No. There are no names for them. The main reason being is that their physical meaning will depend on the particular distributions of charges/currents. I.e. if there exists a frame in which there are no charges present but there is a non-zero current density then the norm is proportional to that current density. If, on the otherhand, there is a frame in which there is no current density but there is a charge density then the norm is proportional that charge density.speeding electron said:Are there names for the Lorentz invariant norm of the four-potential and four-current? I assume that they are invariant under the transformations. Also, is it true that any physical quantities which form a four-vector have an invariant quantity associated with them (i.e. the norm of the corresponding four-vector)? Thanks.
4-vector norms are mathematical tools used to measure the magnitude or size of a 4-vector in four-dimensional space. They are often used in physics and engineering to describe physical quantities.
Physical quantities are properties or characteristics of a physical system that can be measured or described using numerical values. Examples include mass, velocity, and electric charge.
4-vector norms are used to measure and describe physical quantities that have four-dimensional components, such as energy-momentum or electromagnetic fields. They provide a way to quantify these quantities in a consistent and mathematically rigorous manner.
The most commonly used 4-vector norms in physics are the Euclidean norm, Minkowski norm, and Lorentz norm. These norms differ in the way they account for the time component of the 4-vector and are used to describe different physical phenomena.
4-vector norms are used in a variety of practical applications in physics and engineering, such as in relativity, electromagnetism, and quantum mechanics. They provide a mathematical framework for describing and analyzing physical quantities and their relationships in a consistent and precise manner.