The mathematical and philosophical basis for current elementary particle physics is Quantum Field Theory (QFT). Other branches of theoretical physics, such as condensed matter physics and statistical mechanics, use it as well. In a nutshell, QFT is the application of quantum mechanics (QM), which deals with particles, structures, or devices of an infinite number of degrees of freedom. (For more details, see the entry on quantum mechanics.)
QFT has been a more highly debated subject in philosophy of science in the last decade, with issues ranging from methodology to semantics to ontology. When taken seriously in terms of its philosophical ramifications, QFT seems to have a view of the universe that is at odds with central classical concepts of particles and fields, as well as certain aspects of QM. Read more
