Expression that evaluates to a scalar, invariant under any Lorentz transformation in physics
In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of vectors, or from contracting tensors of the theory. While the components of vectors and tensors are in general altered under Lorentz transformations, Lorentz scalars remain unchanged.
A Lorentz scalar is not always immediately seen to be an invariant scalar in the mathematical sense, but the resulting scalar value is invariant under any basis transformation applied to the vector space, on which the considered theory is based. A simple Lorentz scalar in Minkowski spacetime is the spacetime distance ("length" of their difference) of two fixed events in spacetime. While the "position"-4-vectors of the events change between different inertial frames, their spacetime distance remains invariant under the corresponding Lorentz transformation. Other examples of Lorentz scalars are the "length" of 4-velocities (see below), or the Ricci curvature in a point in spacetime from general relativity, which is a contraction of the Riemann curvature tensor there.
Lorentzscalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar...
numbers Scalar (physics), a physical quantity that can be described by a single element of a number field such as a real number Lorentzscalar, a quantity...
particles transform like a scalar under Lorentz transformation (i.e. are Lorentz invariant). A pseudoscalar boson is a scalar boson that has odd parity...
of the rapidity scalar confined to 0 ≤ ζ < ∞, which agrees with the range 0 ≤ β < 1. Defining the coordinate velocities and Lorentz factor by u = d r...
quantities are built out of scalars, four-vectors, four-tensors, and spinors. In particular, a Lorentz covariant scalar (e.g., the space-time interval)...
under any Lorentz transformation. The only fundamental scalar quantum field that has been observed in nature is the Higgs field. However, scalar quantum...
In physics, specifically in electromagnetism, the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point...
and physics, a scalar field is a function associating a single number to every point in a space – possibly physical space. The scalar may either be a...
{\nabla } }}\right)} Note that each 4-vector is related to another by a Lorentzscalar: U = d d τ X {\displaystyle \mathbf {U} ={\frac {d}{d\tau }}\mathbf...
Hendrik Antoon Lorentz (/ˈlɒrənts/; 18 July 1853 – 4 February 1928) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman...
article Lorentz transformation for details. A quantity invariant under Lorentz transformations is known as a Lorentzscalar. Writing the Lorentz transformation...
{\omega }{c}},-k_{x},-k_{y},-k_{z}\right)\end{aligned}}} In general, the Lorentzscalar magnitude of the wave four-vector is: K μ K μ = ( ω c ) 2 − k x 2 −...
frequently confused with Hendrik Lorentz, who has given his name to many concepts in this field. The condition is Lorentz invariant. The Lorenz gauge condition...
In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for...
of hadrons. The observed Lorentz invariance of space-time allows only the formation of condensates which are Lorentzscalars and have vanishing charge...
the Lorentz group, so it is still referred to as a scalar field, in the sense of a Lorentzscalar. The gauge-field is a g {\displaystyle {\mathfrak {g}}}...
change in proper time, which is independent of coordinates, and is a Lorentzscalar. The interval is the quantity of interest, since proper time itself...
quantity expressed as the gradient of the electrostatic potential, which is a scalar quantity denoted by V or occasionally φ, equal to the electric potential...
within the universe). However, space and time took on new meanings with the Lorentz transformation and special theory of relativity. In 1908, Hermann Minkowski...
energy is a scalar quantity, the canonical conjugate to time. In special relativity energy is also a scalar (although not a Lorentzscalar but a time component...
relativistically invariant and their solutions transform under the Lorentz group as Lorentzscalars ((m, n) = (0, 0)) and bispinors respectively ((0, 1/2) ⊕ (1/2...
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