Related papers: Dimensional Reduction without Extra Continuous Dim…
Symmetry under a particular class of non-strictly canonical transformation may be used to identify, and subsequently excise degrees of freedom which do not contribute to the closure of the algebra of dynamical observables. Such redundant…
We initiate a study on a range of new generalized derivations of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. This new generalization of derivations has an analogue in the theory of associative…
We extent the standard approach of dimensional regularization of Feynman diagrams: we replace the transition to lower dimensions by a 'natural' cut-off regulator. Introducing an external regulator of mass Lambda^(2e), we regain in the limit…
This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe…
We introduce an external field to calculate the quantum corrections of the 2d gravity, via trace anomaly. We show that there are black hole type solution even in the absence of matter field and cosmological constant. We also see that these…
These notes explore some aspects of formal derived geometry related to classical field theory. One goal is to explain how many important classical field theories in physics -- such as supersymmetric gauge theories and supersymmetric…
A number of very different approaches to quantum gravity contain a common thread, a hint that spacetime at very short distances becomes effectively two dimensional. I review this evidence, starting with a discussion of the physical meaning…
We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum…
The procedure of null reduction provides a concrete way of constructing field theories with Galilean invariance. We use this to examine Galilean gauge theories, viz. Galilean electrodynamics and Yang-Mills theories in spacetime dimensions 3…
We perform a reduction from three to two spatial dimensions of the physics of a spin-1/2 fermion coupled to the electromagnetic field, by applying Hadamard's method of descent. We consider first the free case, in which motion is determined…
We study some two-dimensional dilaton gravity models using the formal theory of partial differential equations. This allows us to prove that the reduced phase space is two-dimensional without an explicit construction. By using a convenient…
A basic problem of classical field theory, which has attracted growing attention over the past decade, is to find and classify all nonlinear deformations of linear abelian gauge theories. The first part of this paper summarizes and…
We review recent applications of equivariant dimensional reduction techniques to the construction of Yang-Mills-Higgs-Dirac theories with dynamical mass generation and exactly massless chiral fermions.
Dynamical localization of non-Abelian gauge fields in non-compact flat $D$ dimensions is worked out. The localization takes place via a field-dependent gauge kinetic term when a field condenses in a finite region of spacetime. Such a…
We propose a new form of dimensional reduction that constrains dilatation instead of a component of momentum. It corresponds to replacing toroidal compactification in a Cartesian coordinate with that in the logarithm of the radius. Massive…
In recent development of double field theory, as for the description of the massless sector of closed strings, the spacetime dimension is formally doubled, i.e. from D to D+D, and the T-duality is realized manifestly as a global O(D,D)…
It is a general belief that the only possible way to consistently deform the Pauli-Fierz action, changing also the gauge algebra, is general relativity. Here we show that a different type of deformation exists in three dimensions if one…
Gauge fields in exotic representations of the Lorentz group in D dimensions - i.e. ones which are tensors of mixed symmetry corresponding to Young tableaux with arbitrary numbers of rows and columns - naturally arise through massive string…
We introduce a classical field theory based on a concept of extended causality that mimics the causality of a point-particle Classical Mechanics by imposing constraints that are equivalent to a particle initial position and velocity. It…
We prove a decomposition formula for the dimensional reduction of an extended topological field theory that arises as an orbifold of an equivariant topological field theory. Our decomposition formula can be expressed in terms of a…