Related papers: Effective Lagrangians for Scalar Fields and Finite…
These lectures introduce some of the basic ideas of effective field theories. The topics discussed include: relevant and irrelevant operators and scaling, renormalization in effective field theories, decoupling of heavy particles, power…
We consider a neutral self-interacting massive scalar field defined in a d-dimensional Euclidean space. Assuming thermal equilibrium, we discuss the one-loop perturbative renormalization of this theory in the presence of rigid boundary…
We study the $\frac{\lambda}{4!}\phi^{4}$ massless scalar field theory in a four-dimensional Euclidean space, where all but one of the coordinates are unbounded. We are considering Dirichlet boundary conditions in two hyperplanes, breaking…
A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…
We present a comprehensive discussion of the consistency of the effective quantum field theory of a single $Z_2$ symmetric scalar field. The theory is constructed from a bare Euclidean action which at a scale much greater than the…
The effective field theory approach to high temperature field theory can be used to study the phase transition in theories with spontaneously broken symmetry. I construct a sequence of two effective three--dimensional field theories which…
We study several problems related to the construction and the use of effective Lagrangians by considering an extension of the standard model that includes a heavy scalar singlet coupled to the leptonic doublet. Starting from the full…
A classical nonrelativistic effective field theory for a real Lorentz-scalar field $\phi$ is most conveniently formulated in terms of a complex scalar field $\psi$. There have been two derivations of effective Lagrangians for the complex…
Effective Lagrangians were originally used only at the tree level as so-called phenomenological Lagrangians since they were in general non-renormalizable. Today they are treated as effective field theories valid below a characteristic…
We present a formulation of scalar effective field theories in terms of the geometry of Lagrange spaces. The horizontal geometry of the Lagrange space generalizes the Riemannian geometry on the scalar field manifold, inducing a broad class…
We investigate the renormalization of ``nonlocal'' interactions in an effective field theory using dimensional regularization with minimal subtraction. In a scalar field theory, we write an integro-differential renormalization group…
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale…
We analyze the structure of multiloop supergraphs contributing to the effective Lagrangians in 4d supersymmetric gauge theories and in the models obtained from them by dimensional reduction. When d=4, this gives the renormalization of the…
Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda…
We consider a scalar $\phi^4$ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner…
We introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of…
We consider a self-interacting scalar field theory in a slowly varying gravitational background field. Using zeta-function regularization and heat-kernel techniques, we derive the one-loop effective Lagrangian up to second order in the…
The 1--loop effective Lagrangian for a massive scalar field on an arbitrary causality violating spacetime is calculated using the methods of Euclidean quantum field theory in curved spacetime. Fields of spin 1/2, spin 1 and twisted field…
We discuss $d=1, {\cal N}=2$ supersymmetric matrix models and exhibit the associated $d=2$ collective field theory in the limit of dense eigenvalues. From this theory we construct, by the addition of several new fields, a $d=2$…
In a four-dimensional space, I shall construct all of the conformally invariant scalar-tensor field theories, which are flat space compatible; i.e., well-defined and differentiable when evaluated for a flat metric tensor and constant scalar…