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It is argued that Weinberg's approach to the nucleon-nucleon (NN) interaction problem within effective field theory provides a consistent power counting for renormalized diagrams. Within this scheme the NN potential is organized as an…
Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate…
We consider the effective field theory of the NN system in a separable representation. The pionic part of the effective potential is included nonperturbatively and approximated by a separable potential. The use of a separable representation…
Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's…
We present a new method for renormalisation group improvement of the effective potential of a quantum field theory with an arbitrary number of scalar fields. The method amounts to solving the renormalisation group equation for the effective…
We consider the general properties of effective field theories. We note that the freedom to fix the renormalization conditions in the effective field theory is not as great as it seems. The consideration of minimal requirements of…
We discuss in this paper two ways of defining the concept of "effective field theory": effective field theory defined by low energy effectiveness and effective field theory defined by 4D effectiveness out of higher dimensions. We argue that…
Chiral perturbation theory is the effective field theory of the strong interactions at low energies. We will give a short introduction to chiral perturbation theory for mesons and will discuss, as an example, the electromagnetic…
In the perturbative field-theoretical models we investigate the inclusion of the electromagnetic interactions into the purely strong theory that describes hadronic processes. In particular, we study the convention for splitting…
That the exact quantum S-matrix of $\text{T}\bar{\text{T}}$-deformed field theories is known has interesting consequences for their perturbative renormalisation. Recent investigations into the interplay between renormalisation and…
We investigate the renormalization of ``nonlocal" interactions which arise as an infinite sum of higher derivative interactions in an effective field theory. Using dimensional regularization with minimal subtraction in a general scalar…
We consider separable toy models of the nucleon-nucleon interaction inspired by chiral effective field theory. We show that nonlocality of the long-range forces causes the need for nonlocal counter terms, or even makes the whole approach…
These lectures review the formalism of renormalization in quantum field theories with special regard to effective quantum field theories. While renormalization theory is part of every advanced course on quantum field theory, for effective…
We analyze the renormalization of the nucleon--nucleon interaction at low energies in coordinate space for both one and two pion exchange chiral potentials. The singularity structure of the long range potential and the requirement of…
We discuss the renormalisation of the initial value problem in quantum field theory using the two-particle irreducible (2PI) effective action formalism. The nonequilibrium dynamics is renormalised by counterterms determined in equilibrium.…
In this work we use the framework of effective field theory to couple Einstein's gravity to scalar electrodynamics and determine the renormalization of the model through the study of physical processes below Planck scale, a realm where…
Nuclear effective field theory organizes the calculation of observables as a power series in terms of the ratio of soft and hard momentum scales. The rigorous implementation of this idea requires a mixture of perturbative and…
A Lorentz-covariant regularization scheme for effective field theories with an arbitrary number of propagating heavy and light particles is given. This regularization scheme leaves the low-energy analytic structure of Greens functions…
The role of cut-off and dimensional regularizations is discussed in the context of obtaining a renormalized nucleon-nucleon potential from the chiral Lagrangian formulation of the effective field theory due to Weinberg. Both types of…
In this Thesis we study quantum corrections to the classical dynamics for mean values in field theory. To that end we make use of the formalism of the closed time path effective action to get real and causal equations of motion. We…