Related papers: Symmetries in Classical Field Theory
Classical field theory is adequately formulated as Lagrangian theory on fibre bundles and graded manifolds. One however observes that non-trivial higher stage Noether identities and gauge symmetries of a generic reducible degenerate…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} Hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the generalized…
A diagram approach to classical nonlinear stochastic field theory is introduced. This approach is intended to serve as a link between quantum and classical field theories, resulting in an independent constructive characterisation of the…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for…
In contrast with QFT, classical field theory can be formulated in a strict mathematical way if one defines even classical fields as sections of smooth fiber bundles. Formalism of jet manifolds provides the conventional language of dynamic…
We provide an introductory exposition to the sheaf topos theoretic description of classical field theory motivated by the rigorous description of both $\bf{(i)}$ the variational calculus of (infinite dimensional) field-theoretic spaces, and…
We extend the Cauchy residue theorem to a large class of domains including differential chains that represent, via canonical embedding into a space of currents, divergence free vector fields and non-Lipschitz curves. That is, while the…
I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills…
A geometric description is given for the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism. We develop differential geometry on manifolds in which a basic set of…
We study the equilibration properties of classical integrable field theories at a finite energy density, with a time evolution that starts from initial conditions far from equilibrium. These classical field theories may be regarded as…
The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a…
We use the 1+3 frame formalism to write down the evolution equations for spherically symmetric models as a well-posed system of first order PDEs in two variables, suitable for numerical and qualitative analysis.
We present a geometric algorithm for obtaining consistent solutions to systems of partial differential equations, mainly arising from singular covariant first-order classical field theories. This algorithm gives an intrinsic description of…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
After a general description of the tomographic picture for classical systems, a tomographic description of free classical scalar fields is proposed both in a finite cavity and the continuum. The tomographic description is constructed in…
A mathematical framework of cohomological field theories (CohFTs) is formulated in the language of bigraded manifolds. Algebraic properties of operators in CohFTs are studied. Methods of constructing CohFTs, with or without gauge…
We review various aspects of (infinite) quantum group symmetries in 2D massive quantum field theories. We discuss how these symmetries can be used to exactly solve the integrable models. A possible way for generalizing to three dimensions…
In this paper, two things are done. (i) First, it is shown that any global symmetry of a gauge-invariant theory can be extended to the ghosts and the antifields so as to leave invariant the solution of the master-equation (before gauge…