The theoretical description of matter in strong laser fields is a rather challenging task. This is due to the fact that the external laser field is comparable to the atomic binding forces, and the usual theoretical methods considered in optical physics, such as perturbation theory with the laser field, are not applicable. In particular, it is very difficult to apply analytical or semi-analytical methods to such a physical framework. There exists, however, one such method, namely the Strong-Field Approximation. This method has served to establish the main paradigms in strong-field laser physics, and has been employed in over 500 publications in this field of research. In particular, it is very powerful for studying quantum interference effects in detail. This approximation suffers, however, from severe drawbacks, which are particularly critical for molecules and systems involving more than one electron. Such systems can not be described by such an approximation in a satisfactory way, and indicate that new, radical ideas are necessary in order to develop the theory further. In this project, we intend to bring ideas and methods from quantum-field theory and mathematical physics to strong-field laser physics to develop a new semi-analytical approach which replaces such an approximation. As a testing ground, we will use such a theory to describe molecules in strong laser fields, and, simultaneously, make a rigorous assessment of the limitations of the Strong-Field Approximation. Such systems have been chosen not only due to their critical behavior, but also due to the fact that, nowadays, there exists pioneering experiments in Britain, at the Imperial College, involving molecules, which will pave the way towards dynamic measurements of matter with a never-imagined precision. This will not only be important for the specific physical systems above, but will revolutionalize a whole area of research.

The theoretical description of matter in strong laser fields is a rather challenging task. This is due to the fact that the external laser field is comparable to the atomic binding forces, and the usual theoretical methods considered in optical physics, such as perturbation theory with the laser field, are not applicable. In particular, it is very difficult to apply analytical or semi-analytical methods to such a physical framework. There exists, however, one such method, namely the Strong-Field Approximation. This method has served to establish the main paradigms in strong-field laser physics, and has been employed in over 500 publications in this field of research. In particular, it is very powerful for studying quantum interference effects in detail. This approximation suffers, however, from severe drawbacks, which are particularly critical for molecules and systems involving more than one electron. Such systems can not be described by such an approximation in a satisfactory way, and indicate that new, radical ideas are necessary in order to develop the theory further. In this project, we intend to bring ideas and methods from quantum-field theory and mathematical physics to strong-field laser physics to develop a new semi-analytical approach which replaces such an approximation. As a testing ground, we will use such a theory to describe molecules in strong laser fields, and, simultaneously, make a rigorous assessment of the limitations of the Strong-Field Approximation. Such systems have been chosen not only due to their critical behavior, but also due to the fact that, nowadays, there exists pioneering experiments in Britain, at the Imperial College, involving molecules, which will pave the way towards dynamic measurements of matter with a never-imagined precision. This will not only be important for the specific physical systems above, but will revolutionalize a whole area of research.