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May 23, 2010 at 19:27 comment added algori Clay, thanks again! Re Glimm and Jaffe: I took a look at the book "Quantum physics. A functional integral point of view" but wasn't able to find the statement about degree $<7$ polynomials there. I may have missed it since the presentation is a bit heavy (lots of formulas, lots of notation and not much explanation of what is going on). Could you perhaps give a specific reference to that result?
May 17, 2010 at 20:18 comment added Clay Cordova There is a complete answer to the question of which perturbation series are renormalizable in the limit where the difference between the Lagrangian an a non-degenerate quadratic functional is small. For scalars in 3 dimension we need the interaction to be a bounded below polynomial of degree less than 7 (note less than, not less than or equal!). For scalars in 4 dimensions we need a bounded below polynomial interaction of degree less than 5. For details involving other fields see Collins. For the results of Glimm and Jaffe you might start with their book, and the references there.
May 16, 2010 at 19:45 comment added algori Another question: could you give a reference to the result (by Glimm and Jaffe?) that the integral exists once the Lagrangian is minus the Laplacian plus a polynomial of degree $\leq 7$?
May 16, 2010 at 16:01 history edited Clay Cordova CC BY-SA 2.5
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May 16, 2010 at 13:19 comment added algori Thanks, Clay! Re renormalization: will take a look at the book you suggest. In the mean time: is there a mathematical criterion which says which actions give renormalizable integrals and which do not?
May 16, 2010 at 8:24 history edited Clay Cordova CC BY-SA 2.5
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May 16, 2010 at 7:50 history answered Clay Cordova CC BY-SA 2.5