Narrow Results

In [11], Hausel introduced a commutative algebra — the multiplicity algebra — associated to a fixed point of the $C^{\ast }$-action on the Higgs bundle moduli space. Here we describe this algebra for a fixed point consisting of a very stable rank 2 vector bundle and zero Higgs field for a curve of low genus. Geometrically, the relations in the algebra are described by a family of quadrics and we focus on the discriminant of this family, providing a new viewpoint on the moduli space of stable bundles. The discriminant in our examples demonstrates that as the bundle varies, we obtain a continuous variation in the isomorphism class of the algebra.

An SO(3) non-Abelian gauge theory is introduced. The Hamiltonian density is determined and the constraint structure of the model is derived. The first-class constraints are obtained and gauge-fixing constraints are introduced into the model. Finally, using the constraints, the Dirac brackets can be determined and a canonical quantization is found using Dirac's procedure.

Recently, it has been pointed out that dimensionless actions in four-dimensional curved spacetime possess a symmetry which goes beyond scale invariance but is smaller than full Weyl invariance. This symmetry was dubbed restricted Weyl invariance. We show that starting with a restricted Weyl invariant action that includes a Higgs sector with no explicit mass, one can generate the Einstein–Hilbert action with cosmological constant and a Higgs mass. The model also contains an extra massless scalar field which couples to the Higgs field (and gravity). If the coupling of this extra scalar field to the Higgs field is negligibly small, this fixes the coefficient of the nonminimal coupling $R{\Phi }^2$ between the Higgs field and gravity. Besides the Higgs sector, all the other fields of the Standard Model can be incorporated into the original restricted Weyl invariant action.

A generalization of the original Bargmann–Wigner equations for spin-1 massive fields is employed, taking fully into account all internal degrees of freedom associated with the underlying chiral bases of the constituent spin-1/2 representations. Through the specification of a chiral basis, the chiral Bargmann–Wigner equations are reduced to a Proca-like form coupled by chirality to an auxiliary equation for a spin-0 massive field. The coupling derived is a new phenomenon whose physical implications are discussed in the context of identification of this field with the Higgs field and dark matter.

According to Einstein's "Mach Principle" idea, inertia and mass are the result of a dynamical effect — namely a containment–confinement due to a universal energy to energy interaction, dominated by the contribution of the most distant sources in the universe, e.g. if the force weakens with distance like 1/rⁿ, n < 2. In the present treatment of high energy (particle) physics, quarks and leptons acquire their mass by interacting with "Higgs" fields related to symmetry breakdowns. Assuming that these mass-endowing fields in fact collect and channel the cosmical contributions we find that their basic action is repulsive, so that the universal expansion is the recoil of the mass-making.

In early 1970, it was postulated that there exists a zero spin quantum field, called Higgs field, that is present in all universe. The potential energy of the Higgs field is transferred to particles. Hence they acquire mass. These ideas were essential in fulfilling the basic need for a particle, called Higgs, with mass. These particles are called Higgs particles with spin zero with its mass to be $\sim$125 GeV. This raises the question as to its physical effects. If these particles are present, will they exhibit a Casimir effect and also obey the Stefan–Boltzmann Law? Assuming the dynamics of this field, will these effects change with temperature. The present calculation uses thermo field dynamics formalism to calculate temperature effects.

The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and nondiagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants. We study the harmonic oscillator with the interacting potential, ${\lambda }_1{x}^4/6+{\lambda }_2{x}^6/120$, where ${\lambda }_1$ and ${\lambda }_2$ are coupling constants, and $x$ is the position operator. In this study, each perturbed term has an exact solution. We demonstrate the accurate study of the spectrum and $〈x^2〉$ up to the next leading-order correction. In particular, we study a similar problem of Higgs field from the inverted mass term to demonstrate the possible nontrivial application of particle physics.

