Particle Physics and Quantum Chaos

The relationship between chaos theory and particle physics is discussed. It is demonstrated that the mathematical apparatus used in gauge field theories of particle physics can be successfully applied to solve some problems connected with the stability and chaoticity of quantum mechanical systems and vice versa. Namely, we investigate the stability of holonomic quantum computations with respect to unavoidable errors of classical nature in assigning control parameters. We also demonstrate the approach to chaos assisted tunneling regime investigations based on chaotic instanton solutions. On the other hand, reverse influence of chaos theory on particle physics is also briefly discussed. We mainly focus on the problem of chaos in quantum field theory. This work does not give a complete review of all the results obtained in this direction. We discuss only some results on this problem.