ABSTRACT
For the relativistic particle we encountered two actions which were geometric and which were classically (and quantum mechanically) equivalent https://www.w3.org/1998/Math/MathML"> S [ P ( x , y ) ] = m 0 ℓ [ P ( x , y ) ] = m 0 ∫ 0 1 d ξ ( d X i d ξ ) 2 , P : ξ → X i ( ξ ) , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003320562/573084c4-5e38-4573-b4ce-5412e9a1c018/content/math5_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> S [ X , g a b ] = κ 2 ∫ d ξ g ( ξ ) [ g a b ( ξ ) ∂ X i ∂ ξ a ∂ X i ∂ ξ b + λ ] , a , b = 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003320562/573084c4-5e38-4573-b4ce-5412e9a1c018/content/math5_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
