scholarly journals COSMOLOGICAL MODEL WITH BORN–INFELD TYPE SCALAR FIELD

2007 ◽  
Vol 04 (02) ◽  
pp. 249-275 ◽  
Author(s):  
A. TROISI ◽  
E. SÉRIÉ ◽  
R. KERNER
Keyword(s):  
Scalar Field ◽  
Order Term ◽  
Higgs Field ◽  
Natural Generalization ◽  
Relative Strength ◽  
First Approximation ◽  
The Matrix ◽  
Primordial Inflation ◽  
Double Well Potential ◽  
Higgs Fields

The non-abelian generalization of the Born–Infeld non-linear lagrangian is extended to the non-commutative geometry of matrices on a manifold. In this case, not only do the usual SU(n) gauge fields appear, but also a natural generalization of the multiplet of scalar Higgs fields, with the double-well potential as a first approximation. The matrix realization of non-commutative geometry provides a natural framework in which the notion of a determinant can be easily generalized and used as the lowest-order term in a gravitational lagrangian of a new kind. As a result, we obtain a Born–Infeld-like lagrangian as a root of sufficiently high order of a combination of metric, gauge potentials and the scalar field interactions. We then analyze the behavior of cosmological models based on this lagrangian. It leads to primordial inflation with varying speed, with possibility of early deceleration ruled by the relative strength of the Higgs field.

GRADED DIFFERENTIAL LIE ALGEBRAS AND SU(5)×U(1)-GRAND UNIFICATION

1998 ◽  
Vol 13 (15) ◽  
pp. 2627-2692 ◽  
Author(s):  
RAIMAR WULKENHAAR
Keyword(s):  
Mass Matrix ◽  
Algebraic Approach ◽  
Higgs Field ◽  
Higgs Bosons ◽  
Tree Level ◽  
The Matrix ◽  
The Masses ◽  
The Given ◽  
Higgs Fields ◽  
General Gauge

We formulate the flipped SU(5)×U(1)-GUT within a Lie-algebraic approach to non-commutative geometry. It suffices to take the matrix Lie algebra su(5) as the input; the u(1)-part with its representation on the fermions is an algebraic consequence. The occurring Higgs multiplets (24, 5, 45, 50-representations of su(5)) are uniquely determined by the fermionic mass matrix and the spontaneous symmetry breaking pattern to SU(3)C×U(1)EM. We find the most general gauge invariant Higgs potential that is compatible with the given Higgs vacuum. Our formalism yields tree-level predictions for the masses of all gauge and Higgs bosons. It turns out that the low-energy sector is identical with the standard model. In particular, there exists precisely one light Higgs field, whose upper bound for the mass is 1.45 mt. All remaining 207 Higgs fields are extremely heavy.

scholarly journals Linear Energy Density and the Flux of an Electric Field in Proca Tubes

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 640
Author(s):  
Vladimir Dzhunushaliev ◽  
Vladimir Folomeev ◽  
Abylaikhan Tlemisov
Keyword(s):  
Scalar Field ◽  
Electric Field ◽  
Higgs Field ◽  
Meissner Effect ◽  
Coupling Constant ◽  
Cylindrically Symmetric ◽  
Integral Characteristics ◽  
Energy And Momentum ◽  
Energy And Momentum Densities ◽  
Higgs Scalar

In this work, we study cylindrically symmetric solutions within SU(3) non-Abelian Proca theory coupled to a Higgs scalar field. The solutions describe tubes containing either the flux of a color electric field or the energy flux and momentum. It is shown that the existence of such tubes depends crucially on the presence of the Higgs field (there are no such solutions without this field). We examine the dependence of the integral characteristics (linear energy and momentum densities) on the values of the electromagnetic potentials at the center of the tube, as well as on the values of the coupling constant of the Higgs scalar field. The solutions obtained are topologically trivial and demonstrate the dual Meissner effect: the electric field is pushed out by the Higgs scalar field.

