  The canonical quantization of a massive symmetric rank-two tensor in string
theory, which contains two Stueckelberg fields, was studied. As a preliminary
study, we performed a canonical quantization of the Proca model to describe a
massive vector particle that shares common properties with the massive
symmetric rank-two tensor model. By performing a canonical analysis of the
Lagrangian, which describes the symmetric rank-two tensor, obtained by Siegel
and Zwiebach (SZ) from string field theory, we deduced that the Lagrangian
possesses only first class constraints that generate local gauge
transformation. By explicit calculations, we show that the massive symmetric
rank-two tensor theory is gauge invariant only in the critical dimension of
open bosonic string theory, i.e., $d=26$. This emphasizes that the origin of
local symmetry is the nilpotency of the Becchi-Rouet-Stora-Tyutin (BRST)
operator, which is valid only in the critical dimension. For a particular gauge
imposed on the Stueckelberg fields, the gauge-invariant Lagrangian of the SZ
model reduces to the Fierz-Pauli Lagrangian of a massive spin-two particle.
Thus, the Fierz-Pauli Lagrangian is a gauge-fixed version of the
gauge-invariant Lagrangian for a massive symmetric rank-two tensor. By noting
that the Fierz-Pauli Lagrangian is not suitable for studying massive spin-two
particles with small masses, we propose the transverse-traceless (TT) gauge to
quantize the SZ model as an alternative gauge condition. In the TT gauge, the
two Stueckelberg fields can be decoupled from the symmetric rank-two tensor and
integrated trivially. The massive spin-two particle can be described by the SZ
model in the TT gauge, where the propagator of the massive spin-two particle
has a well-defined massless limit.