In this paper, we present a three-parameter model for the distributions of “dark matter” around local spherically symmetric and static distributions of normal matter, usually referred to as “dark matter halos”. The model is based on the assumption that the spontaneous symmetry breaking mechanism involving the Higgs field in the standard model of elementary particle physics leads to the existence of a constant distribution of vacuum energy throughout space–time. This is to be interpreted as a constant distribution of proper energy, as measured by local observers in their proper reference frames. Due to the presence of this universal distribution of vacuum energy, the model requires the introduction of the cosmological term in the Einstein field equations, in order to regulate the behavior of the resulting geometry at cosmologically large distances. By implementing the model on galactic scales, we are able to establish the gravitational consequences of such a homogeneous distribution of proper energy density at these scales. This results in equivalent halo masses and orbital velocity curves that, at least qualitatively, match the observations for galactic “dark matter” halos. Although the detailed realization of the model presented and calculated here cannot be construed as a precise representation of galactic structure, given that most of the actual structure of the galaxy, such as the galactic disk itself, is ignored, and replaced by a single spherically symmetric bulge, in this paper we do introduce the conceptual framework that may be used to construct a more complete galactic model in the future.

It is proposed that the recently announced BICEP2 value of tensor-to-scalar ratio r ~ 0.2 can be explained as containing an extra contribution from the recent acceleration of the universe. In fact this contribution, being robust, recent and of much longer duration (by a large order of magnitude) may dominate the contribution from the inflationary origin. In a possible scenario, matter (dark or baryonic) and radiation etc. can emerge from a single Higgs-like tachyonic scalar field in the universe through a physical mechanism not yet fully known to us. The components interact among themselves to achieve the thermodynamical equilibrium in the evolution of the universe. The field potential for the present acceleration of the universe would give a boost to the amplitude of the tensor fluctuations of gravity waves generated by the early inflation and the net effects may be higher than the earlier Planck bounds. In the process, the dark energy, as a cosmological constant decays into creation of dark matter. The diagnostics for the three-component, spatially homogeneous tachyonic scalar field are discussed in detail. The components of the field with perturbed equation of state (EoS) are taken to interact mutually and the conservation of energy for individual components gets violated. We study mainly the O_m(x) diagnostics with the observed set of H(z) values at various redshifts, and the dimensionless statefinders for these interacting components. This analysis provides a strong case for the interacting dark energy in our model.

It is shown that the creation of primordial massive black holes is accompanied by a local heating of the matter. The developed mechanism is based on the interaction of the Higgs field and a scalar field responsible for black hole formation. We also consider dynamical behavior of parameters such as a scale and chemical composition of such heating regions.

The "electroweak connection", which forms one of the cornerstones of the Standard Model of particle physics, is formulated within the framework of the Generation Model. It is shown that the electroweak connection can be derived assuming that the weak interactions are effective interactions rather than fundamental interactions, arising from a U(1)×SU(2) local gauge invariance, which is spontaneously broken by a Higgs field.

The origin of mass in the standard model of particle physics is discussed and some difficulties pointed out. An alternative model, the generation model, will be shown to lead to a different concept of mass: the mass of a body arises from the energy stored in the motion of its constituents, so that if a particle has mass, then it is composite. It is suggested that gravity is a residual interaction arising from the incomplete cancellation of the super-strong color interactions, which bind the fundamental constituents (rishons) of leptons and quarks.

The nature of the scalar field responsible for the cosmological inflation is found to be rooted in the most fundamental concept of the Weyl’s differential geometry: the parallel displacement of vectors in curved spacetime. Within this novel geometrical scenario, the standard electroweak theory of leptons based on the $SU{(2)}_L\otimes U{(1)}_Y$ as well as on the conformal groups of spacetime Weyl’s transformations is analyzed within the framework of a general-relativistic, conformally-covariant scalar–tensor theory that includes the electromagnetic and the Yang–Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An “effective cosmological potential”: $V_{\mathrm{\text{eff}}}$ is expressed in terms of the dark energy potential: $|V_{\mathrm{\Lambda }}|$ via the “mass reduction parameter”: $|\zeta |\equiv \sqrt{\frac{|V_{\mathrm{\text{eff}}}|}{|V_{\mathrm{\Lambda }}|}}$, a general property of the Universe. The mass of the Higgs boson, which is considered a “free parameter” by the standard electroweak theory, by our theory is found to be proportional to the mass $M_U\equiv \sqrt{|V_{\mathrm{\text{eff}}}|}$ which contributes to the measured Cosmological Constant, i.e. the measured content of vacuum-energy in the Universe. The nonintegrable application of the Weyl’s geometry leads to a Proca equation accounting for the dynamics of a ${\varphi }^{\rho }$-particle, a vector-meson proposed as an optimum candidate for Dark Matter. The peculiar mathematical structure of $V_{\mathrm{\text{eff}}}$ offers a clue towards a very general resolution in 4-D of a most intriguing puzzle of modern quantum field theory, the “cosmological constant paradox”(here referred to as: “$\mathrm{\Lambda }$-paradox”). Indeed, our “universal” theory offers a resolution of the “$\mathrm{\Lambda }$-paradox” for all exponential inflationary potentials: $V_{\mathrm{\Lambda }}(\varphi )\propto e^{-n\varphi }$, and for all linear superpositions of these potentials, where $n$ belongs to the mathematical set of the “real numbers”. An explicit solution of the $\mathrm{\Lambda }$-Paradox is reported for $n=2$. The results of the theory are analyzed in the framework of the recent experimental data of the PLANCK Mission. The average vacuum-energy density in the Universe is found: ${\rho }_{\mathrm{\text{vac}}}={(3.44\times 10^{-3})}^4{(\mathrm{\text{eV}})}^4$, the mass-reduction parameter: $|\zeta |\approx 10^{-38}$ and the value of the “cosmological constant”: $\mathrm{\Lambda }=3,86\times 10^{-64}$(eV/c${}^2{)}^2$. A quite remarkable result of the theory consists of the complete formulation of the Einstein equation including in its structure the “cosmological constant”, $\mathrm{\Lambda }$. This was the term that Einstein added “by hand” to his famous equation. The critical stability of the Universe is also discussed.