Research on a complete model of cosmological evolution a classical scalar field with a Higgs potential. II. Numerical simulation

2021 ◽  
pp. 147-151
Author(s):  
Yu.G. Ignat’ev ◽  
◽  
A.R. Samigullina ◽  
Keyword(s):  
Numerical Simulation ◽  
Computer Simulation ◽  
Scalar Field ◽  
Initial Conditions ◽  
Higgs Field ◽  
Hubble Constant ◽  
Cosmological Evolution ◽  
Higgs Potential ◽  
Complete Model ◽  
Expansion Stage

A study and computer simulation of a complete model of the cosmological evolution of a classical scalar field with a Higgs potential is carried out without the assumption that the Hubble constant is nonnegative. It is shown that in most cases of initial conditions the cosmological model passes from the expansion stage to the compression stage. Thus, cosmological models based on the classical Higgs field are unstable with respect to finite perturbations.

From random matrices to random tensors

2021 ◽  
pp. 166-177
Author(s):  
Adrian Tanasa
Keyword(s):  
Matrix Models ◽  
Random Matrices ◽  
Mathematical Physics ◽  
Natural Generalization ◽  
Random Surface ◽  
The Third ◽  
Planar Surfaces ◽  
Tensor Models ◽  
Feynman Graphs ◽  
The Matrix

After a brief presentation of random matrices as a random surface QFT approach to 2D quantum gravity, we focus on two crucial mathematical physics results: the implementation of the large N limit (N being here the size of the matrix) and of the double-scaling mechanism for matrix models. It is worth emphasizing that, in the large N limit, it is the planar surfaces which dominate. In the third section of the chapter we introduce tensor models, seen as a natural generalization, in dimension higher than two, of matrix models. The last section of the chapter presents a potential generalisation of the Bollobás–Riordan polynomial for tensor graphs (which are the Feynman graphs of the perturbative expansion of QFT tensor models).

scholarly journals A DARK SECTOR EXTENSION OF THE ALMOST-COMMUTATIVE STANDARD MODEL

2014 ◽  
Vol 29 (01) ◽  
pp. 1450005 ◽  
Author(s):  
CHRISTOPH A. STEPHAN
Keyword(s):  
Scalar Field ◽  
Standard Model ◽  
Present Model ◽  
Higgs Field ◽  
Dark Sector ◽  
Spectral Action ◽  
Scalar Particles ◽  
A Value ◽  
The Standard Model ◽  
Model C

We consider an extension of the Standard Model within the framework of Noncommutative Geometry. The model is based on an older model [C. A. Stephan, Phys. Rev. D79, 065013 (2009)] which extends the Standard Model by new fermions, a new U(1)-gauge group and, crucially, a new scalar field which couples to the Higgs field. This new scalar field allows to lower the mass of the Higgs mass from ~170 GeV, as predicted by the Spectral Action for the Standard Model, to a value of 120–130 GeV. The shortcoming of the previous model lay in its inability to meet all the constraints on the gauge couplings implied by the Spectral Action. These shortcomings are cured in the present model which also features a "dark sector" containing fermions and scalar particles.

Energy Spectrum of a Particle Within a Confined Double Well Potential

2006 ◽  
Vol 3 (2) ◽  
pp. 257-262
Author(s):  
J. L. Marin ◽  
G. Campoy ◽  
R. Riera
Keyword(s):  
Energy Levels ◽  
Numerical Approach ◽  
Symmetric Case ◽  
Basis Functions ◽  
Hidden Symmetry ◽  
The Matrix ◽  
Jahn Teller ◽  
Free Case ◽  
Jahn Teller Effect ◽  
Double Well Potential

