The String Deviation Equation

It is well known that the relative motion of many particles can be described by the geodesic deviation equation. Less well known is that the geodesic deviation equation can be derived from the second covariant variation of the point particle’s action. Here it is shown that the second covariant variation of the string action leads to a string deviation equation. This equation is a candidate for describing the relative motion of many strings, and can be reduced to the geodesic deviation equation. Like the geodesic deviation equation, the string deviation equation is also expressible in terms of momenta and projecta. It is also shown that a combined action exists, the first variation of which gives the deviation equations. The combined actions allow the deviation equations to be expressed soley in terms of the Riemann tensor, the coordinates, and momenta. In particular geodesic deviation can be expressed as: Π̇ = R .αβγr P β ẋ, and string deviation can be expressed as: Π̇τ +Π ′μ σ = R μ .αβγr (P β τ ẋ α + P β σ x ). Mathematical Review Classification Scheme: 81T30, Physics and Astronomy Classification Scheme: 12.25+e, Keyword Index: String Deviation, Geodesic Deviation.