The fate of conformal symmetry in the non-linear Schrödinger theory
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The free Schroedinger theory in d space dimensions is a non-relativistic conformal field theory. The interacting non-linear theory preserves this symmetry in specific numbers of dimensions at the classical (tree) level. This holds in particular for the Phi^4-theory in d = 2. We compute the full quantum corrections to the 4-point function to show that the symmetry is broken by an anomalous contribution proportional to the exact beta-function
22 pages, 5 figures. v3: version to be published; reference added; imaginary part of 4-point function corrected, unitarity checked
22 pages, 5 figures. v3: version to be published; reference added; imaginary part of 4-point function corrected, unitarity checked