  In this paper we present a model for the kinematics and dynamics of
optomechanics which describe the coupling between an optical field, here
modeled by a massless scalar field, and the internal (e.g., determining its
reflectivity) and mechanical (e.g., displacement) degrees of freedom of a
moveable mirror. As opposed to implementing boundary conditions on the field we
highlight the internal dynamics of the mirror which provides added flexibility
to describe a variety of setups relevant to current experiments. The inclusion
of the internal degrees of freedom in this model allows for a variety of
optical activities of mirrors from those exhibiting broadband reflective
properties to the cases where reflection is suppressed except for a narrow band
centered around the characteristic frequency associated with the mirror's
internal dynamics. After establishing the model and the reflective properties
of the mirror we show how appropriate parameter choices lead to useful
optomechanical models such as the well known Barton-Calogeracos model [G.
Barton and A. Calogeracos, Ann. Phys. 238, 227 (1995)] and the important yet
lesser explored nonlinear models (e.g., $Nx$ coupling) for small photon numbers
$N$, which present models based on side-band approximations [H. Kimble et al.,
Phys. Rev. D 65, 022002 (2001)] cannot cope with. As a simple illustrative
application we consider classical radiation pressure cooling with this model.
To expound its theoretical structure and physical meanings we connect our model
to field-theoretical models using auxiliary fields and the ubiquitous Brownian
motion model of quantum open systems. Finally we describe the range of
applications of this model, from a full quantum mechanical treatment of
radiation pressure cooling, quantum entanglement between macroscopic mirrors,
to the backreaction of Hawking radiation on black hole evaporation in a moving
mirror analog.
