Teoría de Campo Escalar con un Número Indeterminado de Derivadas
Keywords:
Teoría de Campos, Cuantización Canónica y Altas Derivadas. (es)Field Theory, Canonical Quantization, Higher Derivative. (en)
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En este trabajo se presenta la aplicación del m_etodo Canónico de Ostrogradski a teorías de campo relativista. Se considera una teoría de campo escalar basada en una densidad Lagrangiana con un número infinito de derivadas. Además se obtienen las corrientes y cargas conservadas provenientes de imponer variaciones arbitrarias en las coordenadas y en los campos, también se obtiene la forma más general posible de los momentos canónicamente conjugados para cualquier grado en el número de derivadas y luego se construye el Hamiltoniano y las diferentes relaciones de conmutación que deben cumplir los campos. Finalmente se muestra que los resultados son consistentes con los obtenidos en teorías sin un gran número de derivadas.
I present the application of Ostrogradski Canonical method in relativistic field theories. A scalar field theory based on a Lagrangian density with an infinite number derivatives is considered. I obtain, the currents and conserved charges, when the arbitrary variations in the coordinates and fields are imposed, as well as, the most general form of the canonical conjugated momentums for any order in the derivatives, and the different commutation relations of the fields in the Hamiltonian formalins. Finally, it is shown that our results are consistent with those obtained from second order derivatives.
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