scholarly journals Modifying the theory of gravity by changing independent variables

2018 ◽  
Vol 191 ◽  
pp. 07007
Author(s):  
N.V. Kharuk ◽  
S.N. Manida ◽  
S.A. Paston ◽  
A.A. Sheykin
Keyword(s):  
Symmetry Group ◽  
Electromagnetic Interaction ◽  
Local Symmetry ◽  
Electromagnetic Potential ◽  
Weyl Spinor ◽  
Independent Variables ◽  
Spinor Fields ◽  
Theory Of Gravity ◽  
Natural Way

We study some particular modifications of gravity in search for a natural way to unify the gravitational and electromagnetic interaction. The certain components of connection in the appearing variants of the theory can be identified with electromagnetic potential. The methods of adding matter in the form of scalar and spinor fields are studied. In particular, the expansion of the local symmetry group up to GL(2,C) is explored, in which equations of Einstein, Maxwell and Dirac are reproduced for the theory with Weyl spinor.

Exotic Holonomies ${\rm E}^{(a)}_7$

1997 ◽  
Vol 08 (05) ◽  
pp. 583-594 ◽  
Author(s):  
Quo-Shin Chi ◽  
Sergey Merkulov ◽  
Lorenz Schwachhöfer
Keyword(s):  
Symmetry Group ◽  
Lie Groups ◽  
Lie Group ◽  
Moduli Spaces ◽  
Local Symmetry ◽  
Positive Dimension ◽  
Affine Connections ◽  
Finite Dimensional ◽  
Torsion Free

It is proved that the Lie groups [Formula: see text] and [Formula: see text] represented in ℝ56 and the Lie group [Formula: see text] represented in ℝ112 occur as holonomies of torsion-free affine connections. It is also shown that the moduli spaces of torsion-free affine connections with these holonomies are finite dimensional, and that every such connection has a local symmetry group of positive dimension.

scholarly journals Skyrmions, Quantum Hall Droplets, and one current to rule them all

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Avner Karasik
Keyword(s):  
Vector Fields ◽  
Quantum Hall ◽  
Local Symmetry ◽  
Effective Theory ◽  
Vector Mesons ◽  
Low Energies ◽  
Baryon Current ◽  
Chern Simons ◽  
Natural Way

We introduce a novel Skyrme-like conserved current in the effective theory of pions and vector mesons based on the idea of hidden local symmetry. The associated charge is equivalent to the skyrmion charge for any smooth configuration. In addition, there exist singular configurations that can be identified as N_f=1Nf=1 baryons charged under the new symmetry. Under this identification, the vector mesons play the role of the Chern-Simons vector fields living on the quantum Hall droplet that forms the N_f=1Nf=1 baryon. We propose that this current is the correct effective expression for the baryon current at low energies. This proposal gives a unified picture for the two types of baryons and allows them to continuously transform one to the other in a natural way. In addition, Chern-Simons dualities on the droplet can be interpreted as a result of Seiberg-like duality between gluons and vector mesons.

scholarly journals ELKO SPINOR FIELDS: LAGRANGIANS FOR GRAVITY DERIVED FROM SUPERGRAVITY

2009 ◽  
Vol 06 (03) ◽  
pp. 461-477 ◽  
Author(s):  
ROLDÃO DA ROCHA ◽  
J. M. HOFF DA SILVA
Keyword(s):  
Spinor Field ◽  
Sufficient Conditions ◽  
Dirac Spinor ◽  
Weyl Spinor ◽  
Conjugation Operator ◽  
Spinor Fields ◽  
Mass Dimension ◽  
Majorana Spinor ◽  
Dimension One ◽  
Elko Spinor Fields

Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields) belong — together with Majorana spinor fields — to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class-(5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three respectively corresponding to flagpole, flag-dipole and Weyl spinor fields. Using the mapping from ELKO spinor fields to the three classes Dirac spinor fields, it is shown that the Einstein–Hilbert, the Einstein–Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), as the prime Lagrangian for supergravity. The Holst action is related to the Ashtekar's quantum gravity formulation. To each one of these classes, there corresponds a unique kind of action for a covariant gravity theory. Furthermore we consider the necessary and sufficient conditions to map Dirac spinor fields (DSFs) to ELKO, in order to naturally extend the Standard Model to spinor fields possessing mass dimension one. As ELKO is a prime candidate to describe dark matter and can be obtained from the DSFs, via a mapping explicitly constructed that does not preserve spinor field classes, we prove that — in particular — the Einstein–Hilbert, Einstein–Palatini, and Holst actions can be derived from the QSL, as a fundamental Lagrangian for supergravity, via ELKO spinor fields. The geometric meaning of the mass dimension-transmuting operator — leading ELKO Lagrangian into the Dirac Lagrangian — is also pointed out, together with its relationship to the instanton Hopf fibration.

scholarly journals Gravitoelectromagnetic inflation and seeds of cosmic magnetic fields from geometrical Weyl-invariant scalar–tensor theory of gravity

2019 ◽  
Vol 97 (5) ◽  
pp. 517-523 ◽  
Author(s):  
M. Montes ◽  
José Edgar Madriz Aguilar ◽  
V. Granados
Keyword(s):  
Magnetic Fields ◽  
Power Spectrum ◽  
Electromagnetic Potential ◽  
Scalar Tensor Theory ◽  
Scale Invariant ◽  
Inflaton Field ◽  
Tensor Theory ◽  
Invariant Scalar ◽  
Theory Of Gravity ◽  
Good Agreement

