scholarly journals CLIFFORD VALUED DIFFERENTIAL FORMS, AND SOME ISSUES IN GRAVITATION, ELECTROMAGNETISM AND "UNIFIED" THEORIES

2004 ◽  
Vol 13 (09) ◽  
pp. 1879-1915 ◽  
Author(s):  
W. A. RODRIGUES ◽  
E. CAPELAS DE OLIVEIRA
Keyword(s):  
Lie Algebra ◽  
Differential Forms ◽  
Linear Connection ◽  
Gravitational Theory ◽  
Momentum Conservation ◽  
Unified Field Theory ◽  
Mathematical Methods ◽  
Unified Field ◽  
Theory Of Gravitation ◽  
Local Trivialization

In this paper we show how to describe the general theory of a linear metric compatible connection with the theory of Clifford valued differential forms. This is done by realizing that for each spacetime point the Lie algebra of Clifford bivectors is isomorphic to the Lie algebra of [Formula: see text]. In that way the pullback of the linear connection under a local trivialization of the bundle (i.e., a choice of gauge) is represented by a Clifford valued 1-form. That observation makes it possible to realize immediately that Einstein's gravitational theory can be formulated in a way which is similar to a [Formula: see text] gauge theory. Such a theory is compared with other interesting mathematical formulations of Einstein's theory, and particularly with a supposedly "unified" field theory of gravitation and electromagnetism proposed by M. Sachs. We show that his identification of Maxwell equations within his formalism is not a valid one. Also, taking profit of the mathematical methods introduced in the paper we investigate a very polemical issue in Einstein gravitational theory, namely the problem of the 'energy–momentum' conservation. We show that many statements appearing in the literature are confusing or even wrong.

Unified Field Theory

1950 ◽  
Vol 2 ◽  
pp. 427-439 ◽  
Author(s):  
Max Wyman
Keyword(s):  
Field Theory ◽  
Variational Principle ◽  
Electromagnetic Fields ◽  
Linear Connection ◽  
Hamiltonian Function ◽  
Unified Theory ◽  
Unified Field Theory ◽  
Field Equations ◽  
Unified Field

Introduction. In a recent unified theory originated by Einstein and Straus [l], the gravitational and electromagnetic fields are represented by a single nonsymmetric tensor gy which is a function of four coordinates xr(r = 1, 2, 3, 4). In addition a non-symmetric linear connection Γjki is assumed for the space and a Hamiltonian function is defined in terms of gij and Γjki. By means of a variational principle in which the gij and Γjki are allowed to vary independently the field equations are obtained and can be written(0.1)(0.2)(0.3)(0.4)

The static spherically symmetric solutions in a unified field theory

1957 ◽  
Vol 53 (2) ◽  
pp. 489-493 ◽  
Author(s):  
John Moffat
Keyword(s):  
Charged Particle ◽  
Electric Energy ◽  
Gravitational Theory ◽  
Spherically Symmetric ◽  
Unified Field Theory ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Fundamental Properties ◽  
Unified Field ◽  
Conditions At Infinity

ABSTRACTA brief account is given of the fundamental properties of a new generalization ((1), (2)) of Einstein's gravitational theory. The field equations are then solved exactly for the case of a static spherically symmetric gravitational and electric field due to a charged particle at rest at the origin of the space-time coordinates. This solution provides information about the gravitational field produced by the electric energy surrounding a charged particle and yields the Coulomb potential field. The solution satisfies the required boundary conditions at infinity, and it reduces to the Schwarzschild solution of general relativity when the charge is zero.

