# How is gravity quantized in quantum gravity

**time**(during the first half of the semester): Wed 1 p.m. - 4 p.m.

**place**: Seminar room A of the Dependence (old AKH)

**briefing**: Wed March 8, 2000, 1 p.m.

**procedure**:

During the first half of the summer semester, an introduction to the problems and basic ideas of quantum gravity will be given. Afterwards, activities of the students can be added. (Details will be discussed in the lecture).

**content**:

The current attempts to establish a quantum theory of gravity are technically very demanding. In order to give an introduction in which the fundamental physical problems remain visible and are not covered up by mathematical difficulties, - after an introductory discussion - the simplest possible approach to the topic is chosen. Since only a finite number of degrees of freedom of the gravitational field are treated as dynamic variables, a (formal) quantization is possible. This can serve as a basis for understanding the incompatibility of quantum theory and gravitation theory (which has not yet been overcome) and is a good basis for advancing into more difficult approaches.

The material during the first half of the semester in brief:

- Basic ideas and formalism of general relativity
- Basic ideas and formalism of quantum mechanics. What does "quantization" mean? Canonical quantization, observable.
- Need for quantum gravity
- Discussion based on physical principles: fundamental problems of quantum gravity
- Canonical formalism of general relativity
- Minisuperspace models of gravity (cosmological world models), Lagrange and Hamilton formalism
- Formal canonical quantization of minisuperspace models of gravity: the role of time and finite-dimensional Wheeler-DeWitt equations
- Discussion based on the formalism achieved: fundamental problems of quantum gravity
- Outlook on various attempts to solve the problems

**requirements**:

- Basic facts of general relativity and its formalism are repeated at the beginning, but knowledge of them is useful.
- Basic facts of classical mechanics (Lagrangian formalism) are repeated at the beginning, but knowledge of them is useful.
- Basic facts of quantum mechanics and their formalism are repeated at the given point, but knowledge of them is useful.

*Not*Precondition.

**literature**: is given in the lecture

**Contact**:

Franz Embacher, email: [email protected]

Tel: 4277-51349 or 0664-1431691

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