Related papers: The Tulczyjew triple for classical fields
Given a Lie group $G$, we elaborate the dynamics on $T^*T^*G$ and $T^*TG$, which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew symplectic space $TT^*G$, which may be defined by a Lagrangian or a Hamiltonian function.…
Recent work on Euler hierarchies of field theory Lagrangians iteratively constructed {}from their successive equations of motion is briefly reviewed. On the one hand, a certain triality structure is described, relating arbitrary field…
By means of an appropriate re-scaling of the metric in a Lagrangian, we are able to reduce it to a kinetic term only. This form enables us to examine the extended complexified solution set (complex moduli space) of field theories by finding…
The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be…
We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with…
Finite element representations of Maxwell's equations pose unusual challenges inherent to the variational representation of the `curl-curl' equation for the fields. We present a variational formulation based on classical field theory.…
In this paper we derive the symplectic framework for field theories defined by higher-order Lagrangians. The construction is based on the symplectic reduction of suitable spaces of iterated jets. The possibility of reducing a higher-order…
The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and…
We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first…
A "Master" gauge theory is constructed in 2+1-dimensions through which various gauge invariant and gauge non-invariant theories can be studied. In particular, Maxwell-Chern-Simons, Maxwell-Proca and Maxwell-Chern-Simons -Proca models are…
Hamilton equations based not only upon the Poincare--Cartan equivalent of a first-order Lagrangian, but rather upon its Lepagean equivalent are investigated. Lagrangians which are singular within the Hamilton--De Donder theory, but…
The boundary structure of $3+1$-dimensional gravity (in the Palatini-Cartan formalism) coupled to to gauge (Yang-Mills) and matter (scalar and spinorial) fields is described through the use of the Kijowski-Tulczijew construction. In…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
The aim of this paper is to propose an unambiguous intrinsic formalism for higher-order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, which implies the existence of…
A gauge-invariant formulation of constrained variational calculus, based on the introduction of the bundle of affine scalars over the configuration manifold, is presented. In the resulting setup, the Lagrangian is replaced by a section of a…
We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional and including a Lagrangian formalism in which self-adjoint (Schroedinger) operators are…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
In the first part of the paper we define a perturbative (pre-formal) geometry and formulate a theorem on the relation between the construction of a perturbative neighborhood of affine varieties and the higher tangent bundles. In the second…
We continue the study of symmetries in the Lagrangian formalism of arbitrary order with the help of the so-called Anderson-Duchamp-Krupka equations. For the case of second-order equations and arbitrary vector fields we are able to establish…