The zilch is often described in terms of the zilch tensor, . The latter can be expressed using the dual electromagnetic tensor  as
The zilch tensor is symmetric under the exchange of its first two indices,  and , while it is also traceless with respect to any two indices, as well as divergence-free with respect to any index. 
The conservation law  means that the following ten quantities are time-independent:
:These are the ten zilches (or just the zilch) discovered by Lipkin. In fact, only nine zilches are independent. 
:The time-independent quantity  is known as the 00-zilch  and is equal to the aforementioned optical chirality
:In general, the time-independent quantity  is known as the -zilch  (the indices  run from 0 to 3) and it is clear that there are ten such quantities (nine independent).
It was later demonstrated that Lipkin's zilch is part of an infinite number of zilch-like conserved quantities, a general property of free fields.