Search results
Results from the WOW.Com Content Network
Since every proper, orthochronous Lorentz transformation can be written as a product of a rotation (specified by 3 real parameters) and a boost (also specified by 3 real parameters), it takes 6 real parameters to specify an arbitrary proper orthochronous Lorentz transformation. This is one way to understand why the restricted Lorentz group is ...
For example, they reflect the ... If Λ is a proper orthochronous Lorentz transformation, then T ... one arrives at the transformation law for any tensor quantity T.
Lorentz transformations can be parametrized by rapidity φ for a boost in the direction of a three-dimensional unit vector ^ = (,,), and a rotation angle θ about a three-dimensional unit vector ^ = (,,) defining an axis, so ^ = (,,) and ^ = (,,) are together six parameters of the Lorentz group (three for rotations and three for boosts). The ...
The prime examples of such four-vectors are the four-position and four-momentum of a particle, and for fields the electromagnetic tensor and stress–energy tensor. The fact that these objects transform according to the Lorentz transformation is what mathematically defines them as vectors and tensors; see tensor for a definition.
Many of the representations, both finite-dimensional and infinite-dimensional, are important in theoretical physics. Representations appear in the description of fields in classical field theory, most importantly the electromagnetic field, and of particles in relativistic quantum mechanics, as well as of both particles and quantum fields in quantum field theory and of various objects in string ...
The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems.
The theory of special relativity plays an important role in the modern theory of classical electromagnetism.It gives formulas for how electromagnetic objects, in particular the electric and magnetic fields, are altered under a Lorentz transformation from one inertial frame of reference to another.
In quantum field theory, the Dirac spinor is the spinor that describes all known fundamental particles that are fermions, with the possible exception of neutrinos.It appears in the plane-wave solution to the Dirac equation, and is a certain combination of two Weyl spinors, specifically, a bispinor that transforms "spinorially" under the action of the Lorentz group.