Lorentz invariants are physical parameters that remain the same in all reference frames. They are useful in problems that involve multiple reference frames.

## Phase Space Volume Edit

Phase space volume is the product of real space volume and volume in momentum space (sometimes called reciprocal space). In a boosted frame the real space volume decreases by a Lorentz factor , while the momentum space volume increases by the same amount, so both changes cancel out.

As a corollary, the distribution function i.e. the number of particles per unit phase space, (usually denoted as ) is also constant because the number of particles does not change between reference frames.

## Specific Radiative Intensity Edit

The specific radiative intensity can be related to the distribution function through

Hence is a Lorentz invariant.

## Specific Emissivity Edit

The emissivity can be related to the specific radiative intensity through

where is the optical path. The number of times a certain wavelength fits into the optical path is a Lorentz invariant, hence is also a Loretnz invariant. Hence, is also a Lorentz invariant.