Minkowski Force due to a quadratic in velocity potential

[QFT25]

Homework Statement

A generalized potential suitable for use in a covariant Lagrangian for a single particle. This is Goldstein problem 9 chapter 7.

−Aλν(xμ)uλuν

where Aλν stands for a symmetric world tensor of the second rank and u^v are the components of the world velocity. If the Lagrangian is made up of (1/2)m*u_v*u^v minus U, obtain the Lagrange equations of motion. What is the Minkowski force? Give the components of the force as observed in some Lorentz frame.

Homework Equations

Euler equation of motion where the derivatives are taken with respect to the four velocity and where and the time part if the proper time. Also that the four force is the mass times the four velocity.

The Attempt at a Solution

When I workout the Lagrangian I have an extra term which is proportional to the four acceleration. My first thought is to solve for the four acceleration and then multiply it by the mass to get the Minkowski force. Is that valid? [/B]

 

[lvirany]

Minkowski 4-Force = dP/d-tau where P is 4-momentum;
or 4-Force = gamma(3-Force, id/dt(mc)) where m is relativistic mass.