Geometrical Aspects in Classical and Elementary Particle Physics

There is no doubt that theoretical elementary particle physics achieved great progress in the last decades. However many questions remain unanswered. Some of them play an important role in our investigations:

- Is there a truly unifying geometrical principle from which all interactions can be deduced?
- Does their quantum nature imply that the geometrical framework needs to be enlarged?
- Are there deeper mathematical structures hidden behind the formal calculations of quantum field theory?
- What are the implications of the noncommutative geometry framework?
- Are there general geometrical structures underlying the quantum physics?
- What is the connection between classical and quantum physics? This may have important applications in many fundamental problems in elementary particle physics.

Mathematical structures and methods of differential geometry, algebra and functional analysis are widely used in our investigations.

In many cases, the G-Theory Principle, a method developed by our group, is applied. The G-Theory Principle is an extreme extension of the relativity principle of Poincaré and Einstein and contains in addition – adapted to physics – aspects of the “Erlanger Programm” by Felix Klein in geometry. The G-Theory Principle is a common principle of fundamental theories in physics. It can be applied in classical as well as in quantum physics and could lead to a deeper understanding of quantization.