Topic summary
Phase factor
In physics and representation theory, a phase factor is a multiplier representing the phase of a wave or the phase difference between two quantities. It is formulated as a unit complex number, that is a complex number with absolute value1. For a complex number written in polar form, such as r e, the phase factor is the complex exponential, e, where the variable θ is the phase and i is the imaginary unit. If a quantity like a scalar, vector, or a matrix (representing a wave, state, or operator) is equal to another quantity times a phase factor, then those two quantities are said to be equivalent up to the phase factor, as it leaves the length (or norm) unchanged. As a set, the possible phase factors form the circle group, but the term often refers to a scalar recording a phase choice or convention, or an ambiguity in choosing a representative.