lagrangian density a ball thrown in the air: Once you’ve kicked it up, it has speed -and that is a form of energy, called kinetic energy- and height -and that, too, is a form of energy: potential energy.

http://dorigo.wordpress.com/2007/11/10/the-goldstone-theorem-for-real-dummies/

 In quantum physics, however, a scalar field represents a particle capable of moving and interacting with its peers: doing the things that particles do, that is.

 what is then a lagrangian density ? The lagrangian density is some mathematical scribbling that enshrines the physics of our scalar field. It is defined as L=T-V, where T is the kinetic energy of the field (the particle), and V its potential energy. Think of a ball thrown in the air: Once you’ve kicked it up, it has speed -and that is a form of energy, called kinetic energy- and height -and that, too, is a form of energy: potential energy. You