Related papers: Supermanifold Forms and Integration. A Dual Theory
We use spectral invariants in Lagrangian Floer theory in order to show that there exist \emph{isometric} embeddings of normed linear spaces (finite or infinite dimensional, depending on the case) into the space of Hamiltonian deformations…
We find general non-linear lagrangians of a U(1) field invariant under electric-magnetic duality. They are characterized by an arbitrary function and go to the Maxwell theory in the weak field limit. We give some explicit examples which are…
A dynamical system on the total space of the fibre bundle of second order accelerations, $T^2M$, is defined as a third order vector field $S$ on $T^2M$, called semispray, which is mapped by the second order tangent structure into one of the…
Considering an extension of the principle of covarience to the action along a path in relativistic Lagrangian mechanics, we motivate the use of geometric -- i.e. covariant and parameter invariant -- Lagrangian functions. We then study some…
This review is devoted to some aspects of non-linear Supersymmetry in four dimensions that can be efficiently described via nilpotent superfields, in both rigid and curved Superspace. Our focus is mainly on the partial breaking of rigid…
We construct the Hodge dual for supermanifolds by means of the Grassmannian Fourier transform of superforms. In the case of supermanifolds it is known that the superforms are not sufficient to construct a consistent integration theory and…
In this paper, we extend the collinear superspace formalism to include the full range of $\mathcal{N} = 1$ supersymmetric interactions. Building on the effective field theory rules developed in a companion paper - "Navigating Collinear…
Lepage equivalents of Lagrangians are a higher order, field-theoretical generalization of the notion of Poincare-Cartan form from mechanics and play a similar role: they give rise to a geometric formulation (and to a geometric…
We translate into the double forms formalism the basic identities of Greub and Greub-Vanstone that were obtained in the mixed exterior algebra. In particular, we introduce a second product in the space of double forms, namely the…
Hierarchies of Lagrangians of degree two, each only partly determined by the choice of leading terms and with some coefficients remaining free, are considered. The free coefficients they contain satisfy the most general differential…
We propose a notion of a pluri-Lagrangian problem, which should be understood as an analog of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems…
This article studies the deformation problem for compact special Lagrangians with boundary in a Calabi--Yau manifold, with each boundary component constrained along a given Lagrangian submanifold. The tangent vectors generating such…
A notion of internal Lagrangian for a system of differential equations is introduced. A spectral sequence related to internal Lagrangians is obtained. A connection between internal Lagrangians and presymplectic structures is investigated.…
Lagrangian formalism is established for differential equations with special functions of mathematical physics as solutions. Formalism is based on either standard or non-standard Lagrangians. This work shows that the procedure of deriving…
We take advantage of different generalizations of the tangent manifold to the context of graded manifolds, together with the notion of super section along a morphism of graded manifolds, to obtain intrinsic definitions of the main objects…
We classify all the six derivative Lagrangians of gravity, whose traced field equations are of second or third order, in arbitrary dimensions. In the former case, the Lagrangian in dimensions greater than six, reduces to an arbitrary linear…
We study configurations of disjoint Lagrangian submanifolds in certain low-dimensional symplectic manifolds from the perspective of the geometry of Hamiltonian maps. We detect infinite-dimensional flats in the Hamiltonian group of the…
We discuss the dynamics of a particular two-dimensional (2D) physical system in the four dimensional (4D) (non-)commutative phase space by exploiting the consistent Hamiltonian and Lagrangian formalisms based on the symplectic structures…
The Hamiltonian formulation for the mechanical systems with reparametrization-invariant Lagrangians, depending on the worldline external curvatures is given, which is based on the use of moving frame. A complete sets of constraints are…
We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals…