Solitary Wave Solutions of Delayed Coupled Higgs Field Equation

This paper is devoted to the study of the solitary wave solutions for the delayed coupled Higgs field equation{vtt-uxx-αu+βf*u|u|^(2)-2uv-τu(|u|^(2))x=0 vtt+vxx-β(|u|^(x))xx=0.We first establish the existence of solitary wave solutions for the corresponding equation without delay and perturbation by using the Hamiltonian system method.Then we consider the persistence of solitary wave solutions of the delayed coupled Higgs field equation by using the method of dynamical system,especially the geometric singular perturbation theory,invariant manifold theory and Fredholm theory.According to the relationship between solitary wave and homoclinic orbit,the coupled Higgs field equation is transformed into the ordinary differential equations with fast variables by using the variable substitution.It is proved that the equations with perturbation also possess homoclinic orbit,and thus we obtain the existence of solitary wave solutions of the delayed coupled Higgs field equation.

Self duality solution with a Higgs field

The self-duality concept for the Higgs field is handled in the presence of contact geometry in 5 dimensions. A non-trivial SO（3） Higgs field lives only on the fifth dimension of the contact manifold because of the contact structure, while the SD Yang-Mills field lives in the 4-dimensional hyperplane of the contact manifold. The Higgs and SD Yang-Mills fields do not interact with one another.

A New Interpretation of the Higgs Vacuum Potential Energy Based on a Planckion Composite Model for the Higgs

We present a new interpretation of the Higgs field as a composite particle made up of a positive, with, a negative mass Planck particle. According to the Winterberg hypothesis, space, i.e., the vacuum, consists of both positive and negative physical massive particles, which he called planckions, interacting through strong superfluid forces. In our composite model for the Higgs boson, there is an intrinsic length scale associated with the vacuum, different from the one introduced by Winterberg, where, when the vacuum is in a perfectly balanced state, the number density of positive Planck particles equals the number density of negative Planck particles. Due to the mass compensating effect, the vacuum thus appears massless, chargeless, without pressure, energy density, or entropy. However, a situation can arise where there is an effective mass density imbalance due to the two species of Planck particle not matching in terms of populations, within their respective excited energy states. This does not require the physical addition or removal of either positive or negative Planck particles, within a given region of space, as originally thought. Ordinary matter, dark matter, and dark energy can thus be given a new interpretation as residual vacuum energies within the context of a greater vacuum, where the populations of the positive and negative energy states exactly balance. In the present epoch, it is estimated that the dark energy number density imbalance amounts to, , per cubic meter, when cosmic distance scales in excess of, 100 Mpc, are considered. Compared to a strictly balanced vacuum, where we estimate that the positive, and the negative Planck number density, is of the order, 7.85E54 particles per cubic meter, the above is a very small perturbation. This slight imbalance, we argue, would dramatically alleviate, if not altogether eliminate, the long standing cosmological constant problem.

Reciprocity Relation between Alternative Gravity Formulas

We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.

On the Cosmic Evolution of the Quantum Vacuum Using Two Variable G Models and Winterberg’s Thesis

We work within a Winterberg framework where space, i.e., the vacuum, consists of a two component superfluid/super-solid made up of a vast assembly (sea) of positive and negative mass Planck particles, called planckions. These material particles interact indirectly, and have very strong restoring forces keeping them a finite distance apart from each other within their respective species. Because of their mass compensating effect, the vacuum appears massless, charge-less, without pressure, net energy density or entropy. In addition, we consider two varying G models, where G, is Newton’s constant, and G-1, increases with an increase in cosmological time. We argue that there are at least two competing models for the quantum vacuum within such a framework. The first follows a strict extension of Winterberg’s model. This leads to nonsensible results, if G increases, going back in cosmological time, as the length scale inherent in such a model will not scale properly. The second model introduces a different length scale, which does scale properly, but keeps the mass of the Planck particle as, ± the Planck mass. Moreover we establish a connection between ordinary matter, dark matter, and dark energy, where all three mass densities within the Friedman equation must be interpreted as residual vacuum energies, which only surface, once aggregate matter has formed, at relatively low CMB temperatures. The symmetry of the vacuum will be shown to be broken, because of the different scaling laws, beginning with the formation of elementary particles. Much like waves on an ocean where positive and negative planckion mass densities effectively cancel each other out and form a zero vacuum energy density/zero vacuum pressure surface, these positive mass densities are very small perturbations (anomalies) about the mean. This greatly alleviates, i.e., minimizes the cosmological constant problem, a long standing problem associated with the vacuum.

