|
| Udgave: |
Efterår 2012 NAT |
| Point: |
7,5 |
| Blokstruktur: |
2. blok |
| Skemagruppe: |
A |
| Fagområde: |
fys |
| Institutter: |
Niels Bohr Institutet |
| Uddannelsesdel: |
Kandidat niveau |
| Kontaktpersoner: |
Jan Ambjørn, ambjorn@nbi.dk |
| Skema- oplysninger: |
 Vis skema for kurset
Samlet oversigt over tid og sted for alle kurser inden for Lektionsplan for Det Naturvidenskabelige Fakultet Efterår 2012 NAT |
| Undervisnings- periode: |
19. november, 2012 - 27. januar, 2013 |
| Undervisnings- form: |
Lectures |
| Formål: |
The purpose of this course is to show that the quantum mechanics of the relativistic particle can be understood entirely geometrically as a sum over random paths, and that the quantum mechanics of strings similarly can be understood entirely geometrically as a sum over random surfaces. In particular this will lead to an understanding of two-dimensional quantum gravity coupled to conformal field theories, the only theory we presently know which couples matter and geometry in a fully consistent way. |
| Indhold: |
Definition of the path integral in quantum mechanics. Application to relativistic particles and to strings. This covers selected parts of the book ”Quantum Geometry”. |
| Kompetence- beskrivelse: |
The Student is expected to be able to derive and explain the fundamental representation of particles and strings in terms of random geometry as well as the universality of these results. |
| Målbeskrivelse: |
The purpose of this course is that the student obtains a basic understanding of quantum field theory and string theory from a statistical mechanics point of view, i.e. quantum field theory represented as a theory of random walks and string theory as a theory of random surfaces.
In particular, this means that when the course is finished it is expected that the student is able to:
understand how to quantize the bosonic and fermionic particles using random walk reprentations.
understand how to analyse more general random ensembles, like branched polymers and relate them to particle propagation
understand the concept of random surfaces and how it relates to string theory
have a basic understanding of the fact that bosonic string theory cannot exist in space-time dimensions larger than two
understand the essentials of non-critical string theory
understand how non-critical string theory is related to two-dimensional quantum gravity coupled to matter with central charge less than one
understand how to define the concept of Hausdorff dimension and the concept of fractal dimensions of an ensemble of geometric objects
be able to calculate the fractal dimension for random works and for random surfaces.
The highest mark (12) is given for excellent exam performance that demonstrates full mastering of the above mentioned teaching goals with no or only small irrelevant gaps. The grade 2 is given to a student who has achieved only minimally the course goals.
|
| Lærebøger: |
Jan Ambjorn, B. Durhuus and T. Jonsson,Quantum: Geometry – A Statistical Field Theory Approach, Cambridge Monographs on Mathematical Physics, 1998 |
| Tilmelding: |
Foregår på www.kunet.dk May 15 - june 1. |
| Faglige forudsætninger: |
The course only requires basic knowledge of differentiation, integration and complex numbers and some basic knowledge of statistical mechanics |
| Eksamensform: |
Mundtlig eksamen af en halv times varighed, uden forberedelse, ingen hjælpemidler, intern censur, karakter efter 7-trins-skalaen.
Reeksamen: samme som ordinær. |
| Eksamen: |
Mundtlig prøve den 24. januar 2013.
Reeksamen: Mundtlig prøve den 18. april 2013. |
| Kursus hjemmeside: |
 |
| Undervisnings- sprog: |
Engelsk
|
| Sidst redigeret: |
21/6-2012 |