Related papers: Fundamental Structures of M(brane) Theory
It is shown that a relativistic (i.e. a Poincar{\' e} invariant) theory of extended objects (called p-branes) is not necessarily invariant under reparametrizations of corresponding $p$-dimensional worldsheets (including worldlines for $p =…
The structure of a diffeomorphism invariant Lagrangians for an extended object W embedded in a bulk space M is discussed by following a close analogy with the relativistic particle in electromagnetic field as a system that is…
It is shown that the previously noticed internal dynamical $SO(D-1)$ symmetry arXiv:1003.5189 for relativistic M-branes moving in $D$-dimensional space-time is naturally realized in the (extended by powers of $\frac{1}{p_+}$) enveloping…
M-branes are related to theories on function spaces $\cal{A}$ involving M-linear non-commutative maps from $\cal{A} \times \cdots \times \cal{A}$ to $\cal{A}$. While the Lie-symmetry-algebra of volume preserving diffeomorphisms of $T^M$…
We propose a generalization of spin algebra using multi-index objects, and a dynamical system analogous to matrix theory. The system has a solution described by generalized spin representation matrices and possesses a symmetry similar to…
Extended geometry provides a unified framework for double geometry, exceptional geometry, etc., i.e., for the geometrisations of the string theory and M-theory dualities. In this talk, we will explain the structure of gauge transformations…
The recently discovered dynamical symmetry for relativistic extended objects is derived from first principles, and analogues commutators are obtained for the corresponding formal quantum expressions
We construct a new extension of the Poincar\'e superalgebra in eleven dimensions which contains super one-, two- and five-form charges. The latter two are associated with the supermembrane and the superfivebrane of M-theory. Using the…
An `algebraic' approach to M-theory is briefly reviewed, and a proposal is made for a similar algebraic structure underlying the $T^9$ compactification of `M(embrane) theory', i.e. the M(atrix) model with area-preserving diffeomorphism…
The Poincar\'e algebra can be extended (non-centrally) to the Maxwell algebra and beyond. These extensions are relevant for describing particle dynamics in electro-magnetic backgrounds and possibly including the backreaction due the…
The structure constants for Moyal brackets of an infinite basis of functions on the algebraic manifolds M of pseudo-unitary groups U(N_+,N_-) are provided. They generalize the Virasoro and W_\infty algebras to higher dimensions. The…
We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is…
General structure of classical reparametrization-invariant matter systems, mainly the relativistic particle and its $d$-brane generalization, are studied. The exposition is in close analogy with the relativistic particle in an…
I review the multi-dimensional generalizations of the Virasoro algebra, i.e. the non-central Lie algebra extensions of the algebra vect(N) of general vector fields in N dimensions, and its Fock representations. Being the Noether symmetry of…
Diffeomorphisms and an internal symmetry (e.g., local Lorentz invariance) are typically regarded as the symmetries of any geometrical gravity theory, including general relativity. In the first-order formalism, diffeomorphisms can be thought…
We first consider M-theory formulated on an open eleven-dimensional spin-manifold. There is then a potential anomaly under gauge transformations on the E_8 bundle that is defined over the boundary and also under diffeomorphisms of the…
The fundamental symmetries in gravity and gauge theories, formulated using differential forms, are gauge transformations and diffeomorphisms. These symmetries act in distinct ways on different dynamical fields. Yet, the commutator of these…
The representation theory of non-centrally extended Lie algebras of Noether symmetries, including spacetime diffeomorphisms and reparametrizations of the observer's trajectory, has recently been developped. It naturally solves some…
Canonical quantization of gravity requires knowledge about the representation theory of its constraint algebra, which is physically equivalent to the algebra of arbitrary 4-diffeomorphisms. All interesting lowest-energy representations are…
We describe various structures of algebraic nature on the space of continuous valuations on convex sets, their properties (like versions of Poincar\'e duality and hard Lefschetz theorem), and their relations and applications to integral…