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2 results

  • 5 - Lagrangeans and the Notion of Field; Electromagnetism as a Field Theory

  • 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 46-53

  • Summary

    We define the notion of field, based on the example of electromagnetism. We write the relativistically covariant form of the Maxwell's equations in terms of a gauge field and field strength for it. We define the Euler–Lagrange equations for a field, and based on it, we derive the relativistic Maxwell's equations from a relativistically invariant Maxwell action.

  • 45 - Time-Dependent Gravity: The Friedmann-Lemaître-Robertson-Walker (FLRW) Cosmological Solution

  • 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 433-440

  • Summary

    The Friedmann-Lemaître-Robinson-Walker (FLRW) cosmological solution for the expanding (time dependent) Universe is found. We start with an ansatz for a homogenous and isotropic space in comoving coordinates, and define various coordinate systems and analyze the geometry. The Einstein equations reduce to the Friedmann equation for the “Hubble constant” and the acceleration equation for the scale factor, related through the conservation of the energy-momentum tensor. Given an equation of state for matter, we can solve the Friedmann equation.