Broken Symmetry Group Research Articles

Models of abstract and real systems based on broken symmetry group

This article shows that symmetry groups as well as broken symmetry groups in natural and abstract mathematical may be used as models of development and evolution objects while describing the states and transformations of such systems. It also demonstrates “visualization” methods of PbTe nanostructures, ZN arithmetic, Galois group for the roots of a fourth degree polynomial, and DNA structure in the framework of category theory.

Ultraviolet complete quantum field theory and particle model

An ultraviolet complete particle model is constructed for the observed particles of the standard model. The quantum field theory associates infinite derivative entire functions with propagators and vertices, which make quantum loops finite and maintain Poincar\'e invariance and unitarity of the model. The electroweak model $SU(2)\times U(1)$ group is treated as a broken symmetry group with non-vanishing experimentally determined boson and fermion masses. A spontaneous symmetry breaking of the vacuum by a scalar Higgs field is not invoked to restore boson and fermion masses to the initially massless $SU(2)\times U(1)$ Lagrangian of the standard model. The hierarchy naturalness problem of the Higgs boson mass is resolved and the model contains only experimentally observed masses and coupling constants. The model can predict a stable vacuum evolution. Experimental tests to distinguish the standard model from the alternative model are proposed. The finite quantum field theory can be extended to quantum gravity.

Broken Symmetry Groups, Tables, and Structural Images in the Computer Experiment

The results of investigation of the extended and broken symmetry substitution groups for elements of finite number sets are presented, with examples of the corresponding abstract structures, their computer visualization, and application in description of real structures. When studying the tables of binary transformations with broken symmetry in a computer experiment, transformation subsets (“evolutionary trees”) with convergent and divergent properties of structure oriented graph have been revealed.

Networks of coadjoint orbits: From geometric to statistical mechanics

A class of network models with symmetry group $ G $ that evolve as a Lie-Poisson system is derived from the framework of geometric mechanics, which generalises the classical Heisenberg model studied in statistical mechanics. We considered two ways of coupling the spins: one via the momentum and the other via the position and studied in details the equilibrium solutions and their corresponding nonlinear stability properties using the energy-Casimir method. We then took the example $ G = SO(3) $ and saw that the momentum-coupled system reduces to the classical Heisenberg model with massive spins and the position-coupled case reduces to a new system that has a broken symmetry group $ SO(3)/SO(2) $ similar to the heavy top. In the latter system, we numerically observed an interesting synchronisation-like phenomenon for a certain class of initial conditions. Adding a type of noise and dissipation that preserves the coadjoint orbit of the network model, we found that the invariant measure is given by the Gibbs measure, from which the notion of temperature is defined. We then observed a surprising 'triple-humped' phase transition in the heavy top-like lattice model, where the spins switched from one equilibrium position to another before losing magnetisation as we increased the temperature. This work is only a first step towards connecting geometric mechanics with statistical mechanics and several interesting problems are open for further investigation.

Structure Transformations in Broken Symmetry Groups—Abstraction and Visualization

The work reports the finding and the study of transformation groups with two conditional elements (binary transformations of abstract structures of the finite numerical sets with broken symmetry). The term Broken Symmetry Group (BSG) is introduced. Transformation examples of relevant structures are studied with computer visualization and application in real structure study. A special type of BSG was discovered, which describes the subsets of “evolutionary trees” with convergent and divergent properties of the oriented graph (orgraph) with structure-development direction edges and “growth spirals”.

Группа нарушенной симметрии в октаэдрическом катионе [Me(urea)6]2+,3+ с внутриком-плексными водородными связями

Группа нарушенной симметрии в октаэдрическом катионе [Me(urea)6]2+,3+ с внутриком-плексными водородными связями

Broken Symmetry Group in the Octahedral [Me(urea)6]2+, 3+ Cation With Chelate Hydrogen Bonds

The work reports the study of broken symmetry groups of non-classical substitutions in real heterocomplex compounds with carbamide found in the description of cations with directed hydrogen bonds. Examples of the respective groups of products of non-classical substitutions are considered for the model structures. In the computer experiment, the examination of tables of binary transformations with broken symmetry discovered sets of transformations (“evolutionary trees”) with convergent and divergent properties of the structure orgraph that have not been previously studied.

Spontaneous symmetry breaking in fermion-gauge systems: a non standard approach

We propose a new method for the study of the chiral properties of the ground state in QFTs based on the computation of the probability distribution function of the chiral condensate. It can be applied directly in the chiral limit and therefore no mass extrapolations are needed. Furthermore this approach allows to write up equations relating the chiral condensate with quantities computable by standard numerical methods, the functional form of these relations depending on the broken symmetry group. As a check, we report some results for the compact Schwinger model.

Application of the method of collective coordinates the the quantisation of the two-dimensional higgs model

A comprehensive analysis of the application of the method of collective coordinates to the two dimensional Higgs model is given. First the instanton solution is derived, and the geometry of configuration space, and the construction of Schrodinger wave functionals are discussed. It is then explicitly verified that the Goldstone mode is the projection of the vacuum state onto the generator of the broken symmetry. The elimination of this Goldstone mode by means of the unitary gauge condition is demonstrated to the the crucial point in the construction of a consistent perturbation procedure. The parameter of the broken symmetry group is then used as the collective coordinate for field configurations around a minimum of the interaction. Throughout, the discussion is sufficiently detailed in order to facilitate the application of the method to other fields.

Discrimination between the standard theory of electroweak interactions and its extensions

The effective neutral-current Lagrangian for all the gauge models based on the spontaneously broken symmetry groups G0= SU2,Lx U{1},G0=G0xG′ (where the fermion fields appearing in the standard model transform in the usual way with respect to G0 and are singlets with respect toGLR=GLRxG′ (with some restriction on the manner of symmetry brcaking in this case) can be expressed in terms of five parametersa,b,c,d andx=sin2ϑw. Measurements of low-q2 phenomena are analysed to distinguish between these alternatives.