Wavelet-Based Quantum Field Theory

Abstract

The Euclidean quantum field theory for the fields ${\varphi }_{\Delta x}(x)$, which depend on both the position $x$ and the resolution $\Delta x$, constructed in SIGMA 2 (2006), 046, hep-th/0604170, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.

This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (4)

• Causal sites as quantum geometry
• Simulation of Field Theories in Wavelet Representation
• Scale-Dependent Functions, Stochastic Quantization and Renormalization
• Wavelet based regularization for Euclidean field theory

Cited by in corpus (9)

• Geometry and field theory in multi-fractional spacetime
• Quantum field theory without divergences
• Continuous Wavelet Transform in Quantum Field Theory
• Multiresolution decomposition of quantum field theories using wavelet bases
• Wavelets in field theory
• A remark on gauge invariance in wavelet-based quantum field theory
• Renormalization in Wavelet basis
• Hamiltonian formulation of the $1+1$-dimensional ${\varphi }^4$ theory in a momentum-space Daubechies wavelet basis
• Convergence of quantum electrodynamics on the Poincare group