Renormalization of scalar field theories in rational spacetime dimensions

Abstract

Abstract We renormalize various scalar field theories with a $$\phi ^n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>ϕ</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:math> self interaction such as $$n=5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:math> , 7 and 9 in their respective critical dimensions which are non-integer. The renormalization group functions for the O ( N ) symmetric extensions are also computed.

Topics & Concepts