In gauge theory, Higgs fields are responsible for spontaneous symmetry breaking. In classical gauge theory on a principal bundle P, a symmetry breaking is defined as the reduction of a structure group of this principal bundle to a subgroup H of exact symmetries. This reduction takes place if and only if there exists a global section of the quotient bundle P/H. It is a classical Higgs field. A metric gravitational field exemplifies such a Higgs field. We summarize the basic facts on the reduction in principal bundles and geometry of Higgs fields. Our goal is the particular covariant differential in the presence of a Higgs field.

By virtue of the well-known theorem, a structure Lie group K of a principal bundle P → X is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/K → X. In gauge theory, such sections are treated as Higgs fields, exemplified by pseudo-Riemannian metrics on a base manifold X. Under some conditions, this theorem is extended to principal superbundles in the category of G-supermanifolds. Given a G-supermanifold M and a graded frame superbundle over M with a structure general linear supergroup, a reduction of this structure supergroup to an orthogonal-symplectic supersubgroup is associated to a supermetric on a G-supermanifold M.

In contrast with QFT, classical field theory can be formulated in strict mathematical terms of fibre bundles, graded manifolds and jet manifolds. Second Noether theorems provide BRST extension of this classical field theory by means of ghosts and antifields for the purpose of its quantization.

In this paper, we put forward a systematic and unifying approach to construct gauge invariant composite fields out of connections. It relies on the existence in the theory of a group-valued field with a prescribed gauge transformation. As an illustration, we detail some examples. Two of them are based on known results: the first one provides a reinterpretation of the symmetry breaking mechanism of the electroweak part of the Standard Model of particle physics; the second one is an application to Einstein's theory of gravity described as a gauge theory in terms of Cartan connections. The last example depicts a new situation: starting with a gauge field theory on Atiyah Lie algebroids, the gauge invariant composite fields describe massive vector fields. Some mathematical and physical discussions illustrate and highlight the relevance and the generality of this approach.

We consider the simplest extension of the standard model, where torsion couples to spinor as well as the scalar fields, and in which the cosmological constant problem is solved.

Gravitation theory is formulated as gauge theory on natural bundles with spontaneous symmetry breaking, where gauge symmetries are general covariant transformations, gauge fields are general linear connections, and Higgs fields are pseudo-Riemannian metrics.

A strong follow up of a previous proposal (ICHEP, Valencia 2014) is made leading to the first experiment to observe the gravitational waves at the collision sites at the colliders such as the Large Hadron Collider at CERN. The amplitudes have been calculated with regard to the sensitivity of the detector. Compared with the standard model physics, it is shown to have a measurable impact on the particle motions and corresponds to ‘missing’ energy in form of the gravitational wave loss. This is unlike the cosmological detectors like BICEP2 etc. where the indirect B mode polarization on CMBR were masked by dust. In contrast, this experiment would be the first experiment where the energy-momentum tensor of the source can be controlled.