lagrangian density sentence in Hindi
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- The Lagrangian is a function of time since the Lagrangian density has implicit space dependence via the fields, and may have explicit spatial dependence, but these are removed in the integral, leaving only time in as the variable for the Lagrangian.
- The Lagrangian density \ mathcal { L } is a scalar, and so will infinitesimally transform as \ delta \ mathcal { L } = \ alpha ^ \ mu \ partial _ \ mu \ mathcal { L } under the infinitesimal transformation.
- The Lagrangian density is divided into two parts, the density for the orbiting particle \ mathcal { L } _ p and the density \ mathcal { L } _ e of the gravitational field generated by all other particles including those comprising the earth,
- :: : See Lagrangian density for an integral over 4-dimensional spacetime ( though the article uses only a single integral sign with d 4 " x " )-- talk ) 22 : 41, 6 May 2014 ( UTC)
- As in Hamiltonian mechanics where every generalized coordinate has a corresponding generalized momentum, the field has a "'conjugate momentum field "', defined as the partial derivative of the Lagrangian density with respect to the time derivative of the field,
- More importantly for the Hamiltonian perturbative formalism ( which is carried out not on the fiber bundle but on a local section ), adding a BRST exact term to a gauge invariant Lagrangian density preserves the relation " s B X " = 0.
- Notice that, in the presence of gravity or when using general curvilinear coordinates, the Lagrangian density \ mathcal { L } will include a factor of } } or its equivalent to ensure that it is a scalar density so that the integral will be invariant.
- Analogous to the particle case, for non-relativistic applications the Lagrangian density is also the kinetic energy density of the field, minus its potential energy density ( this is not true in general, and the Lagrangian density has to be " reverse engineered " ).
- Analogous to the particle case, for non-relativistic applications the Lagrangian density is also the kinetic energy density of the field, minus its potential energy density ( this is not true in general, and the Lagrangian density has to be " reverse engineered " ).
- The coupling constants " ? n " in the Lagrangian \ mathcal { L } have dimensions of [ length ] 2 " n " " " D ", although it is usual to normalize the Lagrangian density in units of the Planck scale
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