Related papers: Abelianization of First Class Constraints
Metabelian algebras are introduced and it is shown that an algebra $A$ is metabelian if and only if $A$ is a nilpotent algebra having the index of nilpotency at most $3$, i.e. $x y z t = 0$, for all $x$, $y$, $z$, $t \in A$. We prove that…
The constraint equations for smooth $[n+1]$-dimensional (with $n\geq 3$) Riemannian or Lorentzian spaces satisfying the Einstein field equations are considered. It is shown, regardless of the signature of the primary space, that the…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
We consider mappings, which are structure consisting of a single function (and possibly some number of unary relations) and address the problem of approximating a continuous mapping by a finite mapping. This problem is the inverse problem…
We introduce a class of maps from an affine flat into a Riemannian manifold that solve an elliptic system defined by the natural second order elliptic operator of the affine structure and the nonlinear Riemann geometry of the target. These…
In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in…
We consider the formulation of the gravity theory first suggested by Regge and Teitelboim where the space-time is a four-dimensional surface in a flat ten-dimensional space. We investigate a canonical formalism for this theory following the…
We describe a sufficient condition for the localization functor to be a categorical equivalence. Using this result we explain how to simplify the test for projectivity. This leads to a description of the strictly simple algebras which are…
A group is metabelian if its commutator subgroup is abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear…
The way of finding all the constraints in the Hamiltonian formulation of singular (in particular, gauge) theories is called the Dirac procedure. The constraints are naturally classified according to the correspondig stages of this…
We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and…
This is the second paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. In this work we begin with the simplest examples: Finite dimensional models with…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
We show that a class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular…
Does a space enjoying good finiteness properties admit an algebraic model with commensurable finiteness properties? In this note, we provide a rational homotopy obstruction for this to happen. As an application, we show that the maximal…
Let $A$ be an abelian variety over an algebraically closed field. We show that $A$ is the automorphism group scheme of some smooth projective variety if and only if $A$ has only finitely many automorphisms as an algebraic group. This…
Following the symplectic approach we show how to embed the Abelian Proca model into a first-class system by extending the configuration space to include an additional pair of scalar fields, and compare it with the improved Dirac scheme. We…
First we prove that any inner automorphism in the stabilizer of a graded-simple unital associative algebra whose grading group is abelian is the conjugation by a homogeneous element. Now consider a grading by an abelian group on an…
This work addresses certain ambiguities in the Dirac approach to constrained systems. Specifically, we investigate the space of so-called ``rigging maps'' associated with Refined Algebraic Quantization, a particular realization of the Dirac…
In Dirac-Bergmann constrained dynamics, a first-class constraint typically does not _alone_ generate a gauge transformation. Each first-class constraint in Maxwell's theory generates a change in the electric field E by an arbitrary…