Definition
Fock space is the (Hilbert) direct sum of tensor products of copies of a single-particle Hilbert space
Here represents the states of no particles, the state of one particle, the states of two identical particles etc.
A typical state in is given by
where
- is a vector of length 1, called the vacuum state and is a complex coefficient,
- is a state in the single particle Hilbert space,
- , and is a complex coefficient
- etc.
The convergence of this infinite sum is important if is to be a Hilbert space. Technically we require to be the Hilbert space completion of the algebraic direct sum. It consists of all infinite tuples 
such that the norm, defined by the inner product is finite
where the particle norm is defined by
i.e. the restriction of the norm on the tensor product
For two states
- , and
the inner product on is then defined as
where we use the inner products on each of the -particle Hilbert spaces. Note that, in particular the particle subspaces are orthogonal for different .
Read more about this topic: Fock Space
Famous quotes containing the word definition:
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)