Related papers: A short course in effective Lagrangians
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…
These notes are a self-contained introduction to Galois theory, designed for the student who has done a first course in abstract algebra.
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
Constructions introduced by Dirac for singular Lagrangians are extended and reinterpreted to cover cases when kernel distributions are either nonintegrable or of nonconstant rank, and constraint sets need not be closed.
These notes are based on lecture courses I gave to third year mathematics students at Cambridge. They could form a basis of an elementary one--term lecture course on integrable systems covering the Arnold-Liouville theorem, inverse…
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…
In a recent paper [1] a master formula has been presented for the power counting of a general effective field theory. We first show that this master formula follows immediately from the concept of chiral dimensions (loop counting), together…
We apply the relativistic chiral Lagrangian to the nuclear equation of state. An effective chiral power expansion scheme, which is constructed to work around nuclear saturation density, is presented. The leading and subleading terms are…
These notes form an introduction to Lie algebras and group theory. Most of the material can be found in many works by various authors given in the list of references. The reader is referred to such works for more detail.
In this paper I discuss what, according to my long experience, every computer scientist should know from logic. We concentrate on issues of modeling, interpretability and levels of abstraction. We discuss what the minimal toolbox of logic…
These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for…
The techniques of dispersion relations match very well with those of effective field theory. I describe the techniques for using dispersion relations effectively, and give some pedagogical examples to illustrate the range of applications.
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
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…
A discussion of Lagrangian and Hamiltonian dynamics is presented at a level which should be suitable for advanced high school students. This is intended for those who wish to explore a version of mechanics beyond the usual Newtonian…
The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables…
In this talk I review an effective field theory that has been developed for processes with energetic hadrons, referred to as the Soft-Collinear Effective Theory. After outlining properties of the effective theory I briefly discuss its…
We study a class of weakly coupled Hamilton-Jacobi systems with a specific aim to perform a qualitative analysis in the spirit of weak KAM theory. Our main achievement is the definition of a family of related action functionals containing…
These lecture notes provide an introduction to logarithmic geometry with a view towards recent applications in the desingularization theory.
A derivation of the one-loop effective Lagrangian in the self-interacting $O(N)$ scalar theory, in slowly varying gravitational fields, is presented (using $\zeta$-regularization and heat-kernel techniques). The result is given in terms of…