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Wavelet-based field theory and cross-scale correlations

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1 Author(s)

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.

Published in:

Days on Diffraction, 2008. DD '08. Proceedings of the International Conference

Date of Conference:

3-6 June 2008