Gauge conditions in modern Kaluza–Klein theory

Self Cite

Technical results are presented on motion in N(Ͼ4)D manifolds to clarify the physics of brane theory, Kaluza-Klein theory, induced-matter theory, and string theory. The so-called canonical or warp metric in five dimensions ͑5D͒ effectively converts the manifold from a coordinate space to a momentum space, resulting in a new force ͑per unit mass͒ parallel to the four-dimensional ͑4D͒ velocity. The form of this extra force is actually independent of the form of the metric, but for an unbound particle is tiny because it is set by the energy density of the vacuum or cosmological constant. It can be related to a small change in the rest mass of a particle, and can be evaluated in two convenient gauges relevant to gravitational and quantum systems. In the quantum gauge, the extra force leads to Heisenberg's relation between increments in the position and momenta. If the 4D action is quantized then so is the higher-dimensional part, implying that particle mass is quantized, though only at a level of 10 Ϫ65 g or less, which is unobservably small. It is noted that massive particles which move on timeline paths in 4D can move on null paths in 5D. This agrees with the view from inflationary quantum field theory, that particles acquire mass dynamically in 4D but are intrinsically massless. A general prescription for dynamics is outlined, wherein particles move on null paths in an N(Ͼ4)D manifold which may be flat, but have masses set by an embedded 4D manifold which is curved.

Section: ͑411͒mentioning

confidence: 99%

On higher-dimensional dynamics

Wesson

2002

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“…[14][15][16] Since its inception the Kaluza-Klein idea has been studied under various gauge ͑coordinate͒ conditions. [17][18][19][20] The formalism has also been extended to the process of obtaining D-dimensional matter-gravity equations from (Dϩ1)-dimensional empty space-time Einstein equations. 21 Here we shall restrict ourselves to the original Dϭ4 case.…”

Section: Introductionmentioning

confidence: 99%

Static stringlike solutions in five-dimensional relativity. II

Gravel

2000

In this paper we find five-dimensional static strings solutions to Einstein's equations in the context of the induced-matter approach to higher dimensional relativity. This is done by separating Einstein's equations for a metric depending on a radius and the extra coordinate. Extending previous work, we consider the cases where the separation constants do not vanish. We find all elements of a decomposition of the four-dimensional induced-matter energy-momentum tensor necessary to identify perfect, heat and viscous parts. Corresponding metrics are found.

“…As a possible bridge between classical field theory and quantum theory, there has in recent years been significant work on wavelike solutions on 5D manifolds which might be interpreted as four-dimensional ͑4D͒ particles. [2][3][4][5] In the present work we wish to give fairly generic accounts of three overlapping problems in this area.…”

Section: Introductionmentioning

confidence: 99%

Waves and particles in Kaluza–Klein theory

Sajko

Wesson

Liu

1999

We examine three overlapping problems in the application of five-dimensional ͑5D͒ manifolds to physics. First, we linearize the 5D theory along the lines of the four-dimensional ͑4D͒ theory, using the harmonic gauge condition. The resulting wave equations have sources, and can in principle describe gravitons and scalar particles with finite masses, but the natural choice of gauge parameters makes both massless. Second, we generalize the 5D metric by including separate conformal factors on its 4D and extra parts. Then the 5D harmonic gauge gives back the 4D harmonic gauge of gravitational waves and the Lorentz gauge of electromagnetic waves, but both particles are massless. Third, we again take a conformally rescaled metric, but rewrite the field equations in a novel manner. This allows us to interpret the finite masses of ordinary particles in terms of the wavelengths associated with 4D spaces embedded in a 5D space.