Tomography for several particles with one random variable

The tomographic map of the quantum state of a system with several degrees of freedom, which depends on one random variable, analogous to the rotated and scaled center-of-mass of the system, is constructed. The time-evolution equation of the tomogram for this map is given in the explicit form. The properties of the map such as the transition probabilities between different states and relation to the star-product formalism are elucidated. An example of a multimode oscillator is considered in detail. Identical particles are discussed within the framework of the proposed tomography scheme.