The Three Postulates of the Theory of Everything

The three postulates of the posited dynamic and reversible theory of everything are: 1) the oscil-lating M-theory postulate for the oscillating matter structure, 2) the digital transitional Higgs-reversed Higgs fields postulate for the digital space structure, and 3) the reversible multiverse post-ulate for all physical laws and phenomena. The posited theory of everything based on the three postulates explains cosmology, the composition (baryonic matter, dark matter, and dark energy) in the universe, the periodic table of elementary particles (quarks, leptons, and bosons), the galaxy evolution, superconductivity, black hole, thermodynamic, and quantum mechanics. Oscillating M-theory is derived from oscillating membrane-string-particle whose space-time dimension number oscillates between 11D and 10D and between 10D and 4D. Space-time dimension number between 10 and 4 decreases with decreasing speed of light, decreasing vacuum energy, and in-creasing rest mass. The digital transitional Higgs-reversed Higgs fields are derived from digital attachment-detachment spaces which couple to particles. Under spontaneous symmetry breaking, the coupling of massless particle to zero-energy attachment space (the space for mass) produces the transitional nonzero-energy Higgs field-particle composite which under spontaneous symmetry restoring produces massive particle on zero-energy attachment space with the longitudinal component. The opposite of attachment space is detachment space as the space for kinetic energy and the nonzero-energy reverse Higgs field. The combination of n units of attachment space (de-noted as 1) and n units of detachment space (denoted as 0) brings about the three digital structures: binary partition space (1)n(0)n, miscible space (1 + 0)n, and binary lattice space (1 0)n to account for quantum mechanics, special relativity, and the force fields, respectively. In the third postulate, all physical laws and phenomena are permanently reversible in the multiverse, and temporary irreversible entropy increase is allowed. Our universe is an asymmetrical dual posi-tive-energy-negative-energy universe where the positive-energy universe on attachment space absorbed the interuniversal void on detachment space to result in the combination of attachment space and detachment space, while the negative-energy universe did not absorb the interuniversal void, resulting in temporary irreversible entropy increase through reversibility breaking, sym-metry violation, and low entropy beginning. Guided by the reversible negative-energy universe, our dual universe is a globally reversible cyclic dual universe.

We Are Living in a Computer Simulation

This paper posits that we are living in a computer simulation to simulate physical reality which has the same computer simulation process as virtual reality (computer-simulated reality). The computer simulation process involves the digital representation of data, the mathematical computation of the digitized data in geometric formation and transformation in space-time, and the selective retention of events in a narrative. Conventional physics cannot explain physical reality clearly, while computer-simulated physics can explain physical reality clearly by using the computer simulation process consisting of the digital representation component, the mathematical computation component, and the selective retention component. For the digital representation component, the three intrinsic data (properties) are rest mass-kinetic energy, electric charge, and spin which are represented by the digital space structure, the digital spin, and the digital electric charge, respectively. The digital representations of rest mass and kinetic energy are 1 as attachment space for the space of matter and 0 as detachment space for the zero-space of matter, respectively, to explain the Higgs field, the reverse Higgs field, quantum mechanics, special relativity, force fields, dark matter, and baryonic matter. The digital representations of the exclusive and the inclusive occupations of positions are 1/2 spin fermion and integer spin boson, respectively, to explain spatial translation by supersymmetry transformation and dark energy. The digital representations of the allowance and the disallowance of irreversible kinetic energy are integral electric charges and fractional electric charges, respectively, to explain the confinements of quarks and quasiparticles. For the mathematical computation component, the mathematical computation involves the reversible multiverse and oscillating M-theory as oscillating membrane-string-particle whose space-time dimension (D) number oscillates between 11D and 10D and between 10D and 4D to explain cosmology. For the selective retention component, gravity, the strong force, electromagnetism, and the weak force are the retained events during the reversible four-stage evolution of our universe, and are unified by the common narrative of the evolution.

A New Theory for the Essence and Origin of Electron Spin

Spin is an intrinsic form of angular momentum carried by elementary particles, composite particles, and atomic nuclei. It is wildly believed that spin is a purely quantum mechanical concept and has no classical analogue. In fact, elementary particles are conceived as point objects which have no axis to “spin” around. Therefore, there is no explaining how spin arises at the fundamental level, why particles have the values they do, and what underpins the Pauli Exclusion principle and Bose-Einstein behavior. However, spin is like a vector quantity;it has a definite magnitude, and it has a “direction”, in order to spin should be composite. In this paper we propose a physical explanation for spin of the electron at the sub-particle level, relying on the vortex model of the electron. The electron is described as a superfluid frictionless vortex which has a mass, angular momentum and spin to provide a complete explanation of all properties of the electron: it composite, spinning around its own axis, produces a tiny magnetic fields independent of those from its orbital motions. The classical hydrodynamic laws are used to describe the quantum properties of the electron, such as spin, angular momentum, magnetic momentum and a magnetic dipole. The circulation in the vortex is constant, and the angular momentum of the vortex is conserved and has the same value of Planck constant. The direction of the angular momentum of a spinning electron vortex is along the axis of rotation and determined by the direction of spin. The spin quantum number 1/2 has a fixed value which represents the gap between the circulation rate of the core of the vortex and the boundaries of the vortex. The changeable values +1/2 “spin-up” or -1/2 “spin-down” indicate the direction of the magnetic dipole of the vortex. The relation between spin and Planck constant is discussed and the origin h/4pi angular momentum units are revealed.

Hidden analytic relations for two-loop Higgs amplitudes in QCD

We compute the Higgs plus two-quark and one-gluon amplitudes(H→qqg)and Higgs plus three-gluon amplitudes(H→3 g)in the Higgs effective theory with a general class of operators.By changing the quadratic Casimir CF to CA,the maximally transcendental parts of the H→qqg amplitudes turn out to be equivalent to that of the H→3 g amplitudes,which also coincide with the counterparts in N=4 SYM.This generalizes the so-called maximal transcendentality principle to the Higgs amplitudes with external quark states,thus the full QCD theory.We further verify that the correspondence applies also to two-loop form factors of more general operators,in both QCD and scalar-YM theory.Another interesting relation is also observed between the planar H→qqg amplitudes and the minimal density form factors in N=4 SYM.