Noncovariant gauges in canonical formalism
Within the framework of gauge theories, this book develops a consistent formulation for the handling of noncovariant gauges in the quantization process. Its main concern is to provide the setting of the noncovariant gauge theories on the same levels of consistency as the covariant ones, by means of the canonical formalism. To this goal, two essential facts are addressed: (i) the fact that the gauge fixing - as understood in the quantization procedure, involves three different mechanisms, according to the number of unphysical degrees of freedom left in the theory: class I gauges -- which involve only the physical degrees of freedom; class II gauges, which involve, in addition to the physical degrees of freedom, an unphysical one, and class III gauges, in which are present two unphysical degrees of freedom and their associated Fadeev-Popov ghosts; (ii) the fact that in noncovariant gauges, the non-equivalence of coordinate frames allows the existence of singular frames (which produce ambiguities in the quantization process), which are characterized by a smaller number of degrees of freedom than those needed in general frames. Though the main focus of the volume is noncovariant gauges, in view of making an appropriate distinction between the three classes of gauges, the author has also included a detailed and complete description of the quantization theory of constrained systems. The chapters of the book address the following subtopics: canonical quantization for constrained systems, quantization of the free electromagnetic field in general class III linear gauges and in class II axial gauges, gauge fields interaction, perturbation theory (including renormalization), Slavnov-Taylor identities for Yang-Mills theory, field theory without infinities, and gauges with a singular\ \(C\) matrix. The conclusions, as separate chapter, picture the basic problems which might occur while carelessly dealing with path-integral methods and their solutions. Further, three appendices respectively address: the main notations used throughout the book, a useful Fourier transform employed in covariant gauges, and a brief recollection of main functions used in covariant field theory, accompanied by the description of the elementary solutions associated to the differential operators occurring in the field equations of noncovariant class III gauges. All the chapters of the monograph are accompanied by references, and a practical index of notions is enclosed. All in all, this comprehensive and rigorous monograph represents a gratifying addition for graduate students and researchers from high energy physics, gauge theories and related areas.
Lagrangian formalism, Hamiltonian formalism
scientific article; zbMATH DE number 5303658