Lagrange density

Lagrange density at point of variation, eqn (8.107) magnetization density, eqn (8.272)... 

Within the Higgs mechanism two complex scalar boson fields 4> x) and (t x) are introduced. These two fields form a SU(2)i, doublet, which is called the Higgs field (x). For this field a Lagrange density of the type... 

If these new fields are inserted in the Langrange density (30) and the field strength tensors are expanded, then one obtains the following Lagrange density [74]... 

The meaning of the prime for the down quark will be discussed shortly. Analogously to the leptons, the following Lagrange density Cg for the quarks is added to the full model Lagrange density ... 

The various bilinear fermionic terms in the interaction Lagrangian are four-currents that interact with the gauge bosons. The Lagrange density... 

The Lagrangian of a system is denoted as L. It can be obtained from the Lagrange density C by integration over the space-like coordinates... 

From this Lagrangian, we may immediately state the optimum theorem. Let us define a Lagrange density L(t) such that... 

In analogy with the use of the terms Lagrangian and Lagrange density, we use the term Hamiltonian for the integral of a Hamilton density (recognizing that this usage is not universal). 

Define the Hamilton density as that part of the Lagrange density not containing the differential operator ... 

Also note that the Hamilton and Lagrange densities differ only in terms that are not functions of the control variable. Their extreme values as functions of u only occur for the same value of u. Therefore, the optimum theorem can also be written as... 

V. SYSTEMS WITH STATE RESTRAINTS A. Augmented Lagrange Density... 

New Hamilton and Lagrange densities are defined by adding a term X t)p, thus representing the additional side condition of the restraint, where A" " /) is a further (scalar) Lagrange multiplier. 

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