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TIBOREC --- 12:44:48 30.6.2009
WENCA: to jsem nikde neobjevil, ale tu informaci mam z RSS ScienceWeeku, tak treba se tam pak objevi i vyveseni tech videi.
WENCA --- 19:24:44 28.6.2009
TIBOREC: nevite nekdo kdy se na ty prednasky budem moct podivat? hledal jsem klicovy slovo "feynman" na http://www.gatesfoundation.org/ a nic. :(
MOYYO --- 10:15:04 28.6.2009
jo a tadle sajta je taky dobra:
MOYYO --- 10:08:22 28.6.2009
to je zlato, cisty zlato tendle paper :)
MOYYO --- 10:06:41 28.6.2009
a dost, prece to sem neprepastuju cely :)

More dramatically, both G and Hilb may be replaced by a more general sort of n-category.
This allows for a rigorous treatment of physical theories where physical processes are described by
n-dimensional diagrams. The basic idea, however, is always the same: a physical theory is a map
sending sending `abstract' processes to actual transformations of a specific physical system.
MOYYO --- 10:05:00 28.6.2009
The advantage of this viewpoint is that now the group G can be replaced by a more general
category. Topological quantum field theory provides the most famous example of such a generalization,
but in retrospect the theory of Feynman diagrams provides another, and so does Penrose's
theory of `spin networks'.
MOYYO --- 9:55:33 28.6.2009
In particular, we can roughly distinguish two lines of thought leading towards n-categorical
physics: one beginning with quantum mechanics, the other with general relativity. Since a major
challenge in physics is reconciling quantum mechanics and general relativity, it is natural to hope
that these lines of thought will eventually merge. We are not sure yet how this will happen, but
the two lines have already been interacting throughout the 20th century.
MOYYO --- 9:52:49 28.6.2009
chramostak> zrovna to ctu :)

Before we begin our chronology, to help the reader keep from getting lost in a cloud of details,
it will be helpful to sketch the road ahead. Why did categories turn out to be useful in physics?
The reason is ultimately very simple. A category consists of `objects' x; y; z; : : : and `morphisms'
which go between objects, for example
f : x -> y
A good example is the category of Hilbert spaces, where the objects are Hilbert spaces and the
morphisms are bounded operators. In physics we can think of an object as a `state space' for
some physical system, and a morphism as a `process' taking states of one system to states of
another (perhaps the same one). In short, we use objects to describe kinematics, and morphisms
to describe dynamics.

This escalation of dimensions can continue. In the diagrams Feynman used to describe interacting
particles, we can continuously interpolate between this way of switching two particles.
This requires four dimensions: one of time and three of space. To formalize this algebraically we
need a `symmetric monoidal category', which is a special sort of 4-category.

More general n-categories, including those for higher values of n, may also be useful in physics.
This is especially true in string theory and spin foam models of quantum gravity. These theories
describe strings, graphs, and their higher-dimensional generalizations propagating in spacetimes
which may themselves have more than 4 dimensions.
So, in abstract the idea is simple: we can use n-categories to algebraically formalize physical
theories in which processes can be depicted geometrically using n-dimensional diagrams.


CHRAMOSTAK --- 13:24:53 27.6.2009
MOYYO: Mohu se pozeptati, proč se to bude hodit? Vím, na co Baez a spol. aspirují, ale začíná už být vidět nějaké fyzikální světlo na konci tunelu? Jinak kdysi dávno na n-category Cafe visely i videopřednášky o úvodu do tématu, teď se mi nedaří je najít, ale možná se tam ještě budou válet.
MOYYO --- 23:06:46 26.6.2009
uvod do n-categories
asi se to bude hodit, chca nechca