General formulation and applications of the quasilocal background field method in quantum field theory

• Main Author: Tiamzon, Michelle Magalona
• Format: text
• Language: English
• Published: Animo Repository 1998
• Subjects: Field theory (Physics); Functions; Quantum field theory; Physics
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/2012
• Institution: De La Salle University

A general formulation of the quasilocal background field approach to quantum field theory that accommodates an arbitrary number of covariant derivatives of the field strength tensor, Yuv, is presented and applied to field theories in arbitrary dimensional (flat) spacetime. The background is required to satisfy the restriction that the nth covariant derivative of the field strength tensor vanishes thus allowing in the formalism up to the (n-1)th covariant derivative of the field strength tensor. Similarly, the matrix potential, X, is required to satisfy the restriction that its lth covariant derivative vanishes. Under these restrictions, the most general form of the background connection Nu(x) which defines the field strength tensor, Yuv=auNv-avNu+[Nu,Nv], is established inductively and the general quasilocal Green function equation is derived from this connection. This Green function equation is solved perturbatively under the assumption that the background is strong but slowly-varying. The one-loop effective action with co-variant derivative corrections is then calculated from the coincidence limit of the Green function. The first few terms in this perturbative expansion of the effective action are then evaluated and are found to agree with those obtained using more popular methods. The leading term in this perturbative expansion recovers that of Brown and Duff and hence Schwinger's QED one-loop effective action. The succeeding terms incorporate the higher derivative corrections to the effective action. The results are then used to evaluate the one-loop effective action for Yang-Mills theory in D dimensions. The one-loop effective actions that describe multigluon interactions mediated by meson, Dirac fermion and gauge particle virtual loops with derivative corrections are derived. It is hoped that the general formulation and new results presented in this thesis provide greater insight into the complexities of nonabelian theories in arbitrary dimensions.