operator, the proportionality constant being the speed of light: Using ( is pronounced "d-slash"), according to Feynman slash notation, the Dirac equation becomes: In practice, physicists often use units of measure such that , known as natural units. The equation then takes the simple form A fundamental theorem states that if two distinct sets of matrices are given that both satisfy the Clifford relations, then they are connected to each other by a similarity transformation: If in addition the matrices are all unitary, as are the Dirac set, then itself is unitary; The transformation is unique up to a multiplicative factor of absolute value 1. Let us now imagine a Lorentz transformation to have been performed on the space and time coordinates, and on the derivative operators, which form a covariant vector. For the operator to remain invariant, the gammas must transform among themselves as a contravariant vector with respect to their spacetime index. These new gammas will themselves satisfy the Clifford relations, because of the orthogonality of the Lorentz transformation. By the fundamental theorem, one may replace the new set by the old set subject to a unitary transformation. In the new frame, remembering that the rest mass is a relativistic scalar, the Dirac equation will then take the form If the transformed spinor is defined as then the transformed Dirac equation is produced in a way that demonstrates manifest relativistic invariance: Thus, settling on any unitary representation of the gammas is final, provided the spinor is transformed according to the unitary transformation that corresponds to the given Lorentz transformation. The various representations of the Dirac matrices employed will bring into focus particular aspects of the physical content in the Dirac wave function. The representation shown here is known as the standard representation – in it, the wave function's upper two components go over into Pauli's 2 spinor wave function in the limit of low energies and small velocities in comparison to light. The considerations above reveal the origin of the gammas in geometry, hearkening back to Grassmann's original motivation; they represent a fixed basis of unit vectors in spacetime. Similarly, products of the gammas such as represent oriented surface elements, and so on. With this in mind, one can find the form of the unit volume element on spacetime in terms of the gammas as follows. By definition, it is For this to be an invariant, the epsilon