"The history of our Galaxy, the Milky Way, has been always a subject of debate. How the Galaxy was formed and the ways it has evolved up to the present moment is still something that it is outside our knowledge. Nowadays, we are living an extraordinary scientific moment, since after incredible efforts the technological facilities necessary to disentangle such a relevant matter are available. The study of the fossil stars of the Galaxy, the white dwarf population, is essential to obtain information about its past history. In particular, the cooler objects are the ones that can provide more interesting information, but they are so faint that the current number of identified objects is very low. The project we propose will overcome all the current problems to detect cooler white dwarfs by performing a deep survey of thick disk and halo WDs in a very deep infrared survey (WTS) carried out in the zyJHK filters with the UKIRT telescope. The accuracy of these data will allow us to classify them in thin/thick disk or halo members. Thanks to the new cool white dwarfs detected we will be able to cover the low luminosity end of the thin disk/thick disk/halo luminosity functions, which will provide a wealth of information about the history of the Galaxy (age, star formation rate...)."