  We construct a Ginsburg Landau (GL) theory to study the phases of liquid,
solid, superfluid, especially a possible supersolid and phase transitions among
these phases in a unified framework. In this GL, we put the two competing
orders between the solid component and the superfluid component on the same
footing. We only introduce two parameters: $ v $ which is the repulsive
interaction between the normal component and the local superfluid mode and $ g
$ which is a periodically changing chemical potential for the local superfluid
mode. The microscopic origins of $ v $ and $ g $ are given. By using this GL
action, we study the superfluid to supersolid transition, normal solid to the
supersolid transition and analyze the conditions for the existence of the
supersolid.
