Non-renormalizable theories and finite formulation of QFT

Abstract

In this paper, we show how the finite formulation of QFT based on Callan-Symanzik equations can be generalised to the case of non-renormalizable theories. We derive an equation for effective action for an arbitrary single scalar field theory, allowing us to perform computations without running in intermediate divergencies. We illustrate the method with the use of $\lambda {\varphi }^4+{\varphi }^6/M^2$ theory by the explicit (and fully finite) calculations of the effective potential as well as two-, four- and six-point correlation functions at one loop level and demonstrate that no quantum corrections to scalar mass $m^2$, depending on $M^2$-scale, are generated.

arXiv comment25 pages, 2 figures

References in corpus (16)

• Exact evolution equation for the effective potential
• Nonperturbative Evolution Equation for Quantum Gravity
• The Soft Supersymmetry-Breaking Lagrangian: Theory and Applications
• Asymptotic safety of gravity and the Higgs boson mass
• Naturalness and the Status of Supersymmetry
• Operator bases, $S$-matrices, and their partition functions
• Is SMEFT Enough?
• Ultraviolet Complete Quantum Gravity
• NSVZ scheme with the higher derivative regularization for N=1 SQED
• The Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by higher covariant derivatives in the three-loop approximation
• Effective Scalar Field Theory and Reduction of Couplings
• Renormalization without infinities
• QFT without infinities and hierarchy problem
• Finite Callan-Symanzik renormalisation for multiple scalar fields
• Effective Potential in Finite Formulation of QFT
• Finite Z-less integral expressions for $\beta$-functions in the MS4 scheme

Cited by in corpus (3)

• All-loop effective potential for arbitrary scalar models in curved space-time
• On the link between finite QFT and standard RG approaches
• The Higgs boson, naturalness, and the Universe