission corrections are computed, and the inclusive transition rate is found to be free of singularities, to lowest non-trivial order in perturbation theory. Thus we extend previous investigations restricted to massive fermions and soft gluon emission. Our treatment includes non-leading singularities in the order considered and questions of gauge independence. Renormalization group-type equations which have been proposed, and which are presumed to sum up the singularities in perturbation theory, are described in Chapter 4. From the invariance of the S-matrix under the renormalization group, equations of the Callan-Symanzik type involving variations with respect to the IR cut-off are derived, and their significance is discussed. Questions related to the massive fermion decoupling theorem, zero-mass renormalization and dimensional regularization are also discussed.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available