Related papers: Polysymplectic Hamiltonian Field Theory
By generalizing the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that…
In the context of non-relativistic quantum field theory, a method is proposed for multiplying field operators at the same spatial point and obtaining regular (i.e. rigorously defined) interaction terms for the Hamiltonian. The basic idea is…
We study the Euler-Lagrange cohomology and explore the symplectic or multisymplectic geometry and their preserving properties in classical mechanism and classical field theory in Lagrangian and Hamiltonian formalism in each case…
A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…
Quantum systems governed by non-Hermitian Hamiltonians with $\PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We argue that $\PT$ symmetry may also be important and present at the level…
We make a perturbative analysis of the number of degrees of freedom in a large class of metric theories respecting spatial symmetries, of which the Lagrangian includes kinetic terms of both the spatial metric and the lapse function. We show…
A program searching for symmetry structures behind some features of the standard Model is launched. After addressing known no-go theorems, we construct a novel symmetry mixing gauge and Higgs fields which is a Lorentz symmetry extension…
We introduce a general framework for realizing $\mathcal{PT}$-like phase transitions in non-Hermitian systems without imposing explicit parity--time ($\mathcal{PT}$) symmetry. The approach is based on constructing a Hamiltonian as the…
In the symplectic Lagrangian framework we newly embed an irreducible massive vector-tensor theory into a gauge invariant system, which has become reducible, by extending the configuration space to include an additional pair of scalar and…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose…
In this paper we propose a new supersymmetric extension of conformal mechanics. The Grassmannian variables that we introduce are the basis of the forms and of the vector-fields built over the symplectic space of the original system. Our…
A stochastic field theory approach is applied to a coarse-grained polymer model that will enable studies of polymer behavior under non-equilibrium conditions. This article is focused on the validation of the new model in comparison to…
We introduce a phase space with spinorial momenta, corresponding to fermionic derivatives, for a 2d supersymmetric (1, 1) sigma model. We show that there is a generalisation of the covariant De Donder-Weyl Hamiltonian formulation on this…
We formulate singular classical theories without involving constraints. Applying the action principle for the action (27) we develop a partial (in the sense that not all velocities are transformed to momenta) Hamiltonian formalism in the…
The SU(2) collective coordinates expansion of the Born-Infeld\break Skyrmion Lagrangian is performed. The classical Hamiltonian is computed from this special Lagrangian in approximative way: it is derived from the expansion of this…
This paper considers the enhanced symplectic "category" for purposes of quantizing quasi-Hamiltonian $G$-spaces, where $G$ is a compact simple Lie group. Our starting point is the well-acknowledged analogy between the cotangent bundle…
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined via the (Hamiltonian)…
We study Hamiltonian field theories on the multisymplectic bundle of a principal G-bundle with Hamiltonian densities invariant under a subgroup $H\subset G$. Using the covariant bracket formulation, we reduce the polysymplectic space and…
In this paper we will present Lagrangian and Hamiltonian $k$-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using…