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2 results

  • 42 - Deflection of Light by the Sun and Comparison with General Relativity

  • from Part III - Other Spins or Statistics; General Relativity
  • Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
  • Book:
    Classical Field Theory
    Published online:
    04 March 2019
    Print publication:
    14 March 2019, pp 396-404

  • Summary

    We calculate “deflection of light by the Sun." First, we define a first-order action for a massless particle moving in a gravitational field, and then we calculate the motion of light on a geodesic as motion of light in a medium with a small, position-dependent index of refraction, giving the light deviation for small angles. Then we redo the calculation from the Hamilton–Jacobi formalism by first defining the Hamilton–Jacobi equation for light motion and then solving it. This gives the nonperturbative light deviation that matches the previous calculation at small angles. We end by comparison with the deflection of light by the Sun in special relativity, which is different by a factor of 2.

  • 1 - Short Review of Classical Mechanics

  • from Part I - General Properties of Fields; Scalars and Gauge Fields
  • Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
  • Book:
    Classical Field Theory
    Published online:
    04 March 2019
    Print publication:
    14 March 2019, pp 3-13

  • Summary

    In the first chapter, the most important concepts of classical mechanics are quickly reviewed. The Lagrangian and Hamiltonian formalism are described. The way to deal with systems with constraints is described. Poisson brackets and the use of canonical transformations in the Hamiltonian formalism, as well as the basics of Hamilton–Jacobi theory complete this chapter.