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Continuum mechanics can be formulated in the Lagrangian frame (addressing motion of individual continuum particles) or in the Eulerian frame (addressing evolution of fields in an inertial frame). There is a canonical Hamiltonian structure…
A common approach to the theory of nonlocal Poisson brackets, seen from the operatorial point of view, has been to keep implicit the sets on which these brackets act. In this paper we aim to explicitly define appropriate functional spaces…
We analyze the issue of anomaly-free representations of the constraint algebra in Loop Quantum Gravity (LQG) in the context of a diffeomorphism-invariant gauge theory in three spacetime dimensions. We construct a Hamiltonian constraint…
We apply a simple mean field like variational calculation to compact QED in 2+1 dimensions. Our variational ansatz explicitly preserves compact gauge invariance of the theory. We reproduce in this framework all the known results, including…
It is well known that the validity of the so called Lenard-Magri scheme of integrability of a bi-Hamiltonian PDE can be established if one has some precise information on the corresponding 1st variational Poisson cohomology for one of the…
We develop flexible methods of deriving variational inference for models with complex latent variable structure. By splitting the variables in these models into "global" parameters and "local" latent variables, we define a class of…
We study the relationship between the equations of first order Lagrangian field theory on fiber bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. The…
We consider a geometric framework for analytical mechanics with external forces. Four versions of this framework are considered. A variational principle with boundary terms and external forces.The second and the third versions are the…
In (3+1) Hamiltonian form, the conditions for the electric/magnetic invariance of generic self-interacting gauge vector actions and the definition of the duality generator are obvious. Instead, (3+1) actions are not intrinsically Lorentz…
The general structure of the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism, the so called triplectic quantization, as presented in our previous paper with…
Taking the St\"uckelberg Lagrangian associated with the abelian self-dual model of P.K. Townsend et al as a starting point, we embed this mixed first- and second-class system into a pure first-class system by following systematically the…
Gauge invariant Lagrangian descriptions of irreducible and reducible half-integer higher-spin mixed-symmetric massless and massive representations of the Poincare group with off-shell algebraic constraints are constructed within a…
Using the multisymplectic Hamiltonian formalism, we propose a Poisson bracket for the electromagnetic field that, in addition to satisfying the restricted principle of relativity, reproduces well-established results from the standard…
In this work we take into consideration a generalization of Gauge Theories based on the analysis of the structural characteristics of Maxwell theory, which can be considered as the prototype of such kind of theories (Maxwell-like). Such…
In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…
Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to…
We present the BFV and the BV extension of the Poisson sigma model (PSM) twisted by a closed 3-form H. There exist superfield versions of these functionals such as for the PSM and, more generally, for the AKSZ sigma models. However, in…
We will pick up the concepts of partial and complete observables introduced by Rovelli in order to construct Dirac observables in gauge systems. We will generalize these ideas to an arbitrary number of gauge degrees of freedom. Different…
We extend the covariant canonical formalism recently discussed in ref. [1] to geometric theories coupled to both bosonic and fermionic $p$-forms. This allows a covariant hamiltonian treatment of supergravity theories. As examples we present…
We introduce the concept of partial Poisson structure on a manifold $M$ modelled on a convenient space. This is done by specifying a (weak) subbundle $T^{\prime}M$ of $T^{\ast}M$ and an antisymmetric morphism $P:T^{\prime}M\rightarrow TM$…