相关论文: On incompleteness of classical field theory
Classical gravitation theory is formulated as gauge theory on natural bundles where gauge symmetries are general covariant transformations and a gravitational field is a Higgs field responsible for their spontaneous symmetry breaking.
We use geometric ideas coming from certain classic algebraic constructions to associate, to every classical field theory, a symmetric monoidal double functor from the double category of cobordisms with corners to a certain symmetric…
We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply…
In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of $k$-cosymplectic geometry. We discuss the relation between Lagrangian and Hamiltonian…
We give a mathematical definition of quantum field theory on a manifold, and definition of quantization of a classical field theory given by a variational principle.
A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation…
Making use of the Lagrange anchor construction introduced earlier to quantize non-Lagrangian field theories, we extend the Noether theorem beyond the class of variational dynamics.
In this work, we develop a Lagrangian reduction theory for covariant field theories with gauge symmetries. These symmetries are modeled by a Lie group fiber bundle acting fiberwisely on a configuration bundle. In order to reduce the…
We consider a classical test particle subject to electromagnetic and gravitational fields, described by a Lagrangian depending on the acceleration and on a fundamental length. We associate to the particle a moving local reference frame and…
Whether Jordan's and Einstein's frame descriptions of F(R) theory of gravity are physically equivalent, is a long standing debate. However, practically none questioned on true mathematical equivalence, since classical field equations may be…
We define a new homotopy algebraic structure, that we call a braided $L_\infty$-algebra, and use it to systematically construct a new class of noncommutative field theories, that we call braided field theories. Braided field theories have…
We prove that, given a time-independent Lagrangian defined in the first tangent bundle of configuration space, every infinitesimal Noether symmetry that is defined in the $n$-tangent bundle and is not vanishing on-shell, can be written as a…
We apply the technique of formal geometry to give a necessary and sufficient condition for a line bundle supported on a smooth Lagrangian subvariety to deform to a sheaf of modules over a fixed deformation quantization of the structure…
Symmetries and, in particular, Cartan (Noether) symmetries and conserved quantities (conservation laws) are studied for the multisymplectic formulation of first and second order Lagrangian classical field theories. Noether-type theorems are…
A classical nonrelativistic effective field theory for a real Lorentz-scalar field $\phi$ is most conveniently formulated in terms of a complex scalar field $\psi$. There have been two derivations of effective Lagrangians for the complex…
A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization.
The teleparallel equivalent of general relativity (TEGR) is represented in a field-theoretical form, where tetrad and matter perturbations are propagated on a background solution of TEGR. Thus, the background tetrad and metric satisfy the…
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…
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…
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…