Related papers: $A_\infty$ perspective to Sen's formalism
We discuss general properties of $A_\infty$-algebras and their applications to the theory of open strings. The properties of cyclicity for $A_\infty$-algebras are examined in detail. We prove the decomposition theorem, which is a stronger…
We present a novel, manifestly Lorentz-invariant, polynomial, and straightforwardly quantisable action for duality-symmetric gauge theories formulated using gauge potentials. Central to our construction is the identification of a harmonic…
Using arbitrary symplectic structures and parametrization invariant actions, we develop a formalism, based on Dirac's quantization procedure, that allows us to consider theories with both space-space as well as space-time noncommutativity.…
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…
Given a fibration over the circle, we relate the eigenspace decomposition of the algebraic monodromy, the homological finiteness properties of the fiber, and the formality properties of the total space. In the process, we prove a more…
A discrete field formalism exposes the physical meaning and the origins of gauge fields and of their symmetries and singularities.
A $k$-symplectic framework for classical field theories subject to nonholonomic constraints is presented. If the constrained problem is regular one can construct a projection operator such that the solutions of the constrained problem are…
We develop the General Theory of Relativity in a formalism with extended causality that describes physical interaction through discrete, transversal and localized pointlike fields. The homogeneous field equations are then solved for a…
Nonholonomic systems are variational models commonly used for mechanical systems with ideal no-slip constraints. This note provides a differential-geometric derivation of the nonholonomic equations of motion for an arbitrary rigid body…
In this paper, we derive a "hamiltonian formalism" for a wide class of mechanical systems, including classical hamiltonian systems, nonholonomic systems, some classes of servomechanism... This construction strongly relies in the geometry…
A consistent action for heterotic and type II superstring field theory was recently proposed by Sen. We give an algebraic formulation of this action in terms of certain twisted $L_\infty$-algebra. We further show that Sen's Wilsonian…
Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $\tau$. In this paper we extend the…
Sen's superstring field theory successfully formulates perturbative superstring theory but has a number of unusual features. The action is not background independent and the resulting effective field theory does not appear to have standard…
After explicitly constructing the symmetric space sigma model lagrangian in terms of the coset scalars of the solvable Lie algebra gauge in the current formalism we derive the field equations of the theory.
The jet formalism for Classical Field theories is extended to the setting of Lie algebroids. We define the analog of the concept of jet of a section of a bundle and we study some of the geometric structures of the jet manifold. When a…
Formal methods refer to rigorous, mathematical approaches to system development and have played a key role in establishing the correctness of safety-critical systems. The main building blocks of formal methods are models and specifications,…
A comprehensive approach to the theory of higher spin gauge fields is proposed. By explicitly separating out details of implementation from general principles, it becomes possible to focus on the bare minimum of requirements that such a…
We give an example of how conventional gauging methods obstruct a systematic analysis of gauged supergravities. We discuss how the embedding tensor formalism deals with these problems and argue that the gauge algebra related to the…
Dendroidal sets offer a formalism for the study of $\infty$-operads akin to the formalism of $\infty$-categories by means of simplicial sets. We present here an account of the current state of the theory while placing it in the context of…
We introduce a new formulation of the real-spectral-triple formalism in non-commutative geometry (NCG): we explain its mathematical advantages and its success in capturing the structure of the standard model of particle physics. The idea,…