Massive tensor fields in Kaluza-Klein theory and BRS symmetry

This is the first paper in a series of three papers on a new approach for space-time-matter (STM) theory. The main purpose of this approach is to replace the Levi-Civita connection on the space-time from the classical Kaluza–Klein theory by what we call the Riemannian horizontal connection on the general Kaluza–Klein space. This is done by a development of a 4D tensor calculus whose geometrical objects live in a 5D space. The 4D tensor calculus and the Riemannian horizontal connection enable us to define in a 5D space some 4D differential operators: horizontal differential, horizontal gradient, horizontal divergence and horizontal Laplacian, which have a great role in the presentation of the STM theory in a covariant form. Finally, we introduce and study the horizontal electromagnetic tensor field, the horizontal Ricci tensor and the horizontal Einstein gravitational tensor field, which replace the well-known tensor fields from the classical Kaluza–Klein theory.

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A DISCRETIZED VERSION OF KALUZA–KLEIN THEORY WITH TORSION AND MASSIVE FIELDS

International Journal of Modern Physics A ◽

10.1142/s0217751x96001206 ◽

1996 ◽

Vol 11 (13) ◽

pp. 2403-2418 ◽

Cited By ~ 7

Author(s):

NGUYEN AI VIET ◽

KAMESHWAR C. WALI

Keyword(s):

Noncommutative Geometry ◽

Vector Fields ◽

Complex Structure ◽

Scalar Fields ◽

Type Model ◽

Internal Space ◽

Tensor Fields ◽

Fifth Dimension ◽

Klein Theory ◽

Kaluza Klein

We consider an internal space of two discrete points in the fifth dimension of the Kaluza–Klein theory by using the formalism of noncommutative geometry — developed in a previous paper1 — of a spacetime supplemented by two discrete points. With the non-vanishing internal torsion two-form there are no constraints implied on the vielbeins. The theory contains a pair of tensor fields, a pair of vector fields and a pair of scalar fields. Using the generalized Cartan structure equation we are able to uniquely determine not only the Hermitian and metric-compatible connection one-forms, but also the nonvanishing internal torsion two-form in terms of vielbeins. The resulting action has a rich and complex structure, a particular feature being the existence of massive modes. Thus the nonvanishing internal torsion generates a Kaluza–Klein type model with zero and massive modes.

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Kaluza-Klein theory and extended BRS symmetry

Physics Letters B ◽

10.1016/0370-2693(82)90352-5 ◽

1982 ◽

Vol 114 (5) ◽

pp. 315-318 ◽

Cited By ~ 3

Author(s):

Yoshiaki Ohkuwa

Keyword(s):

Klein Theory ◽

Brs Symmetry ◽

Kaluza Klein

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Supersymmetry: Kaluza-Klein theory, anomalies, and superstrings

Uspekhi Fizicheskih Nauk ◽

10.3367/ufnr.0146.198508e.0655 ◽

1985 ◽

Vol 146 (8) ◽

pp. 655 ◽

Cited By ~ 38

Author(s):

I.Ya. Aref'eva ◽

I.V. Volovich

Keyword(s):

Klein Theory ◽

Kaluza Klein

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Euler-Poincaré lagrangians and Kaluza-Klein theory

Physics Letters B ◽

10.1016/0370-2693(87)91276-7 ◽

1987 ◽

Vol 189 (1-2) ◽

pp. 96-98 ◽

Cited By ~ 16

Author(s):

M. Arik ◽

T. Dereli

Keyword(s):

Klein Theory ◽

Kaluza Klein

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4D Einstein equations in a general gauge Kaluza–Klein space

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s021988781550036x ◽

2015 ◽

Vol 12 (03) ◽

pp. 1550036

Author(s):

Aurel Bejancu ◽

Constantin Călin

Keyword(s):

Einstein Equations ◽

Tensor Fields ◽

New Approach ◽

Higher Dimensional ◽

High Level ◽

General Gauge ◽

Kaluza Klein

Using the new approach on higher-dimensional Kaluza–Klein theories developed by the first author, we obtain the 4D Einstein equations on a (4 + n)D relativistic gauge Kaluza–Klein space. Adapted frame and coframe fields, adapted tensor fields, and the Riemannian adapted connection, have a fundamental role in the study. The high level of generality of the study, enables us to recover several results from earlier papers on this matter.

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PHYSICAL ASPECTS OF SOLITONS IN (4+1) GRAVITY

International Journal of Modern Physics D ◽

10.1142/s0218271895000430 ◽

1995 ◽

Vol 04 (05) ◽

pp. 639-659 ◽

Cited By ~ 12

Author(s):

ANDREW BILLYARD ◽

PAUL S. WESSON ◽

DIMITRI KALLIGAS

Keyword(s):

Physical Properties ◽

Extra Dimension ◽

Dimensional Case ◽

Schwarzschild Solution ◽

Circular Orbits ◽

Know How ◽

Fifth Dimension ◽

Klein Theory ◽

Limiting Case ◽

Kaluza Klein

The augmentation of general relativity’s spacetime by one or more dimensions is described by Kaluza-Klein theory and is within testable limits. Should an extra dimension be observable and significant, it would be beneficial to know how physical properties would differ from “conventional” relativity. In examining the class of five-dimensional solutions analogous to the four-dimensional Schwarzschild solution, we examine where the origin to the system is located and note that it can differ from the four-dimensional case. Furthermore, we study circular orbits and find that the 5D case is much richer; photons can have stable circular orbits in some instances, and stable orbits can exist right to the new origin in others. Finally, we derive both gravitational and inertial masses and find that they do not generally agree, although they can in a limiting case. For all three examinations, it is possible to obtain the four-dimensional results in one limiting case, that of the Schwarzschild solution plus a flat fifth dimension, and that the differences between 4D and 5D occur when the fifth dimension obtains any sort of significance.

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