Lectures on the functional renormalization group method

These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum field theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained in a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed briefly as an alternative way to arrive at the renormalization group equation. The scaling laws and fixed points are considered from local and global points of view. Instability induced renormalization and new scaling laws are shown to occur in the symmetry broken phase of the scalar theory. The flattening of the effective potential of a compact variable is demonstrated in case of the sine-Gordon model. Finally, a manifestly gauge invariant evolution equation is given for QED.Comment: 47 pages, 11 figures, final versio

Radio Astronomy

Contains table of contents for Section 4 and reports on eight research projects.National Science Foundation Grant AST 88-19848National Aeronautics and Space Administration Goddard Space Flight Center Grant NAGW-2310SM Systems and Research, IncNational Aeronautics and Space Administration Goddard Space Flight Center Grant NAG 5-537National Aeronautics and Space Administration Goddard Space Flight Center Grant NAG 5-10Leaders for Manufacturing ProgramNational Aeronautics and Space Administration Goddard Space Flight Center Grant NAS 5-3079

Radio Astronomy

Contains table of contents for Section 4 and reports on ten research projects.National Science Foundation Grant AST 90-22501Alfred P. Sloan FellowshipDavid and Lucile Packard Fellowship Award for Science and EngineeringNational Aeronautics and Space AdministrationNational Science Foundation Presidential Young Investigator AwardNational Aeronautics and Space Administration Grant NAGW-2310MIT Lincoln Laboratory Agreement BX-4975National Aeronautics and Space Administration/Goddard Space Flight Center Contract NAS 5-31276MIT Leaders for Manufacturing Progra

Radio Astronomy

Contains table of contents for Section 4 and reports on twelve research projects.National Science Foundation Grant AST 88-19848Jet Propulsion Laboratory Contract 957687National Aeronautics and Space Administration Grant NAGW 1386National Science Foundation Grant AST 88-19848Annie Jump Cannon AwardSM Systems and Research, Inc.U.S. Navy Office of Naval Research Contract N00014-88-K-2016NASA/Goddard Space Flight Center Grant NAG 5-537NASA/Goddard Space Flight Center Grant NAG 5-10Woods Hole Oceanographic Institution Contract SC-28860Leaders for Manufacturing Progra

Radio Astronomy

Contains table of contents for Section 4 and reports on nine research projects.National Science Foundation Grant AST 88-19848National Science Foundation Grant AST 90-22501Alfred P. Sloan FellowshipNational Science Foundation Presidential Young Investigator AwardNational Aeronautics and Space Administration Grant NAGW-2310David and Lucile Packard FellowshipSM Systems and Research CorporationNational Aeronautics and Space Administration/Goddard Space Flight Center Contract NAS 5-30791National Aeronautics and Space Administration/Goddard Space Flight Center Grant NAG5-10Leaders for Manufacturing Progra

Radio Astronomy

Contains table of contents for Section 4 and reports on ten research projects.National Science Foundation Grant AST 90-22501National Aeronautics and Space Administration Grant NAGW 1386National Science Foundation Presidential Young Investigator AwardDavid and Lucile Packard Fellowship for Science and EngineeringNational Aeronautics and Space Administration Grant NAGW-2310MIT Lincoln LaboratorySM Systems and Research CorporationNational Aeronautics and Space Administration/Goddard Space Flight Center Contract NAS 5-30791National Aeronautics and Space Administration/Goddard Space Flight Center Grant NAG 5-10MIT Leaders for Manufacturing Progra