相关论文: Higher-order Cartan symmetries in k-symplectic fie…
The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class…
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is…
In contrast to Hamiltonian perturbation theory which changes the time evolution, "spacelike deformations" proceed by changing the translations (momentum operators). The free Maxwell theory is only the first member of an infinite family of…
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…
A generalization of the KP equation involving higher-order dispersion is studied. This equation appears in several physical applications. As new results, the Lie point symmetries are obtained and used to derive conservation laws via…
We consider a scalar quantum field theory, in which the interaction takes the form of a field cutoff; the energy diverges to infinity whenever the value of the field at some point falls outside a finite interval. In a simple…
We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit, K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original…
This book is devoted to review two of the most relevant approaches to the study of classical field theories of first order, say k-symplectic and k-cosymplectic. In the last part, we relate the k-symplectic and k-cosymplectic manifolds with…
A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. While the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation theory…
Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are…
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…
Explicit expressions are constructed for a locally conserved vector current associated with a continuous internal symmetry and for energy-momentum and angular-momentum density tensors associated with the Poincar\'e group in field theories…
The paper deals with a cosmological model containing two scalar fields which can be considered as an extension of the Brans-Dicke scalar field model. Due to highly coupled non linear field equations, Noether Symmetry analysis has been…
Multisymplectic geometry is an adequate formalism to geometrically describe first order classical field theories. The De Donder-Weyl equations are treated in the framework of multisymplectic geometry, solutions are identified as integral…
In the present paper correspondence between non-Noether symmetries and bi-Hamiltonian structures is disscussed. We show that in regular Hamiltonian systems presence of the global bi-Hamiltonian structure is caused by symmetry of the space…
In earlier work, we have developed a nonequilibrium statistical field theory description of cosmic structure formation, dubbed Kinetic Field Theory (KFT), which is based on the Hamiltonian phase-space dynamics of classical particles and…
We construct a quantum thermal field theory for scalar particles in the case of infinite statistics. The extension is provided by working out the Fock space realization of a "quantum algebra", and by identifying the hamiltonian as the…
We review in detail the Hamiltonian dynamics for constrained systems. Emphasis is put on the total Hamiltonian system rather than on the extended Hamiltonian system. We provide a systematic analysis of (global and local) symmetries in total…
We consider the two scalar field cosmology in a FRW spatially flat spacetime where the scalar fields interact both in the kinetic part and the potential. We apply the Noether point symmetries in order to define the interaction of the scalar…
We summarize the use of Noether symmetries in Minisuperspace Quantum Cosmology. In particular, we consider minisuperspace models, showing that the existence of conserved quantities gives selection rules that allow to recover classical…