Wavelet-based field theory and cross-scale correlations
M. V. Altaĭsky · Days on Diffraction · 2008
We consider application of continuous wavelet transform to the field theory of the fields phialpha(x) depending on both the position x and the resolution a. The correlation functions langphialpha(x)phialpha' (x')rang for such fields may be finite at x = x'. In case of the gauge fields the nonlocality of the wavelet transform makes the theory more complicated, but the gauge symmetry for each scale is observed. This approach provides a possibility to estimate the causal effect of the large-scale wave envelope to the small scale entities. The same approach can be applied to the Langevin-type stochastic differential equations, treated within the framework of quantum field theory, time series analysis etc.