Particles and Gravity I

The course should be accessible already to 3rd year students, and fully understandable to 4th and 5th year students. There will be lecture notes available for students in a form of .pdf files. The course is taught in English. For the lecture notes and more information see the 2010/2011 course web page

http://www.fuw.edu.pl/~bohdang/wyklady/particles_and_gravity/P&G_I_11_12/PGI_11_12.html .

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This course is intended to provide a basic link between the high-energy physics thought of as a quantum field theory and gravity understood as a theory of fluctuations of a graviton field around certain background. We shall try to introduce at elementary level tools allowing consistent description of the Standard Model degrees of freedom interacting with gravity within the framework of field theory, and at the same time to discuss the most interesting phenomena in the realm of particle physics that are sensitive to gravitational interactions.

Course objective:

Gravitational interactions are often considered to be extremely week at energies accessible in contemporary particle accelerators, hence they are usually neglected in quantitative discussions of particle physics near the electroweak scale. However, there are good reasons to go beyond this standard approach:

• Cosmological applications of particle physics become increasingly relevant, and their better theoretical understanding turns out to be a pressing and demanding challenge.

• Theories unifying elementary interactions, like the string theory and local supersymmetry, necessarily include gravity and electroweak and strong interactions at equal footing.

Incorporation of gravity into unified picture of fundamental interactions always leads to modifications of 4-dimensional Einstein gravity. Often the electroweak interactions are also influenced by modifications of gravity and mixing between electroweak and gravitational degrees of freedom emerges. It opens up a fascinating new perspective for going beyond the Standard Model of electroweak interactions. This course is intended to provide a basic link between the high-energy physics thought of as a quantum field

theory and gravity understood as a theory of fluctuations of a graviton field around certain background. We shall try to introduce at elementary level tools allowing consistent description of Standard Model degrees of freedom interacting with gravity within the framework of field theory, and at the same time to discuss most interesting phenomena in the realm of particle physics that are ensitive to gravitational interactions.

Program:

• Brief introduction to classical field theory

• Basics of quantum field theory

• Gravity as a field theory of spin 2 gravitons

• The General Relativity

• Experimental tests of the General Relativity

• Particles in a curved spacetime

• Perturbation expansion and Feynman rules for gravitational interactions

The course could be considered as an independent, alternative course on gravity, however the main goal is to provide a basic knowledge needed for “Particles and Gravity II” and also for “Cosmology”.

1. S. Weinberg, ``Gravitation and cosmology : principles and applications of the general theory of relativity'',

2. R. Feynman, F. Morinigo and W.~Wagner, ``Feynman Lectures on Gravitation”,

3. A. Zee, ``Quantum field theory in a nutshell'',

4. L. Landau and E. Lifshitz, ``The Classical Theory of Fields''

A student who completes the course should have a sufficient background to study extra-dimensional theories of fundamental interactions such as for instance the Randal-Sundrum model or other extensions of the Standard Model that imply modifications of General Relativity. The course should also provide a necessary knowledge to study cosmology.

Oral exam