Open Access
June 2011 On a possible approach to general field theories with nonpolynomial interactions
Franco Ferrari
Adv. Theor. Math. Phys. 15(3): 783-799 (June 2011).


In this work, a class of field theories with self-interactions described by a potential of the kind $V (\phi(x) − \phi(x_0))$ is studied. $\phi$ is a massive scalar field and $x$, $x_0$ are points in a $d$-dimensional space. Under the condition that the potential admits the Fourier representation, it is shown that such theories may be mapped into a standard field theory, in which the interaction of the new fields is a polynomial of fourth degree. With some restrictions, this mapping allows the perturbative treatment of models that are otherwise intractable with standard field theoretical methods. A nonperturbative approach to these theories is attempted. The original scalar field $\phi$ is integrated out exactly at the price of introducing auxiliary vector fields. The latter are treated in a mean field theory approximation. The singularities that arise after the elimination of the auxiliary fields are cured using the dimensional regularization. The expression of the counterterms to be subtracted is computed.


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Franco Ferrari. "On a possible approach to general field theories with nonpolynomial interactions." Adv. Theor. Math. Phys. 15 (3) 783 - 799, June 2011.


Published: June 2011
First available in Project Euclid: 11 June 2012

zbMATH: 1258.81061
MathSciNet: MR2929689

Rights: Copyright © 2011 International Press of Boston

Vol.15 • No. 3 • June 2011
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