Selfdual Gauge Field Vortices: An Analytical Approach: 72 - Rilegato

Tarantello, Gabriella

Rilegato

ISBN 10: 0817643109 ISBN 13: 9780817643102

Casa editrice: Birkhauser, 2008

Riassunto

This monograph discusses specific examples of selfdual gauge field structures, including the Chern–Simons model, the abelian–Higgs model, and Yang–Mills gauge field theory. The author builds a foundation for gauge theory and selfdual vortices by introducing the basic mathematical language of gauge theory and formulating examples of Chern–Simons–Higgs theories (in both abelian and non-abelian settings). Thereafter, the Electroweak theory and self-gravitating Electroweak strings are examined. The final chapters treat elliptic problems involving Chern–Simmons models, concentration-compactness principles, and Maxwell–Chern–Simons vortices.

Su questo libro

Recensione:

From the reviews:

“This monograph is devoted to a mathematical study of selfdual gauge theories using critical point theory and some analytical and topological techniques. ... The book ends with a substantial bibliography and a useful index. This monograph, dealing in a clear way with some ‘hot’ topics of theoretical physics and geometry, will be of interest both to mathematicians and physicists.” (Jean Mawhin, Zentralblatt MATH, Vol. 1177, 2010)

Dalla quarta di copertina:

In modern theoretical physics, gauge field theories are of great importance since they keep internal symmetries and account for phenomena such as spontaneous symmetry breaking, the quantum Hall effect, charge fractionalization, superconductivity and supergravity. This monograph discusses specific examples of gauge field theories that exhibit a selfdual structure.

The author builds a foundation for gauge theory and selfdual vortices by introducing the basic mathematical language of the subject and formulating examples ranging from the well-known abelian–Higgs and Yang–Mills models to the Chern–Simons–Higgs theories (in both the abelian and non-abelian settings). Thereafter, the electroweak theory and self-gravitating electroweak strings are also examined, followed by the study of the differential problems that have emerged from the analysis of selfdual vortex configurations; in this regard the author treats elliptic problems involving exponential non-linearities, also in relation to concentration-compactness principles and blow-up analysis.

Many open questions still remain in the field and are examined in this comprehensive work in connection with Liouville-type equations and systems. The goal of this text is to form an understanding of selfdual solutions arising in a variety of physical contexts. Selfdual Gauge Field Vortices: An Analytical Approach is ideal for graduate students and researchers interested in partial differential equations and mathematical physics.

Su questa edizione

• Editore: Birkhauser
• Data di pubblicazione: 2008
• ISBN 10: 0817643109
• ISBN 13: 9780817643102
• Rilegatura: Copertina rigida
• Numero di pagine: 325