Search results
Results From The WOW.Com Content Network
The Lagrangian and Eulerian specifications of the kinematics and dynamics of the flow field are related by the material derivative (also called the Lagrangian derivative, convective derivative, substantial derivative, or particle derivative). [1] Suppose we have a flow field u, and we are also given a generic field with Eulerian specification F ...
In field theory, the independent variable is replaced by an event in spacetime (x, y, z, t), or more generally still by a point s on a Riemannian manifold.The dependent variables are replaced by the value of a field at that point in spacetime (,,,) so that the equations of motion are obtained by means of an action principle, written as: =, where the action, , is a functional of the dependent ...
The Lagrangian density for classical electrodynamics is composed by two components: a field component and a source component: = + =. In the interaction term, the four-current should be understood as an abbreviation of many terms expressing the electric currents of other charged fields in terms of their variables; the four-current is not itself ...
From a theoretical viewpoint, field equations can be formulated in the frameworks of Lagrangian field theory, Hamiltonian field theory, and field theoretic formulations of the principle of stationary action. [4] Given a suitable Lagrangian or Hamiltonian density, a function of the fields in a given system, as well as their derivatives, the ...
For each group generator there necessarily arises a corresponding field (usually a vector field) called the gauge field. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called gauge invariance). When such a theory is quantized, the quanta of the gauge fields are called gauge bosons.
The Stueckelberg extension of the Standard Model (StSM) consists of a gauge invariant kinetic term for a massive U(1) gauge field.Such a term can be implemented into the Lagrangian of the Standard Model without destroying the renormalizability of the theory and further provides a mechanism for mass generation that is distinct from the Higgs mechanism in the context of Abelian gauge theories.
Delbrück scattering of gamma rays was observed in 1953 by Robert Wilson. [3] Photon splitting in strong magnetic fields was measured in 2002. [4] Light-by-light scattering can be studied using the strong electromagnetic fields of the hadrons collided at the LHC, [5] [6] and its observation was reported by the ATLAS Collaboration in 2019.
A Lagrangian density L (or, simply, a Lagrangian) of order r is defined as an n-form, n = dim X, on the r-order jet manifold J r Y of Y. A Lagrangian L can be introduced as an element of the variational bicomplex of the differential graded algebra O ∗ ∞ ( Y ) of exterior forms on jet manifolds of Y → X .