Physics and Astronomy Colloquium

Examples of quantum many-body systems abound in Nature. Thus, it is clear that in fields like molecular, solid-state, and nuclear physics most of the fundamental objects of discourse are interacting many-body systems. But even in elementary particle physics one is usually dealing with more than one particle. For example, at some level of reality a nucleon comprises three quarks interacting via gluons and surrounded by a cloud of mesons, which are themselves made of quark-antiquark pairs. Even more fundamentally, even the “physical vacuum” of any quantum field theory is endowed with an enormously complex infinite many-body structure due to virtual excitations. A key central role in modern physics is thus occupied by quantum many-body theory, where we are especially interested in the possible existence of any universal techniques that are powerful enough to treat the full range of many-body and field-theoretic systems. One such method is the coupled cluster method. This has become one of the most pervasive (possibly the most pervasive), most powerful, and most successful of all fully microscopic formulations of quantum many-body theory. It has probably been applied to more systems in quantum field theory, quantum chemistry, nuclear, subnuclear, condensed matter and other areas of physics than any other competing method. It has yielded numerical results which are among the most accurate available for an incredibly wide range of both finite and extended systems on either a spatial continuum or a regular discrete lattice. In this talk I aim to give an overview of the method itself and some illustrative examples of its power and range of applicability.