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The interface between Physics and Mathematics has been increasingly
spotlighted by the discovery of algebraic, geometric, and
topological properties in physical phenomena. A profound example is
the relation of noncommutative geometry, arising from algebras in
mathematics, to the so-called quantum groups in the physical
viewpoint. Two apparently unrelated puzzles - the solubility of
some lattice models in statistical mechanics and the integrability
of differential equations for special problems - are encoded in a
common algebraic condition, the Yang-Baxter equation. This backdrop
motivates the subject of this book, which reveals Knot Theory as a
highly intuitive formalism that is intimately connected to Quantum
Field Theory and serves as a basis to String Theory.This book
presents a didactic approach to knots, braids, links, and
polynomial invariants which are powerful and developing techniques
that rise up to the challenges in String Theory, Quantum Field
Theory, and Statistical Physics. It introduces readers to Knot
Theory and its applications through formal and practical
(computational) methods, with clarity, completeness, and minimal
demand of requisite knowledge on the subject. As a result, advanced
undergraduates in Physics, Mathematics, or Engineering, will find
this book an excellent and self-contained guide to the algebraic,
geometric, and topological tools for advanced studies in
theoretical physics and mathematics.
The interface between Physics and Mathematics has been increasingly
spotlighted by the discovery of algebraic, geometric, and
topological properties in physical phenomena. A profound example is
the relation of noncommutative geometry, arising from algebras in
mathematics, to the so-called quantum groups in the physical
viewpoint. Two apparently unrelated puzzles - the solubility of
some lattice models in statistical mechanics and the integrability
of differential equations for special problems - are encoded in a
common algebraic condition, the Yang-Baxter equation. This backdrop
motivates the subject of this book, which reveals Knot Theory as a
highly intuitive formalism that is intimately connected to Quantum
Field Theory and serves as a basis to String Theory.This book
presents a didactic approach to knots, braids, links, and
polynomial invariants which are powerful and developing techniques
that rise up to the challenges in String Theory, Quantum Field
Theory, and Statistical Physics. It introduces readers to Knot
Theory and its applications through formal and practical
(computational) methods, with clarity, completeness, and minimal
demand of requisite knowledge on the subject. As a result, advanced
undergraduates in Physics, Mathematics, or Engineering, will find
this book an excellent and self-contained guide to the algebraic,
geometric, and topological tools for advanced studies in
theoretical physics and mathematics.
This book focuses on the unifying power of the geometrical language
in bringing together concepts from many different areas of physics,
ranging from classical physics to the theories describing the four
fundamental interactions of Nature - gravitational,
electromagnetic, strong nuclear, and weak nuclear.The book provides
in a single volume a thorough introduction to topology and
differential geometry, as well as many applications to both
mathematical and physical problems. It is aimed as an elementary
text and is intended for first year graduate students.In addition
to the traditional contents of books on special and general
relativities, this book discusses also some recent advances such as
de Sitter invariant special relativity, teleparallel gravity and
their implications in cosmology for those wishing to reach a higher
level of understanding.
This book focuses on the unifying power of the geometrical language
in bringing together concepts from many different areas of physics,
ranging from classical physics to the theories describing the four
fundamental interactions of Nature - gravitational,
electromagnetic, strong nuclear, and weak nuclear.The book provides
in a single volume a thorough introduction to topology and
differential geometry, as well as many applications to both
mathematical and physical problems. It is aimed as an elementary
text and is intended for first year graduate students.In addition
to the traditional contents of books on special and general
relativities, this book discusses also some recent advances such as
de Sitter invariant special relativity, teleparallel gravity and
their implications in cosmology for those wishing to reach a higher
level of understanding.
Teleparallel Gravity (TG) is an alternative theory for gravitation,
which is equivalent to General Relativity (GR). However, it is
conceptually different. For example in GR geometry replaces the
concept of force, and the trajectories are determined by geodesics.
TG attributes gravitation to torsion, which accounts for
gravitation by acting as a force. TG has already solved some old
problems of gravitation (like the energy-momentum density of the
gravitational field). The interest in TG has grown in the last few
years. The book here proposed will be the first one dedicated
exclusively to TG, and will include the foundations of the theory,
as well as applications to specific problems to illustrate how the
theory works.
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