A new kind of squeezed thermal state of continuum variables in degenerate case

In thermal field dynamics usually for every real field operator acting on a real space has an image acting on a fictitious space. In this work we construct a new kind of squeezed thermal state of continuum variables in which two real modes share one fictitious mode, this can be named the degenerate case. We also prove that this state-set makes up a new quantum-mechanical representation and show its application in solving some master equation.