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The multiplicative Lagrangian and Hamiltonian introduce an additional parameter that, despite its variation, results in identical equations of motion as those derived from the standard Lagrangian. This intriguing property becomes even more…
Dualities are hidden symmetries that map seemingly unrelated physical systems onto each other. The goal of this work is to systematically construct families of Hamiltonians endowed with a given duality and to provide a universal description…
In this paper, we apply the methods developed in recent work for constructing A-twisted (2,2) Landau-Ginzburg models to analogous (0,2) models. In particular, we study (0,2) Landau-Ginzburg models on topologically non-trivial spaces away…
A dual action is obtained for a general non-abelian and non-supersymmetric gauge theory at the classical level. The construction follows steps similar to those used in pure abelian gauge theory. As an example we study the spontaneously…
A first-order Lagrangian $L^\nabla $ variationally equivalent to the second-order Einstein-Hilbert Lagrangian is introduced. Such a Lagrangian depends on a symmetric linear connection, but the dependence is covariant under diffeomorphisms.…
Lagrangian cobordisms between Legendrian knots arise in Symplectic Field Theory and impose an interesting and not well-understood relation on Legendrian knots. There are some known "elementary" building blocks for Lagrangian cobordisms that…
Let $L \subset \mathbb R \times J^1(M)$ be a spin, exact Lagrangian cobordism in the symplectization of the 1-jet space of a smooth manifold $M$. Assume that $L$ has cylindrical Legendrian ends $\Lambda_\pm \subset J^1(M)$. It is well known…
We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a…
We show how to generalize the classical duals found by Gabadadze {\it et al} to a very large class of self-interacting theories. This enables one to adopt a perturbative description beyond the scale at which classical perturbation theory…
The construction of gauge theories beyond the realm of Lie groups and algebras leads one to consider Lie groupoids and algebroids equipped with additional geometrical structures which, for gauge invariance of the construction, need to…
We define an abstract notion of double Lie algebroid, which includes as particular cases: (1) the double Lie algebroid of a double Lie groupoid in the sense of the author, such as the iterated tangent bundle of an ordinary manifold, and…
Time and again, non-conventional forms of Lagrangians with non-quadratic velocity dependence have found attention in the literature. For one thing, such Lagrangians have deep connections with several aspects of nonlinear dynamics including…
An analogue of the correspondence between GL(k)-conjugacy classes of matricial polynomials and line bundles is given for K-conjugacy classes, where K is one of the following: maximal parabolic, maximal torus, GL(k-1) embedded diagonally.…
In this paper, the theory of smooth action-dependent Lagrangian mechanics (also known as contact Lagrangians) is extended to a non-smooth context appropriate for collision problems. In particular, we develop a Herglotz variational principle…
Motivated by the problem of global stability of thermodynamical equilibria in non-equilibrium thermodynamics formulated in a recent paper [12], we introduce some mechanisms for constructing semi-infinite orbits of contact Hamiltonian…
These notes grew out of a lecture course on mathematical methods of classical physics for students of mathematics and mathematical physics at the master's level. Also, physicists with a strong interest in mathematics may find this text…
Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…
We discuss continuous duality transformations and the properties of classical theories with invariant interactions between electromagnetic fields and matter. The case of scalar fields is treated in some detail. Special discrete elements of…
In this paper we show how the well-know local symmetries of Lagrangeans systems, and in particular the diffeomorphism invariance, emerge in the Hamiltonian formulation. We show that only the constraints which are linear in the momenta…
We analyze the dynamics of gauge theories and constrained systems in general under small perturbations around a classical solution (background) in both Lagrangian and Hamiltonian formalisms. We prove that a fluctuations theory, described by…