Higgs Scalar Fields and Discrete Symmetry

Multi - resolution Modeling of Discrete Scalar Fields

Thanks to improvement in simulation, high resolution scanning facilities and multidimensional medical imaging, the size of geometrical dataset is rapidly increasing, and huge datasets are commonly available. The purpose of this thesis is dealing with large sets of twoor three-dimensional discrete data sets describing scalar fields, by using a multiresolution approach. Specifically our aim is in...

Fold-change detection and scalar symmetry of sensory input fields.

Recent studies suggest that certain cellular sensory systems display fold-change detection (FCD): a response whose entire shape, including amplitude and duration, depends only on fold changes in input and not on absolute levels. Thus, a step change in input from, for example, level 1 to 2 gives precisely the same dynamical output as a step from level 2 to 4, because the steps have the same fold...

Symmetry Factors of Feynman Diagrams for Scalar Fields

The symmetry factor of Feynman diagrams for real and complex scalar fields is presented. Being analysis of Wick expansion for Green functions, the mentioned factor is derived in a general form. The symmetry factor can be separated into two ones corresponding to that of connected and vacuum diagrams. The determination of symmetry factors for the vacuum diagrams is necessary as they play a role i...

Discrete Killing Fields for Pattern Synthesis and Symmetry Detection

Scalar Gravity and Higgs Mechanism

The role of the auxiliary scalar field φ in Brans-Dicke theory is discussed. If a constant vacuum energy is assumed to be the origin of dark energy, then the corresponding density parameter would be a quantity varying with φ; and almost all of the fundamental components of our universe can be unified into the dynamical equation for φ. As a generalization of Brans-Dicke theory, we propose a new ...