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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.

Gauge fields (Physics). --- Mathematical physics. --- Quantum theory. --- Differential equations, Elliptic --- Differential equations, Partial --- Differential equations, Nonlinear --- Gauge fields (Physics) --- Quantum field theory --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Differential equations, Nonlinear. --- Nonlinear differential equations --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Physics. --- Partial differential equations. --- Quantum physics. --- Physics, general. --- Partial Differential Equations. --- Quantum Physics. --- Theoretical, Mathematical and Computational Physics. --- Nonlinear theories --- Field theory (Physics) --- Group theory --- Symmetry (Physics) --- Differential equations, partial. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Partial differential equations --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Physical mathematics

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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.

Partial differential equations --- Mathematical physics --- Quantum mechanics. Quantumfield theory --- differentiaalvergelijkingen --- quantumfysica --- wiskunde --- fysica

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This volume contains lecture notes on some topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics. The presentation of the material should be rather accessible to non-experts in the field, since the presentation is didactic in nature. The reader will be provided with a survey containing some of the most exciting topics in the field, with a series of techniques used to treat such problems.

Partial differential equations --- Mathematical physics --- differentiaalvergelijkingen --- wiskunde --- fysica