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2011

A new perspective on renormalization: the scattering transformation

Glinsky, Michael E.

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The scattering transformation developed by Mallat is put into the perspective of field theory.

It is shown to be a simultaneous transformation of the field and the "time" parameter explicitly used in the definition of path integrals central to the Lagrangian approach and in the definition of the "time" ordered products used in the Hamiltonian (or canonical) approach.
This transformation preserves the form of the S-matrix as "time" ordered products.
The transformed "time" coordinate is the inverse "time" scale.

A new perspective on renormalization: the scattering transformation · Around

Built on

K. Wilson, Phys. Rev. B 4
1971
Earlier work this paper cites.
P. Ramond, Field Theory: A Modern Primer (Westview Press, 1990) pp. 70–87, 152–159
1990
Earlier work this paper cites.

Similar

M. Maggiore, A Modern Introduction to Quantum Field Theory (Oxford University Press, Oxford, 2010) pp. 43–50, 109–116, 144–153, 231–241
2010
Cited alongside, same era.
S. Mallat, “Group invariant scattering,” (2011), arXiv:1101.2286
Original
2011
Cited alongside, same era.
J. Bruna and S. Mallat, “Classification with scattering operators,” (2011a), arXiv:1011.3023
Original
Cited in the paper.
J. Bruna and S. Mallat, “Classification with invariant scattering representations,” (2011b), arXiv:1112.1120
Original
Cited in the paper.

Then

J. Bruna and S. Mallat, “Invariant scattering convolution networks,” (2012), arXiv:1203.1513
Original
2012
Closest in time.
J. Bruna, S. Mallat, E. Bacry, and J.-F. Muzy, “Intermittent process analysis with scattering moments,” (2013), arXiv:1311.4104
Original
2013
Closest in time.

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