Sunday, December 12, 2004

What is the Ultimate Theory of Physics?

It is always very interesting for me to try and understand how such short distances could have begun to have some visual world possibilities? When mathematics begins to develope a method to describing that same small world.

Shahn Majid's research explores the world of quantum geometry, on the frontier between pure mathematics and the foundations of theoretical physics. He uses mathematical structures from algebra and category theory to develop ideas concerning the structure of space and time. His research philosophy drives a search for the right mathematical language for a unified expression for the ideas of quantum physics, founded on the notion of non-commutative geometry

It is not always clear to me what would have arisen out of the possibilties of what could possibly lies beneath, but any emergent principal wuld have to be able to describe its origination(the geometry)?

If we thought for a moment that there was a guiding principal in the higg's field, how would we have perceptably explained this in conglomerations of students who would gather around their professors? In a strange sense, one could intuitively feel this gathering consequence, as a consolidation of dominante principles, around which the matter states could easily have resigned themselves?

Braided independence is another of the conceptual ideas going into the modern approach to quantum geometry. When electrons pass each other either in physical space or lexicographically during a calculation, their exchange involves an additional -1 factor. Building on this idea, one is led to a kind of braided mathematics in which the outputs of calculations are `wired' into the inputs of further calculations much like the way information flows inside a computer. Only now, when wires cross each other there is a nontrivial operator, in fact a different one for when one wire goes under the other and when it goes over. Here is a typical calculation in braided-mathematics

Noncommutative Geometry, Monday July 24th 2006 - Friday December 22nd 2006

Noncommutative geometry aims to carry over geometrical concepts to a a new class of spaces whose algebras of functions are no longer commutative. The central idea goes back to quantum mechanics, where classical observables such as position and momenta no longer commute. In recent years it has become appreciated that such noncommutative spaces retain a rich topology and geometry expressed first of all in K-theory and K-homology, as well as in finer aspects of the theory. The subject has also been approached from a more algebraic side with the advent of quantum groups and their quantum homogeneous spaces.

The subject in its modern form has also been connected with developments in several different fields of both pure mathematics and mathematical physics. In mathematics these include fruitful interactions with analysis, number theory, category theory and representation theory. In mathematical physics, developments include the quantum Hall effect, applications to the standard model in particle physics and to renormalization in quantum field theory, models of spacetimes with noncommuting coordinates. Noncommutative geometry also appears naturally in string/M-theory. The programme will be devoted to bringing together these different streams and instances of noncommutative geometry, as well as identifying new emerging directions.

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