We investigate cosmological inflationary scenarios from a gravitoelectromagnetic theory. Our work is formulated in light of a recently introduced geometrical Weyl-invariant scalar–tensor theory of gravity, where the nature of both the electromagnetic potential and the inflaton field is attributed to the space–time geometry. We obtain a Harrison–Zeldovich power spectrum for quantum fluctuations of the inflaton field. In our model the electromagnetic fields also have a nearly scale-invariant power spectrum for a power-law inflation. We found that the seed magnetic fields have a nearly scale-invariant power spectrum and generate at the present time cosmic magnetic fields of the order ≲10−9 G, in good agreement with CMB observations.

scholarly journals Comparing the constructions of Goldberg, Fuller, Caspar, Klug and Coxeter, and a general approach to local symmetry-preserving operations

2017 ◽  
Vol 473 (2206) ◽  
pp. 20170267 ◽  
Author(s):  
Gunnar Brinkmann ◽  
Pieter Goetschalckx ◽  
Stan Schein
Keyword(s):  
Symmetry Group ◽  
Local Symmetry ◽  
Icosahedral Symmetry ◽  
Platonic Solids ◽  
Global Properties ◽  
Archimedean Solids

The use of operations on polyhedra possibly dates back to the ancient Greeks, who were the first to describe the Archimedean solids, which can be constructed from the Platonic solids by local symmetry-preserving operations (e.g. truncation) on the solid. By contrast, the results of decorations of polyhedra, e.g. by Islamic artists and by Escher, have been interpreted as decorated polyhedra—and not as new and different polyhedra. Only by interpreting decorations as combinatorial operations does it become clear how closely these two approaches are connected. In this article, we first sketch and compare the operations of Goldberg, Fuller, Caspar & Klug and Coxeter to construct polyhedra with icosahedral symmetry, where all faces are pentagons or hexagons and all vertices have three neighbours. We point out and correct an error in Goldberg’s construction. In addition, we transform the term symmetry-preserving into an exact requirement. This goal, symmetry-preserving, could also be obtained by taking global properties into account, e.g. the symmetry group itself, so we make precise the terms local and operation . As a result, we can generalize Goldberg’s approach to a systematic one that uses chamber operations to encompass all local symmetry-preserving operations on polyhedra.

Tetrads in SU(N) Yang–Mills geometrodynamics

2019 ◽  
Vol 34 (29) ◽  
pp. 1950161 ◽  
Author(s):  
Alcides Garat
Keyword(s):  
Gravitational Field ◽  
Symmetry Group ◽  
Particle Physics ◽  
Local Symmetry ◽  
Lorentzian Space ◽  
Gauge Groups ◽  
Yang Mills ◽  
Quantum Numbers ◽  
Products Of Groups ◽  
Group Of Symmetries

The discovery of the [Formula: see text] symmetry was fundamental as to establishing an ordering principle in particle physics. We already studied how to couple the [Formula: see text] symmetry to the gravitational field in four-dimensional curved Lorentzian space–times. The multiplets of equal quantum numbers are translated through natural elements in Riemannian geometry into local multiplets of equal gravitational field. As quark physics developed since in the 1970s, it was necessary to incorporate new symmetries to the models, that ensued in the incorporation of new quantum numbers like charm, for example, charm is an additive quantum number like isospin [Formula: see text] and hypercharge [Formula: see text] and the standard [Formula: see text] diagrams were extended onto another third axis. Then, instead of the fundamental triplet, we have a quartet [Formula: see text] as the smallest representation of the symmetry group, leading to the introduction of [Formula: see text] as the new group of symmetries. In this paper, we will not restrict ourselves exclusively to the symmetry group [Formula: see text] and we will set out to analyze the coupling of the [Formula: see text] symmetry to the gravitational field. To this end, new tetrads will be introduced as we did for the [Formula: see text] case. These tetrads have outstanding properties that enable these constructions. New theorems will be proved regarding the isomorphic nature of these local symmetry gauge groups and tensor products of groups of local tetrad transformations. This is a paper about grand field unification in four-dimensional curved Lorentzian space–times.

scholarly journals Topological states from topological crystals

2019 ◽  
Vol 5 (12) ◽  
pp. eaax2007 ◽  
Author(s):  
Zhida Song ◽  
Sheng-Jie Huang ◽  
Yang Qi ◽  
Chen Fang ◽  
Michael Hermele
Keyword(s):  
Symmetry Group ◽  
Local Symmetry ◽  
Real Space ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Space Groups ◽  
Topological States ◽  
Topological Crystalline Insulators ◽  
Symmetry Protected ◽  
Open Edge

We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry-protected topological states can be adiabatically deformed into a special class of states we call topological crystals. A topological crystal in, for example, three dimensions is a real-space assembly of finite-sized pieces of topological states in one and two dimensions protected by the local symmetry group alone, arranged in a configuration invariant under the spatial group and glued together such that there is no open edge or end. As a demonstration of principle, we explicitly enumerate all inequivalent topological crystals for noninteracting time-reversal symmetric electronic insulators with spin-orbit coupling and any one of the 230 space groups. This enumeration gives topological crystalline insulators a full classification.

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