Searcharxiv⌕ Search

arXiv subjects

Richard Kerner

Publications and source records attributed to Richard Kerner.

At least 37 records · Page 2Linked to original sources
arXiv2013

Time-reparametrization invariance and Hamilton-Jacobi approach to the cosmological sigma-model

The construction of physical models with local time-reparametrization invariance is reviewed. Negative-energy contributions to the hamiltonian are shown to be crucial for the realization of this reparametrization symmetry. The covariant formulation of the dynamics is used to develop a time and gauge invariant Hamilton-Jacobi theory. This formalism is applied to solve for the cosmology of a homogeneous universe of the Friedmann-Lemaitre-Robertson-Walker type. After a discussion of empty universes, the FLRW theory is extended with homogeneous scalar fields generically described by a $\sg$-model on some scalar manifold. An explicit gauge-invariant solution is constructed for the non-linear O(N)-models.

hep-th↗
arXiv2011

Spacetime Symmetries and Z_3-graded Quark Algebra

We investigate certain $Z_3$-graded associative algebras with cubic $Z_3$-invariant constitutive relations. The invariant forms on finite algebras of this type are given in the low dimensional cases with two or three generators. We show how the Lorentz symmetry represented by the $SL(2, {\bf C})$ group emerges naturally without any notion of Minkowskian metric, just as the invariance group of the $Z_3$-graded cubic algebra and its constitutive relations. Its representation is found in terms of Pauli matrices. The relationship of this construction with the operators defining quark states is also considered, and a third-order analogue of the Klein-Gordon equation is introduced. Cubic products of its solutions may provide the basis for the familiar wave functions satisfying Dirac and Klein-Gordon equations.

hep-th↗
arXiv2011

Interaction of Flexural Phonons with Electrons in Graphene: A Generalized Dirac Equation in Corrugated Surfaces

A generalized Dirac equation is derived in order to describe charge carriers moving in corrugated graphene, which is the case for temperatures above 10°K due to the presence of flexural phonons. Such interaction is taken into account by considering an induced metric, in the same spirit as the general relativity approach for the description of fermionic particle moving in a curved space-time. The resulting equation allows to include in a natural way the presence of other phonon branches as well as an external electromagnetic field. It also predicts non-linear effects which are not present in the usual vector potential approximation used in most of publications on the subject, as well as the possibility of controlling electronic conductivity using pure sinusoidal strain fields. The non-linear terms are important at high temperatures, and can also lead to interesting effects, like e.g. resonances between flexural phonons and external electromagnetic fields.

cond-mat.mtrl-sci↗
arXiv2008

Approximate solutions in General Relativity via deformation of embeddings

A systematic study of deformations of four-dimensional Einsteinian space-times embedded in a pseudo-Euclidean space $E^N$ of higher dimension is presented. Infinitesimal deformations, seen as vector fields in $E^N$, can be divided in two parts, tangent to the embedded hypersurface and orthogonal to it; only the second ones are relevant, the tangent ones being equivalent to coordinate transformations in the embedded manifold. The geometrical quantities can be then expressed in terms of embedding functions $z^A$ and their infinitesimal deformations $v^A z^A \to {\tilde{z}}^A = z^A + εv^A$. The deformations are called Einsteinian if they keep Einstein equations satisfied up to a given order in $ε$. The system so obtained is then analyzed in particular in the case of the Schwarzschild metric taken as the starting point, and some solutions of the first-order deformation of Einstein's equations are found. We discuss also second and third order deformations leading to wave-like solutions and to the departure from spherical symmetry towards an axial one (the approximate Kerr solution)

gr-qc↗
arXiv2006

Cosmological model with Born-Infeld type scalar field

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 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.

gr-qc↗
arXiv2006

Structure and Function of Window Glass and Pyrex

Window glass is a ternary mixture, while pyrex (after window glass, the most common form of commercial glass) is a quaternary. Building on our previous success in deriving the composition of window glass (sodium calcium silicate) without adjustable parameters, and borrowing from known reconstructed crystalline surfaces, we model pyrex as silica clusters with a specific ternary interface. Our global model explains the thermal expansivity contours of ternary sodium borosilicates, and it is consistent with the optimized resistance of pyrex to mechanical and thermal shocks. It suggests new directions for studying the nanoscopic structure of these remarkable materials.

