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Jouko Mick=
elsson

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10 cu.

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Advanced studies

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Certain mathematical maturity in abstract algebra and Hilbert space theo=
ry, which can be obtained from the algebra/functional analysis courses at t=
he mathematics department or through self studies. On the physics side, in =
order

to understand the motivation for the aims of CFT, it is

recom=
mended to have as prerequisites the basics in relativity theory and in quan=
tum mechanics (from the standard theoretical physics courses).

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### Contents:<=
/h3>=20

Conformal field theory (CFT) in a two dimensional space-time is importan=
t for at least two reasons: First, CFT models can be mathematically rigorou=
sly constructed in contrast to nontrivial quantum field theory models in fo=
ur dimensions, and they are also a rich source for interesting problems in =
pure mathematics. Secondly, some of the CFT models can be actually applied =
to interesting physical problems in surface physics, with links to quantum =
statistical mechanics.

The present course is more mathematics oriented =
and is therefore recommended for advanced undergraduate and PhD mathematics=
students as well as for advanced theoretical physics students.

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Some topics to be covered: Conformal transformations in two and higher d=
imensions. The energy momentum tensor in 2D CFT and the Virasoro algebra. R=
epresentations of the Virasoro algebra. Wess-Zumino-Witten model; geometric=
al and algebraic aspects. Affine Lie algebras and their representations. CF=
T from vertex operator algebras.

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Weeks 36-42 and 44-50, Monday 10-12 in room C123, Tuesday 10-12 in room =
B322. Two hours of exercise classes per week.

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Martin Schottenloher: A Mathematical Introduction to Conformal Field The=
ory. Lecture Notes in Physics 759.

Springer Verlag, second edition(2008=
).

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Did you forget to register? What to do.

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Group | Day | Time | Place | Instructor |
---|

1. | Wed | 10-12 | B322 | Kalle Kyt=C3=B6l=C3=A4 |

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