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The quantity on the left is called the spacetime interval between events a 1 = (t 1, x 1, y 1, z 1) and a 2 = (t 2, x 2, y 2, z 2). The interval between any two events, not necessarily separated by light signals, is in fact invariant, i.e., independent of the state of relative motion of observers in different inertial frames, as is shown using ...
Assume two inertial reference frames (t, x, y, z) and (t′, x′, y′, z′), and two points P 1, P 2, the Lorentz group is the set of all the transformations between the two reference frames that preserve the speed of light propagating between the two points:
In the fundamental branches of modern physics, namely general relativity and its widely applicable subset special relativity, as well as relativistic quantum mechanics and relativistic quantum field theory, the Lorentz transformation is the transformation rule under which all four-vectors and tensors containing physical quantities transform from one frame of reference to another.
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.
Then, for example, (0, 3 / 2 ) and (1, 1 / 2 ) are a spin representations of dimensions 2⋅ 3 / 2 + 1 = 4 and (2 + 1)(2⋅ 1 / 2 + 1) = 6 respectively. According to the above paragraph, there are subspaces with spin both 3 / 2 and 1 / 2 in the last two cases, so these representations cannot likely ...
In a relativistic theory of physics, a Lorentz scalar is a scalar expression whose value is invariant under any Lorentz transformation. A Lorentz scalar may be generated from, e.g., the scalar product of vectors, or by contracting tensors. While the components of the contracted quantities may change under Lorentz transformations, the Lorentz ...
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.
The Lorentz factor or Lorentz term (also known as the gamma factor [1]) is a dimensionless quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves. The expression appears in several equations in special relativity, and it arises in derivations of the Lorentz transformations.