Renormalization Group (Physics Notes) - Brossura

Benfatto, Giuseppe

Brossura

ISBN 10: 0691044465 ISBN 13: 9780691044460

Casa editrice: Princeton University Press, 1995

Riassunto

Scaling and self-similarity ideas and methods in theoretical physics have, in the last twenty-five years, coalesced into renormalization-group methods. This book analyzes, from a single perspective, some of the most important applications: the critical-point theory in classical statistical mechanics, the scalar quantum field theories in two and three space-time dimensions, and Tomonaga's theory of the ground state of one-dimensional Fermi systems.

The dimension dependence is discussed together with the related existence of anomalies (in Tomonaga's theory and in 4 -e dimensions for the critical point). The theory of Bose condensation at zero temperature in three space dimensions is also considered. Attention is focused on results that can in principle be formally established from a mathematical point of view. The 4 -e dimensions theory, Bose condensation, as well as a few other statements are exceptions to this rule, because no complete treatment is yet available. However, the truly mathematical details are intentionally omitted and only referred to. This is done with the purpose of stressing the unifying conceptual structure rather than the technical differences or subtleties.

Su questo libro

L'autore:

Giuseppe Benfatto is Professor of Mathematical Physics at the University of Rome-Tor Vergata, and Giovanni Gallavotti is Professor of Rational Mechanics at the University of Rome-La Sapienza.

Contenuti:

	Preface
Ch. 1	Introduction	3
Ch. 2	Problems Equivalent to the Analysis of Suitable Functional Integrals: Critical Point and Field Theory	5
Ch. 3	Other Functional Integrals: Fermi Sphere and Bose Condensation	12
Ch. 4	Effective Potentials and Schwinger Functions	19
Ch. 5	Multiscale Decomposition of Propagators and Fields: Running Effective Potentials	22
Ch. 6	Renormalization Group: Relevant and Irrelevant Components of the Effective Potentials	27
Ch. 7	Asymptotic Freedom: Upper Critical Dimension	34
Ch. 8	Beyond the Linear Approximations: The Beta Function and Perturbation Theory	38
Ch. 9	The Beta Function as a Dynamical System: Asymptotic Freedom of Marginal Theories	52
Ch. 10	Anomalous Dimension	56
Ch. 11	The Fermi Liquid and the Luttinger Model	66
Ch. 12	The Generic Critical Point for d = 3, [Gamma] = 0: The [Epsilon]-Expansion	70
Ch. 13	Bose Condensation: Reformulation	75
Ch. 14	Bose Condensation: Effective Potentials	81
Ch. 15	The Beta Function for the Bose Condensation	87
	A Brief Historical Note	96
	Bibliographical Notes	100
	Appendix 1. The Free Fermion Propagator	104
	Appendix 2. Grassmannian Integration	106
	Appendix 3. Trees and Feynman Graphs	111
	Appendix 4. Schwinger Functions and Anomalous Dimension	120
	Appendix 5. Propagators for the Bose Gas	124
	Appendix 6. The Beta Function for the Bose Gas	126
	References	135
	Subject Index	141
	Citation Index	143

Su questa edizione

• Editore: Princeton University Press
• Data di pubblicazione: 1995
• ISBN 10: 0691044465
• ISBN 13: 9780691044460
• Rilegatura: Copertina flessibile
• Numero di pagine: 152