The equations of motion in the non-symmetric unified field theory

1954 ◽  
Vol 226 (1166) ◽  
pp. 366-377 ◽  
Keyword(s):  
Equations Of Motion ◽  
Coulomb Force ◽  
Unified Field Theory ◽  
Field Equations ◽  
Original Theory ◽  
Unified Field ◽  
Theory Of Gravitation ◽  
The One ◽  
A Charge ◽  
Weak Fields

The field equations of the non-symmetric unified theory of gravitation and electromagnetism are changed so that they imply the existence of the Coulomb force between electric charges. It is shown that the equations of motion of charged masses then follow correctly to the order of approximation considered. The equations for weak fields in the modified theory are derived and shown to lead to Maxwell’s equations together with a restriction on the current density. This restriction is different from that in the original theory, and in the static, spherically symmetric case permits a charge distribution more likely to correspond to a particle. The failure of the original theory to lead to the equations of motion is related to the structure of the quantities appearing in it, and reasons are given for supposing that no nonsymmetric theory simpler than the one put forward is likely to give these equations in their conventional form.

A unified field theory of gravitation and electromagnetism

1953 ◽  
Vol 10 (3) ◽  
pp. 230-235 ◽  
Author(s):  
G. Stephenson ◽  
C. W. Kilmister
Keyword(s):  
Field Theory ◽  
Unified Field Theory ◽  
Unified Field ◽  
Theory Of Gravitation

scholarly journals Solution with Axial Symmetry of Einstein's Equations of Teleparallelism

1932 ◽  
Vol 3 (1) ◽  
pp. 37-45 ◽  
Author(s):  
J. D. Parsons
Keyword(s):  
Field Theory ◽  
General Solution ◽  
Axial Symmetry ◽  
Unified Field Theory ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
Unified Field ◽  
Theory Of Gravitation

In a recent paper Dr G. C. McVittie discussed the solution with axial symmetry of Einstein's new field-equations in his Unified Field Theory of Gravitation and Electricity. Owing to an error in his calculation of the field equations, Dr McVittie did not obtain the general solution, which we discuss in the present paper.

The Kerr–Newman metric in the nonsymmetric unified field theory

1976 ◽  
Vol 54 (12) ◽  
pp. 1274-1276 ◽  
Author(s):  
D. H. Boal
Keyword(s):  
Field Theory ◽  
Electromagnetic Field ◽  
Charged Particle ◽  
Unified Field Theory ◽  
Maxwell Theory ◽  
Antisymmetric Part ◽  
Unified Field ◽  
Theory Of Gravitation

The method introduced by Newman and Janis for obtaining the metric of a rotating, charged particle in the Einstein–Maxwell theory of gravitation and electromagnetism is examined in the context of the nonsymmetric unified field theory. It is found that a transformation very similar to theirs, when applied to the antisymmetric part of the tensor gμv, will generate the required electromagnetic field associated with the Kerr–Newman metric.

scholarly journals THE EXCEPTIONAL E8 GEOMETRY OF CLIFFORD (16) SUPERSPACE AND CONFORMAL GRAVITY YANG–MILLS GRAND UNIFICATION

2009 ◽  
Vol 06 (03) ◽  
pp. 385-417 ◽  
Author(s):  
CARLOS CASTRO PERELMAN
Keyword(s):  
Field Theory ◽  
Planck Scale ◽  
Gravitational Theory ◽  
Spin Connection ◽  
Conformal Gravity ◽  
Unified Field Theory ◽  
Yang Mills ◽  
Unified Field ◽  
Curved Slice ◽  
Symplectic Clifford Algebras

We continue to study the Chern–Simons E8 Gauge theory of Gravity developed by the author which is a unified field theory (at the Planck scale) of a Lanczos–Lovelock Gravitational theory with a E8 Generalized Yang–Mills (GYM) field theory, and is defined in the 15D boundary of a 16D bulk space. The Exceptional E8 Geometry of the 256-dim slice of the 256 × 256-dimensional flat Clifford (16) space is explicitly constructed based on a spin connection [Formula: see text], that gauges the generalized Lorentz transformations in the tangent space of the 256-dim curved slice, and the 256 × 256 components of the vielbein field [Formula: see text], that gauge the nonabelian translations. Thus, in one-scoop, the vielbein [Formula: see text] encodes all of the 248 (nonabelian) E8 generators and 8 additional (abelian) translations associated with the vectorial parts of the generators of the diagonal subalgebra [Cl(8) ⊗ Cl(8)] diag ⊂ Cl(16). The generalized curvature, Ricci tensor, Ricci scalar, torsion, torsion vector and the Einstein–Hilbert–Cartan action is constructed. A preliminary analysis of how to construct a Clifford Superspace (that is far richer than ordinary superspace) based on orthogonal and symplectic Clifford algebras is presented. Finally, it is shown how an E8 ordinary Yang–Mills in 8D, after a sequence of symmetry breaking processes E8 → E7 → E6 → SO(8, 2), and performing a Kaluza–Klein–Batakis compactification on CP2, involving a nontrivial torsion, leads to a (Conformal) Gravity and Yang–Mills theory based on the Standard Model in 4D. The conclusion is devoted to explaining how Conformal (super) Gravity and (super) Yang–Mills theory in any dimension can be embedded into a (super) Clifford-algebra-valued gauge field theory.

