{"id":662,"date":"2018-11-12T08:29:43","date_gmt":"2018-11-12T08:29:43","guid":{"rendered":"http:\/\/phyp01.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=662"},"modified":"2019-04-29T06:56:07","modified_gmt":"2019-04-29T06:56:07","slug":"classical-theory-of-fields-ii","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phyp01\/chapter\/classical-theory-of-fields-ii\/","title":{"rendered":"Classical Theory of Fields II"},"content":{"raw":"
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  1. Introduction<\/strong><\/li>\r\n<\/ol>\r\n \r\n

    Historically the concept of Action at a distance was developed to explain the force experienced by a body in the presence of gravitation and electro\u2013magnetic forces. The concept of fields was later developed by Faraday and Maxwell to account for action at a distance experienced by a charge particle in the presence of other charged and currents. Maxwell developed the theory of electro\u2013magnetic fields through Maxwell equations which accounted for all electro\u2013magnetic interactions including light. In Maxwell\u2019s theory fields are physical entities. The Lagrangian and Hamiltonian formulation of electro\u2013magnetic fields was later developed. The quantization of electro\u2013magnetic fields was achieved by Werner Heisenberg, Wolfgang Pauli and Paul Dirac among others to give the theory of Quantum Electro\u2013dynamics. The theory turned out to be the most accurate theory for the prediction of electro\u2013magnetic phenomenon and predicted the existence of photons as light particles mediating electro\u2013magnetic interactions between charged particles. The theory of Quantum Electro\u2013dynamics has been tested to unprecedented accuracy to as much a nine decimal points agreement between theory and experimental observation. It remains as the crowning glory of the success of quantum mechanics.<\/p>\r\n\r\n

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    1. Electro\u2013Magnetic Fields<\/strong><\/li>\r\n<\/ol>\r\n \r\n\r\nMaxwell equations relate electro\u2013magnetic field to charge and current densities. The equations are :\r\n\r\n \r\n\r\n\"\"\r\n

      There are six components of electric and Magnetic fields, but they are related by Maxwell equations<\/p>\r\n \r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n

      For the electromagnetic Lagrangian in free space<\/p>\r\n \r\n\r\n\"\"\r\n\r\nThe Lagrangian is not unique and neither is it gauge invariant. We can always add the four divergence of a vector without changing the action and hence the equations of motion remain unchanged. Thus adding a term \u00a0to the energy momentum tensor (28.28) we get\r\n\r\n \r\n\r\n\"\"\r\n\r\n\"\"\r\n

      In General Theory of Relativity, the matrix \u00a0is no longer constant and depends on the space-time coordinates. Thus<\/p>\r\n\"\"\r\n\r\n\"\"\r\n

      we obtain the equation of motion in a gravitational field as<\/p>\r\n \r\n\r\n\"\"\r\n

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      1. Summary<\/strong><\/li>\r\n<\/ol>\r\n