Weyl Gauge Field Research Articles

Weyl's Gauge Field and Its Behavior

Using a manifestly gauge-invariant Lagrangian density of a system in which a real scalar field (matter field) is interacting with itself and with Weyl's gauge field, we shall study equations of the real scalar field and of Weyl's gauge field, and discuss the self-interacting term of the real scalar field. For a special self-interacting term, we shall obtain an equation of only Weyl's gauge field which plays an important role in solving the equation of Weyl's gauge field interacting with the real scalar field. By making use of the above mentioned equation we shall obtain a rigorous solution for Weyl's gauge field. Next, combining the equation of only Weyl's gauge field with the condition in Weyl's gauge field that the length scale of any vector changes under parallel transfer, we shall obtain a nonlinear equation for the length scale of Weyl's gauge field, which may be important in mathematical physics and is shown to have meron-type solution. By making use of the same techniques being used above, we shall study solution of equation of gradient Weyl's gauge field and as a result, obtain a nonlinear equation of the same type as being found above. Finally we shall study relation between local gauge transformation and symmetric connection in space-time. As a result, we can partly make clear relation between the change in the measure of length scale of a vector due to an infinitesimal parallel transfer and the coefficients of affine connection of Weyl's geometry.

Conformal invariance and space-time torsion

A new conformal invariant theory of gravitation is proposed. It is based on the Riemann-Cartan geometry of space-time the torsion playing the role of the effective Weyl gauge field. This theory naturally arises in the framework of the Poincaré gauge theory, providing new insight into the underlying fibre bundle structure.

Weyl scalings and spinor matter interactions in scalar-tensor theories of gravitation

An SL(2, C) gauge formulation of a scalar-tensor theory of gravitation is related to the Brans-Dicke theory in the absence of spinorial matter couplings although the natural connection of space-time has a torsion determined by the scalar field. Simplified scaling properties of gravitational variables are elucidated in this geometry. In the presence of matter with intrinsic spin a natural scalar-spinor coupling is exposed. A locally scale invariant limit exists without a Weyl gauge field.

Remarks on Weyl's Gauge Field

As opposed to a recent claim that Weyl’s gauge field has a negative energy density, it is shown that the gauge field has a positive energy density, thus having a normal behaviour. Furthermore, Weyl’s gauge field is shown to interact with a special kind of spin-1/2 non-canonical spinor field, while a previous paper shows that it does not couple to a spin-1/2 canonical spinor field. It is, however, found that Weyl’s gauge field cannot have such a universal geometrical nature at all as the gravitational field gµν has, contrary to the original Weyl’s intention.

Elementary Particles and Weyl's Gauge Field

The first equation on p. 437 should read: Aijλ = A[ij]λ = Δijλ + Kijλ + eλk (GkiBj - GkjBi).

Elementary Particles and Weyl's Gauge Field

Elementary Particles and Weyl's Gauge Field

Elementary Particles and Weyl's Gauge Field

In the conventional theory of the conformal transformation of the metric tensor, only tensor fields can be treated. A general theoretical framework is presented such that both tensor and spinor fields can be incorporated. We define a conformal transformation of a metric spinor, for which a spinor basis is invariant, and we also define a scale transformation of a spinor basis, for which a metric spinor is invariant. It is shown that a particular mixing of a conformal transformation and a scale transformation gives rise to the usual conformal transformation of the metric tensor. Furthermore, it is proven that Weyl's gauge field does not couple to any elementary particle of spin 1/2, quite independently of its conformal weight.

Some structurological remarks on a nonlocal field

In this paper, continued from the last paper (Ikeda, 1974), two kinds of structurological generalizations of our nonlocal field (i.e., the (x, ψ) field) are considered physicogeometrically. One is a Finslerian generalization, where the base field [i.e., the (x) field] is extended to a Finslerian field and Weyl's gauge field (i.e., the electromagnetic potential) is physically identified with the directional vector adopted as the internal variable in the ordinary nonlocal field theory. Another is a generalization by which the spinor (ψ) itself is taken as an independent variable, where some inherent characteristics ofψ are fused into the spatial structure. The latter is regarded as a “nonlocalization” of the (x) field accomplished by attachingψ to each point, in the true sense of the word. Particularly, the spatial structures of these generalized nonlocal fields are described in detail.

On Weyl's gauge field

A new scalar field, called a measure field, is proposed which plays a role of measure assigned to each world point. By measuring all the quantities with a standard given by the above mentioned measure field, it is shown to be possible to write all the field equations in a manifestly gauge-invariant manner. Weyl's gauge field, when it is written in this fashion, is proved to have a negative energy density and has a tachyon-like property inside material particles. It is shown, however, that such a strange field can not come out of the matter.

On Weyl's Gauge Field. II

On Weyl's Gauge Field. II

On weyl's gauge field in a non-local field

In this paper, a non-local field (i.e. the (x, ψ)-field) is constructed by regarding the spinor (ψ) as the internal freedom attached to each point (x). Since this field is likened to a unified field between the (x)- and (ψ)-fields, the metric is given bydσψ=gλ dxλψ. Concerning this, some conformally equivalent relations are considered. Next, Weyl's gauge field is introduced into the concept of connection in order to consider the gauge invariance. Finally, some essential features underlying our non-local field are grasped by formulating some fundamental equations of the spin curvature tensors.

On Weyl's Gauge Field

A new scalar field, called a measure field, is proposed which plays a role of measure assigned to each world point. By measuring all the quantities with a standard given by the above mentioned measure field, it is shown to be possible to write all the field equations in a manifestly gauge-invariant manner. Weyl's gauge field, when it is written in this fashion, is proved to have a negative energy density and has a tachyon-like property inside material particles. It is shown, however, that such a strange field can not come out of the matter.