El principio de Acción Mínima en el centenario del Quantum
A brief historical review of the Principle of Least Action is given, and it's methodological importance is emphasized: the basic equations of Classical Mechanics can be derived from the conjunction of the Principle Least Action with the Galilean Principle of Relativity and the hypothesis of hom...
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| Published: |
2000
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| Online Access: |
http://dialnet.unirioja.es/servlet/oaiart?codigo=62240 |
| Summary: | A brief historical review of the Principle of Least Action is given, and it's methodological importance is emphasized: the basic equations of Classical Mechanics can be derived from the conjunction of the Principle Least Action with the Galilean Principle of Relativity and the hypothesis of homogeneity and isotropy of space and the homogeneity of time. In classical electrodinamics, the situation is similar: one can build the action keeping now in mind the Einstein's Principle of Relativity. By means of the solution of the Euler-Lagrange equations one obtain the equations of motion of charges in given fields (Lorentz force) and the first pair of Maxwell equations. Also, starting from the sources of the field (charges and currents), the second pair of Maxwell equations is obtained.
In the case of the General Relativity, the trajectories of a free particle are given by the geodesic lines in space-time. The Einstein equations are also obtained by finding the extreme of some action. A brief historical review of quantum theory is given, starting from the introduction of the quantum of action in physics, to the Schrödinger equation, which can be obtained from a variational principle, and the Heisenberg Uncertainty Principle. Interesting is the role of the classical action in the formulation of quantum mechanics by means of the Feynman path integrals. In it, the classical trajectory in the motion of a system between two configurations, it corresponds the limit in which the Planck constant tends to zero. In quantum electrodinamics, it is required also to start from a Lagrangian together with the properties of space-time simmetry, the gauge invariance and the CPT invariance. Finally, mention is made to the electroweak theory and to quantum cromodynamics |
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