Gauge Field Theories

Abstract

Quantum field theory forms the present theoretical framework for our understanding of the fundamental interactions of particle physics. This up-dated and expanded text examines gauge theories and their symmetries with an emphasis on their physical and technical aspects. Beginning with a new chapter giving a systematic introduction to classical field theories and a short discussion of their canonical quantization and the discrete symmetries C, P and T, the book provides a brief exposition of perturbation theory, the renormalization programme, and the use of the renormalization group equation. It then explores topics of current research interest including chiral symmetry and its breaking, anomalies, and low energy effective lagrangians and some basics of supersymmetry. A chapter on basics of the electroweak theory is now included. Professor Pokorski, a distinguished theoretical physicist, has presented here a self-contained text for graduate courses in physics; the only prerequisite is some grounding in quantum field theory.

Renormalization of the vector current in QED

“…Since this second term involves a double time derivative of the gauge field, the equations of motion must be applied to write it in terms of elementary fields and their canonical momenta, if we are to use canonical commutation and anticommutation relations. This gives extra terms, so the commutators of Q phys and Q N with elementary fields are not simply related byẐ 3 . The appropriate formula to use is, in fact, either of the two last parts of Eq.…”

“…A classic statement about the electromagnetic current in quantum field theory is that because it is conserved it needs no renormalization -see, e.g., [1], page 341, [2], page 430, [3], Section 10.1, and [4], page 16. In fact this result is false, as we will explain in detail.…”

“…Finiteness of the right-hand side might lead one to conclude incorrectly that Green functions (and hence matrix elements) of j N are finite, so that the current is not renormalized. Certainly an extra multiplicative factor is excluded [1,3,5], and a closely related argument proves that the sum of nonpenguin graphs [ Fig. 1(a)] is finite: the factor Z 2 in Z 2 takes care of divergences in these graphs.…”

Goldberger–Treiman relation and from the three quark BS/Faddeev approach in the NJL model

“…However, at this stage it is still difficult to evaluate h A (q 2 ) for non-vanishing momentum transfer in the relativistic Faddeev approach 16 . We confine ourselves to evaluate the off-shell g πN N (q 2 = 0) ≡g πN N defined by the single-pole dominance approximation to h A (q 2 ) as…”

Aspectos de Teoria de Campos e Mecânica Estatística

“…Relações do tipo (4.10) são conhecias como identidades de Ward e estabelecem relações entre as funções de Green. As identidades de Ward tem um papel fundamental em diversos aspectos da teoria de campos [45,48]. A relação (4.10)é uma expressão formal que ainda necessita de uma prescrição para ser feita precisa.…”