scholarly journals Uniting the wave and the particle in quantum mechanics

2019 ◽  
Vol 7 (1) ◽  
pp. 155-178 ◽  
Author(s):  
Peter Holland
Keyword(s):  
Quantum Mechanics ◽  
Time Reversal ◽  
Particle Interaction ◽  
Momentum Conservation ◽  
Quantum Potential ◽  
Inhomogeneous Equation ◽  
Unified Field Theory ◽  
Unified Field ◽  
Energy And Momentum ◽  
De Broglie Bohm

Abstract We present a unified field theory of wave and particle in quantum mechanics. This emerges from an investigation of three weaknesses in the de Broglie–Bohm theory: its reliance on the quantum probability formula to justify the particle-guidance equation; its insouciance regarding the absence of reciprocal action of the particle on the guiding wavefunction; and its lack of a unified model to represent its inseparable components. Following the author’s previous work, these problems are examined within an analytical framework by requiring that the wave–particle composite exhibits no observable differences with a quantum system. This scheme is implemented by appealing to symmetries (global gauge and spacetime translations) and imposing equality of the corresponding conserved Noether densities (matter, energy, and momentum) with their Schrödinger counterparts. In conjunction with the condition of time-reversal covariance, this implies the de Broglie–Bohm law for the particle where the quantum potential mediates the wave–particle interaction (we also show how the time-reversal assumption may be replaced by a statistical condition). The method clarifies the nature of the composite’s mass, and its energy and momentum conservation laws. Our principal result is the unification of the Schrödinger equation and the de Broglie–Bohm law in a single inhomogeneous equation whose solution amalgamates the wavefunction and a singular soliton model of the particle in a unified spacetime field. The wavefunction suffers no reaction from the particle since it is the homogeneous part of the unified field to whose source the particle contributes via the quantum potential. The theory is extended to many-body systems. We review de Broglie’s objections to the pilot-wave theory and suggest that our field-theoretic description provides a realization of his hitherto unfulfilled ‘double solution’ programme. A revised set of postulates for the de Broglie–Bohm theory is proposed in which the unified field is taken as the basic descriptive element of a physical system.

scholarly journals Weyl’s Raum-Zeit-Materie and the Philosophy of Science

2020 ◽  
pp. 185-196
Author(s):  
Silvia De Bianchi
Keyword(s):  
Field Theory ◽  
Philosophy Of Science ◽  
Western Philosophy ◽  
Unified Field Theory ◽  
Mathematical Methods ◽  
Important Distinction ◽  
Unified Field ◽  
History Of ◽  
Conceptual Underpinning ◽  
Philosophical Underpinning

Abstract In this contribution I explore  the philosophical underpinning of Weyl’s interpretation of Relativity as emerging from Raum-Zeit-Materie.  I emphasize the important distinction between the philosophical and the mathematical methods, as well as the dichotomy and relationship between time and consciousness. Weyl identified the latter as the conceptual engine moving the whole history of Western philosophy. and the revolutionary relevance of relativity for its representation is investigated together with the conceptual underpinning of Weyl’s philosophy of science. In identifying the main traits of Weyl’s philosophy of science in 1918, I also offer a philosophical analysis of some underlying concepts of unified field theory.

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