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Unification through higher dimensions

Thomas W. Appelquist

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Abstract

A brief history and a summary of recent developments in Kaluza‐Klein theories is presented. In these theories a unification of gravity with the other forces of nature is attempted by starting with a purely gravitational (or super‐gravitational) theory in more than four space‐time dimensions. Some dynamical schemes are described for the necessary compactification of the extra dimensions into manifolds with a size on the order of the Planck length. Special emphasis is given to the possible role of quantum effects, in the form of Casimir energies associated with the compact geometries. Finally, the major problems which stand in the way of generating realistic Kaluza‐Klein theories are outlined.

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What this paper is about

A brief history and a summary of recent developments in Kaluza‐Klein theories is presented. In these theories a unification of gravity with the other forces of nature is attempted by starting with a purely gravitational (or super‐gravitational) theory in more than four space‐time dimensions. Some dynamical schemes are described for the necessary compactification of the extra dimensions into manifolds with a size on the order of the Planck length. Special emphasis is given to the possible role of quantum effects, in the form of Casimir energies associated with the compact geometries. Finally, the major problems which stand in the way of generating realistic Kaluza‐Klein theories are outlined.

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Available abstract

A brief history and a summary of recent developments in Kaluza‐Klein theories is presented. In these theories a unification of gravity with the other forces of nature is attempted by starting with a purely gravitational (or super‐gravitational) theory in more than four space‐time dimensions. Some dynamical schemes are described for the necessary compactification of the extra dimensions into manifolds with a size on the order of the Planck length. Special emphasis is given to the possible role of quantum effects, in the form of Casimir energies associated with the compact geometries. Finally, the major problems which stand in the way of generating realistic Kaluza‐Klein theories are outlined.

Key concepts: Kaluza–Klein theory, Unification, Theoretical physics, Extra dimensions, Gravitation, Casimir effect, Compactification (mathematics), Physics

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