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Low-energy nuclear weak-interaction processes play important roles in many astrophysical contexts, and effective field theory is believed to be a highly useful framework for describing these processes in a model-independent manner. I…
We consider the initial value problem and its renormalisation in the framework of the two-particle-irreducible (2PI) effective action. We argue that in the case of appropriately chosen self-consistent initial conditions, the counterterms…
I review some older work on the effective potentials of quantum field theories, in particular the use of anomalous symmetries to constrain the form of the effective potential, and the background field method for evaluating it…
The infrared effects for light minimally coupled scalar fields with quartic self-interaction in de Sitter space is investigated using the 2PI effective action formalism. This formalism partially resums infinite series of loop diagrams, and…
In the low-energy limit, non-relativistic particles with short-range interactions exhibit universal behavior that is largely independent of microscopic details. This universality is typically described by effective field theory, in which…
Some considerations showing that renormalizable theories with consistent perturbative theries can not be nonperturbatively finite (in terms of bare parameters) are provided. Accordingly any fundamental unified theory has to be either non…
Effective interactions can be obtained from a renormalization group analysis in two complementary ways. One can either explicitly integrate out higher energy modes or impose given conditions at low energies for a cut-off theory. While the…
We study the impact of the leading non-renormalizable terms in the effective field theory that describes general extensions of the Standard Model with vector-like quarks. Dropping the usual assumption of renormalizability has several…
The observed IR and the spectator UV particles of a regulated, cutoff quantum field theory are entangled by their interactions; hence, the IR sector can be described by the help of the density matrix only. The tree-level renormalized…
These notes are based on five lectures presented at the 2004 Theoretical Advanced Study Institute (TASI) on ``Physics in D>=4''. After a brief motivation of flavor physics, they provide a pedagogical introduction to effective field theory,…
The study of the effective potential for non-renormalisable scalar SO(N) symmetric theories leads to recurrence relations for the coefficients of the leading logarithms. These relations can be transformed into generalised…
We consider classical and quantum integrable sigma models and their relations with the solutions of renormalization group equations. We say that an integrable sigma model possesses the "nice" duality property if the dual quantum field…
The Schrodinger equation with a two-dimensional delta-function potential is a simple example of an asymptotically free theory that undergoes dimensional transmutation. Renormalization requires the introduction of a mass scale, which can be…
We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be…
We consider renormalization of the three-body scattering problem in low-energy effective field theory of self-interacting scalar particles by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation. The…
Equivalence criteria are established for an effective Yukawa-type theory of composite fields representing two-particle fermion bound states with the original "microscopic" theory of interacting fermions based on the spectral decomposition…
It is shown that pions can be included perturbatively into effective field theory only for the external momenta, well below the pion mass. But for such low energies it is not necessary to include pions explicitly.
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
Nonlocal effective interactions are inherent to non-relativistic quantum many-body systems, but their systematic resummation poses a significant challenge known as the ``vertex problem" in many-body perturbation theory. We introduce a…
The contents of renormalization group invariance and equations under tight constraints are explored and demonstrated with closed-form on-shell $T$ matrices of pionless effective field theory for nuclear forces right within the effective…