cond-mat.mtrl-sci↗
arXiv2005

Combinatorial rules of icosahedral capsid growth

A model of growth of icosahedral viral capsids is proposed. It takes into account the diversity of hexamers' compositions, leading to definite capsid size. We show that the observed yield of capsid production implies a very high level of self-organization of elementary building blocks. The exact number of different protein dimers composing hexamers is related to the size of a given capsid, labeled by its T-number. Simple rules determining these numbers for each value of T are deduced and certain consequences are discussed.

q-bio.QM↗
arXiv2004

Born-Infeld inspired bosonic action in a noncommutative geometry

The Born-Infeld lagrangian for non-abelian gauge theory is adapted to the case of the generalized gauge fields arising in non-commutative matrix geometry. Basic properties of static and time dependent solutions of the scalar sector of this model are investigated.

hep-th↗
arXiv2004

Non-Abelian generalization of Born-Infeld theory inspired by non-commutative geometry

We present a new non-abelian generalization of the Born-Infeld Lagrangian. It is based on the observation that the basic quantity defining it is the generalized volume element, computed as the determinant of a linear combination of metric and Maxwell tensors. We propose to extend the notion of determinant to the tensor product of space-time and a matrix representation of the gauge group. We compute such a Lagrangian explicitly in the case of the SU(2) gauge group and then explore the properties of static, spherically symmetric solutions in this model. We have found a one-parameter family of finite energy solutions. In the last section, the main properties of these solutions are displayed and discussed.

hep-th↗
arXiv2003

Axion Bremsstrahlung

A new mechanism of cosmic axion production is proposed: axion bremsstrahlung from collisions of straight global strings. This effect is of the second order in the axion coupling constant, but the resulting cosmological estimate is likely to be of the same order as that corresponding to radiation from oscillating string loops. This may lead to a further restriction on the axion window.

astro-ph↗
arXiv2001

Stochastic Description of Agglomeration and Growth Processes in Glasses

We show how growth by agglomeration can be described by means of algebraic or differential equations which determine the evolution of probabilities of various local configurations. The minimal fluctuation condition is used to define vitrification. Our methods have been successfully used for the description of glass formation.

cond-mat.stat-mech↗
arXiv2001

Cherenkov radiation in a gravitational wave background

A covariant criterion for the Cherenkov radiation emission in the field of a non-linear gravitational wave is considered in the framework of exact integrable models of particle dynamics and electromagnetic wave propagation. It is shown that vacuum interacting with curvature can give rise to Cherenkov radiation. The conically shaped spatial distribution of radiation is derived and its basic properties are discussed.

gr-qc↗
arXiv2000

Ternary algebraic structures and their applications in physics

We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras, which may find more interesting applications in the years to come.

math-ph↗
arXiv2000

Geodesic Deviation in Kaluza-Klein Theories

We study in detail the equations of the geodesic deviation in multidimensional theories of Kaluza-Klein type. We show that their 4-dimensional space-time projections are identical with the equations obtained by direct variation of the usual geodesic equation in the presence of the Lorentz force, provided that the fifth component of the deviation vector satisfies an extra constraint derived here.

gr-qc↗
arXiv1999

Classical glueballs in non-Abelian Born-Infeld theory

It is shown that the Born-Infeld-type modification of the quadratic Yang-Mills action suggested by the superstring theory gives rise to classical particle-like solutions prohibited in the standard Yang-Mills theory. This becomes possible due to the scale invariance breaking by the Born-Infeld non-linearity. New classical glueballs are sphaleronic in nature and exhibit a striking similarity with the Bartnik-McKinnon solutions of the Yang-Mills theory coupled to gravity.

hep-th↗
arXiv1999

The Born-Infeld electromagnetism in Kaluza-Klein theory

We investigate the properties of non-linear electromagnetism based on the Born-Infeld Lagrangian in multi-dimensional theories of Kaluza-Klein type. We consider flat space-time solutions only, which means that the space-time metric is constant, and the only supplementary variable is the dilaton field, a scalar. We show that in the case of Kaluza-Klein theory, the Born-Infeld Lagrangian describes an interesting interaction between the electromagnetic and scalar fields, whose propagation properties are modified in a non-trivial manner.

hep-th↗
arXiv1997

Shadow of noncommutativity

We analyse the structure of the $κ=0$ limit of a family of algebras $A_κ$ describing noncommutative versions of space-time, with $κ$ a parameter of noncommutativity. Assuming the Poincaré covariance of the $κ=0$ limit, we show that, besides the algebra of functions on Minkowski space, $A_0$ must contain a nontrivial extra factor $A^I_0$ which is Lorentz covariant and which does not commute with the functions whenever it is not commutative. We give a general description of the possibilities and analyse some representative examples.

q-alg↗