Books on Selberg Trace /Noncommutative geometry

In summary, the individual is looking for two books - one about a "pedestrian introduction" to noncommutative geometry and another about Selberg Trace. They mention their background as a physicist with knowledge in differential geometry, calculus, quantum mechanics, and mathematical physics. They express gratitude in advance for any book recommendations and mention "Chaos in Classical and Quantum Mechanics" by Martin C. Gutzwiller as a potential resource.
  • #1
mhill
189
1
I am looking for a good book , for 'pedestrian (aka Dummies ) introduction to noncommutative geometry and another book about Selberg Trace.

I am a physicist, hence perhaps my math knowledge is not high i know

- a bit of differential geometry

- Calculus (real and complex)

- Quantum mechanics

- a bit of Mathematical Physics

if possible and someone can recommend me a book, thanks in advance,
 
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  • #3
thank you very much..
 

1. What is Selberg Trace / Noncommutative Geometry?

Selberg Trace / Noncommutative Geometry is a mathematical theory that combines concepts from geometry, analysis, and algebra to study noncommutative spaces. It was developed by Atle Selberg in the 1960s as a way to generalize Riemannian geometry to noncommutative spaces.

2. How does Selberg Trace / Noncommutative Geometry relate to books?

There are many books on Selberg Trace / Noncommutative Geometry that explain the theory, its history, and its applications. These books may also provide exercises and examples for readers to practice and deepen their understanding of the topic.

3. What makes Selberg Trace / Noncommutative Geometry a unique field?

Selberg Trace / Noncommutative Geometry is unique in that it studies spaces where the order of operations matters, unlike traditional geometry which focuses on commutative spaces. This allows for a deeper understanding of noncommutative structures and their applications in mathematics and physics.

4. Who can benefit from studying books on Selberg Trace / Noncommutative Geometry?

Anyone with a background in mathematics, particularly in geometry and analysis, can benefit from studying books on Selberg Trace / Noncommutative Geometry. This includes undergraduate and graduate students, researchers, and professionals in related fields such as physics and engineering.

5. Can Selberg Trace / Noncommutative Geometry be applied to real-world problems?

Yes, Selberg Trace / Noncommutative Geometry has applications in various fields such as quantum mechanics, string theory, and cryptography. It can also be used to study noncommutative phenomena in physics and other areas of mathematics.

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