Quantum Triangulations

Moduli Spaces, Strings, and Quantum Computing

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, General Physics
Cover of the book Quantum Triangulations by Mauro Carfora, Annalisa Marzuoli, Springer Berlin Heidelberg
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Author: Mauro Carfora, Annalisa Marzuoli ISBN: 9783642244407
Publisher: Springer Berlin Heidelberg Publication: January 14, 2012
Imprint: Springer Language: English
Author: Mauro Carfora, Annalisa Marzuoli
ISBN: 9783642244407
Publisher: Springer Berlin Heidelberg
Publication: January 14, 2012
Imprint: Springer
Language: English

Research on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment.

* *

The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest.

* *

*This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications.  *

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Research on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment.

* *

The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest.

* *

*This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications.  *

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