On Weyl's gauge field

Utiyama, Ryôyû

doi:10.1007/bf00766599

Cited by 26 publications

(36 citation statements)

References 2 publications

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“…Its vector potential is the Weyl vector, and its strength is Weyl's segmental curvature tensor arising in the geometrical interpretation of the theory together with the curvature and torsion tensors. The dilatation gauge field does not coincide with electromagnetic field (that has been asserted by Weyl in his basic work [2]) but represents a field of another type [3]. In particular, quanta of this field can have nonzero rest masses.…”

Section: Introductionmentioning

confidence: 99%

Dark Energy as a Cosmological Consequence of Existence of the Dirac Scalar Field in Nature

Babourova

Frolov

2015

Physics Research International

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The solution of the field equations of the conformal theory of gravitation with Dirac scalar field in Cartan-Weyl spacetime at the very early Universe is obtained. In this theory dark energy (described by an effective cosmological constant) is a function of the Dirac scalar field . This solution describes the exponential decreasing of at the inflation stage and has a limit to a constant value of the dark energy at large time. This can give a way to solving the fundamental cosmological constant problem as a consequence of the fields dynamics in the early Universe.

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Section: Introductionmentioning

confidence: 99%

Dark Energy as a Cosmological Consequence of Existence of the Dirac Scalar Field in Nature

Babourova

Frolov

2015

Physics Research International

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“…Second, in contrast to [27], [28], this Lagrangian retains gauge invariance but allows a nonzero mass for the quantum of the Weyl nonmetricity vector field and hence also for the dilatation gauge field. This suggests that the gauge field introduced in localizing the group of scale transformations is not an electromagnetic field (in contrast to Weyl's initial idea) but a field of a different nature, as indicated in [40]- [42]. The existence of the Weyl field mass can play a positive role in interpreting modern observational data based on using post-Riemannian cosmological models [37], [38] and also in possibly explaining a graceful exit from the inflationary stage.…”

Section: Discussionmentioning

confidence: 89%

A Weyl-Cartan space-time model based on the gauge principle

2008

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Based on the requirement that the gauge invariance principle for the Poincaré-Weyl group be satisfied for the space-time manifold, we construct a model of space-time with the geometric structure of a WeylCartan space. We show that three types of fields must then be introduced as the gauge ("compensating") fields: Lorentz, translational, and dilatational. Tetrad coefficients then become functions of these gauge fields. We propose a geometric interpretation of the Dirac scalar field. We obtain general equations for the gauge fields, whose sources can be the energy-momentum tensor, the total momentum, and the total dilatation current of an external field. We consider the example of a direct coupling of the gauge field to the orbital momentum of the spinor field. We propose a gravitational field Lagrangian with gauge-invariant transformations of the Poincaré-Weyl group.

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“…Bramson (1974) gives a spinor formulation. Pandres and Zund (1974) derive them from Dirac's (1973) theory-which is identical in structure to the theories proposed by Omote (1971Omote ( , 1974, Lord (1972), Freund (1974 and Utiyama (1975) -Hoyle andNarlikar (1964, 1974) derive them as a smooth-fluid approximation to their conformally invariant action-at-a-distance theory, and most recently Canuto er a1 (1977) have used the same equations, i.e. invariant under the transformation 0305-4470/79/030367 + 07$01.00 @ 1979 The Institute of Physics Now, in units with c = h = 1 so that length and time are measured with the same unit and mass with the inverse length unit (the mass of a particle m is given by m = qu where q is a dimensionless constant associated with the particle, called its inertial charge), the transformation (2) represents a space-time-dependent change in the length unit.…”

Section: Introductionmentioning

confidence: 73%

Rearrangements in Vinyl Cations

Щеголев¹,

Kanishchev²

1981

Russ. Chem. Rev.

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In this, the first of a pair of related papers, it is argued that general relativity allows more freedom in the choice of the metric than is usually supposed. In particular, conformally equivalent classes of metrics are to be regarded as physically equivalent. The theory is thus conformally invariant-a fact which is obscured by the non-conformally covariant way in which the field equations are usually written. Furthermore, there may be situations in which this usual way of writing the field equations is liable to give misleading results in the same way that a bad choice of coordinate system can lead to non-physical results. Another representation is given which does not suffer from this disadvantage and in a companion paper we shall apply this new representation to the problem of black holes and obtain some rather surprising results.

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On Weyl's gauge field

Cited by 26 publications

References 2 publications

Dark Energy as a Cosmological Consequence of Existence of the Dirac Scalar Field in Nature

Dark Energy as a Cosmological Consequence of Existence of the Dirac Scalar Field in Nature

A Weyl-Cartan space-time model based on the gauge principle

Rearrangements in Vinyl Cations

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