The energy levels of a particle within a confined double well potential are studied in this work. The spectrum of the particle can be obtained by solving the corresponding Schrödinger equation but, for practical purposes, we have used a numerical approach based in the diagonalization of the matrix related to the Hamiltonian when the wavefunction is represented as an expansion in terms of "a particle-in-a-box" basis functions. The results show that, in the symmetric confining case, the energy levels are degenerate and a regular pairwise association between them is observed, similarly as it occurs in the free case. Moreover, when the confining is asymmetric, the degeneration is partially lifted but the pairwise association of the energy levels becomes irregular. The lifting of the degeneration in the latter case is addressed to the lack of symmetry or distortion of the system, namely, to a sort of Jahn-Teller effect which is common in the energy levels of diatomic molecules, to which a double well potential can be crudely associated. In the symmetric case, the states with nodes at the origin are recognized to be the same as those of the harmonic oscillator confined by two impenetrable walls, in such a way that the system presented in this work would be interpreted as half the solution of the problem of a particle within a confined four well potential. The latter suggests the existence of a sort of hidden symmetry which remains to be studied in a more detailed way.

Residual strain energy in composites containing particles

1996 ◽  
Vol 11 (2) ◽  
pp. 483-494 ◽  
Author(s):  
Toshiaki Mizutani
Keyword(s):  
Strain Energy ◽  
Crystal Lattices ◽  
Composite Systems ◽  
Surrounding Matrix ◽  
Dispersed Particles ◽  
First Approximation ◽  
Bulk Stress ◽  
The Matrix ◽  
Unit Cells ◽  
Physical Validity

Selsing's formula for radial tension at the particle-matrix interface is extended into a general formula which includes the effects of the amount of dispersed particles. A relationship is derived between individual volumes of strained unit cells in the crystal lattices of the particles and of the surrounding matrix. These relationships are used to predict the effect of the particles (2H−TiB2, 2H−ZrB2, and t−WB) on their unit cells and on the unit cell of the surrounding 6H–SiC matrix. The precision of these predictions was 7.1% or better. Hence, in principle, it is possible to investigate the distributions of residual bulk stress/strain. Estimates of characterizing values of the three composite systems are attempted on the rough basis of the elastic constants of the SiC matrix, confirming the physical validity of this approach as a first approximation. Further, the residual bulk strain energies of the particles and the matrix are discussed in connection with the elastic term involved in the fracture energy of such composites.

THE COMPLEXITY OF WORD CIRCUITS

2010 ◽  
Vol 02 (04) ◽  
pp. 483-492
Author(s):  
XUE CHEN ◽  
GUANGDA HU ◽  
XIAOMING SUN
Keyword(s):  
Directed Acyclic Graph ◽  
Order Term ◽  
General Setting ◽  
Natural Generalization ◽  
Input Word ◽  
Boolean Circuit ◽  
Binary Function ◽  
Open Problems ◽  
Necessary And Sufficient ◽  
Word Function

A word circuit [1] is a directed acyclic graph in which each edge holds a w-bit word (i.e., some x ∈ {0, 1}w) and each node is a gate computing some binary function g : {0, 1}w × {0, 1}w → {0, 1}w. The following problem was studied in [1]: How many binary gates are needed to compute a ternary function f : ({0, 1}w)3 → {0, 1}w. They proved that (2 + o(1))2w binary gates are enough for any ternary function, and there exists a ternary function which requires word circuits of size (1 - o(1))2w. One of the open problems in [1] is to get these bounds tight within a low order term. In this paper we solved this problem by constructing new word circuits for ternary functions of size (1 + o(1))2w. We investigate the problem in a general setting: How many k-input word gates are needed for computing an n-input word function f : ({0, 1}w)n → {0, 1}w (here n ≥ k). We show that for any fixed n, (1 - o(1))2(n - k)w basic gates are necessary and (1 + o(1))2(n - k)w gates are sufficient (assume w is sufficiently large). Since word circuit is a natural generalization of boolean circuit, we also consider the case when w is a constant and the number of inputs n is sufficiently large. We show that [Formula: see text] basic gates are necessary and sufficient in this case.

Sign in / Sign up

Export Citation Format

Share Document