Canonical Transformation and renormalization

  • Thread starter eljose79
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Canonical Transformation and renormalization....

Let be L a lagrangian of a Non-Renormalizable theory..then we could take its hamiltonian.

Then after taking Hamiltonian you could take a Canonical Transformation to find another (renormalizable) Hamiltonian..and solve it..¿why this trick is not valid?...
 

arivero

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Hmm, I can not see why not. Perhaps it is just complicated. First it is field theory, so the canonical transformations must be generated by functional derivatives from an action or so. Secondly, even in quantum mechanics one has that ordering problems are more evident in the transformed equation, for instance if one changes to action-angle variables. Third, can one grant that the new theory is going to be renormalizable? The perturbative approach at least is systematic, an universal recipe.

Still, some people uses "perfect actions", mapping into themselves under renormalization group. Perhaps this is close to the canonical transf approach, I do not know for sure.

In any case, I prefer to see the scaling procedure working, instead of hidding it under the carpet of calculus.
 

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