# Lagrangian density

## Lagrangian density

[lə′grän·jē·ən ′den· səd·ē]
(mechanics)
For a dynamical system of fields or continuous media, a function of the fields, of their time and space derivatives, and the coordinates and time, whose integral over space is the Lagrangian.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
The fractional counterpart for this Lagrangian density is
[zeta] can be regarded as a Lagrangian density characterizing a specific vacuum background field which pre-exists in the absence of matter.
In the present work, we propose another hierarchy of generalized KdV equations based on modifying the Lagrangian density whose induced action functional is extremized by the KdV equation.
The Lagrangian is L = T - V = [[integral].sup.L.sub.0] [LAMBDA] dx in which the Lagrangian density [LAMBDA] is
where L is electromagnetic Lagrangian density. The conventional classical electrodynamics provides the Lagrange function for EM field L in explicit form as
A Lagrangian density per unit volume of the reference configuration is introduced in [1-4,7,8,13]
The above equations show that matter Lagrangian density and a generic function have a significant importance to discuss the dynamics of curvature-matter coupled theories.
The same applies then to the "Lagrangian density" L = L[square root of (-g)]; that is, the latter is a smooth real function L = L([q.sup.A], [q.sup.A.sub.[mu]][[g.bar].sup.[mu]v], [[g.bar].sup.[mu]v.sub.[rho]]).
Using the phase velocity (6) and adding the interaction terms with the gauge field, we can identify the full Lagrangian density as
The lagrangian density must distinguish electrons and positron by their charge only.
However, we note that the anti-co-BRST charge [Q.sup.([bar.[lambda]]).sub.ad] (derived from the Lagrangian density [L.sup.([bar.[lambda]]).sub.B]) and co-BRST charge [Q.sup.([lambda]).sub.d] (derived from the Lagrangian density [L.sup.([lambda]).sub.[bar.B]]) would be different from (8).
The Lagrangian density of the (1 + 1) dimensional Chern-Simons-Higgs system is given by

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