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MathematicalPhysicist
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can someone explain to me this term?
i know that's it is concenered to commutivity (or the lack of it).
i know that's it is concenered to commutivity (or the lack of it).
Originally posted by Lonewolf
I think it's some kind of tensor product between quantum groups. This is off the top of my head from a book I picked up about six months ago, so it's more than likely inaccurate...
Connes fusion, also known as noncommutative geometry, is a mathematical framework developed by French mathematician Alain Connes. It aims to extend geometry to include noncommutative spaces, where the order of operations matters, rather than just commutative spaces where the order does not affect the outcome. This framework has applications in physics, particularly in quantum mechanics.
The main connection between Connes fusion and commutivity is that Connes fusion is a way to extend commutative geometry to include noncommutative spaces. This means that Connes fusion takes into account the order of operations, which is a crucial aspect in noncommutative spaces.
Connes fusion has various applications in physics, particularly in quantum mechanics. It provides a mathematical framework for understanding noncommutative spaces and their properties, which are essential for studying quantum systems. It has also been used in string theory and in the development of noncommutative field theories.
One real-world example of Connes fusion is the use of noncommutative geometry in the study of quasicrystals, which are materials with a special type of order that cannot be described using traditional commutative geometry. Another example is the use of noncommutative geometry in the development of quantum computers, where the order of operations is crucial in computations.
Current research topics related to Connes fusion include its applications in quantum information theory, the study of noncommutative spaces in cosmology, and its connections to other areas of mathematics such as number theory and topology. There is also ongoing research on extending Connes fusion to higher dimensions and developing new techniques for studying noncommutative spaces.