Boson condensation in topological quantum field theories (TQFT) has been
previously investigated through the formalism of Frobenius algebras and the use
of vertex lifting coefficients. While general, this formalism is physically
opaque and computationally arduous: analyses of TQFT condensation are
practically performed on a case by case basis and for very simple theories
only, mostly not using the Frobenius algebra formalism. In this paper we
provide a new way of treating boson condensation that is computationally
efficient. With a minimal set of physical assumptions, such as commutativity of
lifting and the definition of confined particles, we can prove a number of
theorems linking Boson condensation in TQFT with chiral algebra extensions, and
with the factorization of completely positive matrices over the nonnegative
integers. We present numerically efficient ways of obtaining a condensed theory
fusion algebra and S matrices; and we then use our formalism to prove several
theorems for the S and T matrices of simple current condensation and of
theories which upon condensation result in a low number of confined particles.
We also show that our formalism easily reproduces results existent in the
mathematical literature such as the noncondensability of 5 and 10 layers of the
Fibonacci TQFT.Comment: 29 page