Cartan theory of gravitation with elko spinors as sources of curvature and torsion. The dynamical structure of the einsteincartansciama. It has been shown that unlike the consequences of exterior derivative in einstein spacetime, the repetition of d on a form of any degree is not zero. Evans, alpha institute for advanced study, civil list scientist. In this work we analyze in detail the physics of einstein cartan theory with dirac and maxwell fields minimally coupled to the. On the role of einstein cartan gravity in fundamental particle physics this site is for comments and questions about our recent paper, entitled on the role of einstein cartan gravity in fundamental particle physics, which can be found here. The dynamical variables in einstein cartan theory are the vierbein and the spin connection 6. Gravity meets particle physics via einsteincartan torsion. I believe the term that has been adopted in the literature is einstein cartan theory. Abstract einstein cartan theory is an extension of the standard formulation of general relativity where torsion the antisymmetric part of the af. Einsteincartanevans theory or ece theory was an attempted unified theory of physics proposed by the welsh chemist and physicist myron wyn evans may 26, 1950 may 2, 2019, which claimed to unify general relativity, quantum mechanics and electromagnetism. Delphenich in the following pages, i propose to discuss, in a geometrically intuitive fashion, the unitary theory of gravitation and electricity that einstein, in collaboration with mayer, published in 1931 in the sitzungsberichte of the berlin academy 1. Felker, reno, nevada, usa version 2a, updated 20200504 summary although physicists have struggled in vain for over a halfcentury to encompass all natural forces within a unified theory, chemical physicist myron w. H in this paper, we show that a generalized or powerlaw inflationary and superinflationary epoch arises naturally and inevitably in the early universe in a cosmological model in the einstein cartan gravitation theory with the improved energymomentum.
Einstein cartan theory is an extension of the standard formulation of general relativity characterized by a nonvanishing torsion. On the interpretation of the einsteincartan formalism 479 material charges and currents. In hehls opinion einsteincartan theory is an even more beautiful theory than einstein s general relativity because of its relation to the poincare group. The einstein cartan theory of gravitation and the classical theory of defects in an elastic medium are presented and compared. I in a riemann cartan spacetime the di erence between the. The einsteincartan theory ect of gravity is a modification of general relativity theory grt, allowing spacetime to have torsion, in addition to curvature, and relating torsion to the density of intrinsic angular momentum. The einsteincartan theory ect of gravity is a modi. Physicists still need to combine the einstein cartan sciamakibble theory fully with quantum mechanics into a quantum theory of gravity. In general relativity, an analysis of the theory of spacelike congruence, i. I just tought since i ran accross this question without an. This book presents the first of the unified field theory papers starting from 2003, after the above problems were finally addressed. Einsteincartan theory, and its derivation from an action i think this is usually presented in the tetrad formalism, but obviously is a more specific thing and possibly harder to find.
Just as the spacetime metric is sourced by the stressenergy tensor of the matter fields, torsion is sourced via the spin density tensor, whose physical effects become relevant at very high spin densities. The hypothesis was largely published in the journal foundations of physics letters between 2003 and 2005. We see that the einstein connection is the gravitational analogue of the g field in electrodynamics. Like the gap field, the tap field is symmetric in its indices. Emergent cosmos in einsteincartan theory pdf paperity.
Pdf einsteincartan theory as a theory of defects in. It is asymmetric in the lower indices and its antisymmetric part is the torsion tensor. The former is an extension of general relativity and refers to fourdimensional spacetime, while we introduce the latter as. One of the major issues that must be addressed by any uni ed theory is the disparity in the approaches to the sm and gr. To find the simplest hamiltonian formalism for this theory, we choose one leg of the vierbein field to be normal to the hypersurface x0 const. This site uses cookies to deliver our services, improve performance, for analytics, and if not signed in for advertising.
On the conformal unity between quantum particles and. Topological gauge theory, cartan geometry, and gravity by derek keith wise. Free fulltext pdf articles from hundreds of disciplines, all in one place. In his analysis he has introduced an observer moving with a 4velocity wa. Einsteincartan gravity in particle physics and cosmology. Supported in part by the national science foundation under grants gf. Merge articles on einstein cartan theory and einstein cartan sciamakibble theory. Cartan s equations of structure are also derived through the new derivative operator. There have been many different attempts at constructing an ideal theory of gravity these attempts can be split into four broad categories based on their scope. Einsteincartandirac gravity with u 1 symmetry breaking. It has been described as the most beautiful of all the existing physical theories 1. After minimally coupling the elko spinors to torsion, the spin angular mome.
The cartan size may introduce an effective uv cutoff for fermionic quantum field theory. On the interpretation of the einsteincartan formalism. The einstein cartan theory ect of gravity is a modification of general relativity theory grt, allowing spacetime to have torsion, in addition to curvature, and relating torsion to the density of intrinsic angular momentum. I agree with the suggestion to merge the wikipedia articles on einstein cartan theory ec and einstein cartan sciamakibble theory ecsk.
Einsteincartan theory as an averaged theory of gravity. Derivation of the local lorentz gauge transformation of a dirac spinor field in quantum einstein cartan theory rainer w. In addition to introducting matter injection through a scalar field determined by prycehoyle tensor, we also combine with a bcde bransdicke and einstein. A key result of the paper is the following fundamental radius, which is a function only of the planck length and the fine structure constant. The coupling between the spin of elementary particles and torsion in the einstein cartan theory of gravity generates gravitational repulsion at extremely high densities in fermionic matter, approximated as a spin. In einstein s theory of gravitation, mass directly influences the geometry but spin. Topological gauge theory, and gravity derek keith wise. Introducing ece theory 19251950 einstein struggled unsuccessfully to combine electromagnetism and gravity using a torsion based geometry developed by cartan.
Einstein cartan theory is an extension of the standard formulation of general relativity where torsion the antisymmetric part of the affine connection is nonvanishing. We discuss the formalism of principal bundles, principal connections, curvature forms, gauge. Annals of physics 158, 320373 1984 the dynamical structure of the einsteincartan sciamakibble theory of gravity wiktor szczyrba institute of mathematics, polish academy of sciences, ul. This modification was put forward in 1922 by elie cartan, before the discovery of spin. Cartan proposed einstein cartan theory ec to einstein in the 1920s because affine torsion is basic differential geometry. This is because the os model is rather idealized and pressures as well as. But in 3 dimensions the einstein tensor vanishes if and only if the full riemann curvature tensor does.
Einstein cartan theory with the raysmalley improved energymomentum tensor with spin. Introduction einstein s general theory of relativity is the most successful theory of gravitation. The einsteincartan theory of gravitation in a hamiltonian. The latter is sourced by the matter fields via the spin tensor, and its effects are expected to be important at very high spin densities. Elie cartan, author of the theory of spinors, on librarything. The einsteincartan theory ect of gravity is a modification of general relativity theory grt, allowing spacetime to have torsion, in addition to curvature, and relating torsion to the. It also appears as a remedy to several major problems of current theory of gravity and cosmology. Phantom dark ghost in einstein cartan gravity phantom dark ghost in einstein cartan gravity. The einstein cartan theory of gravitation is discussed in a hamiltonian form. What makes a gauge theory topological is a somewhat subjective matter. Derivation of the local lorentz gauge transformation of a.