Related papers: Stress theory for classical fields
Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…
The physical meaning and the geometrical interpretation of causality implementation in classical field theories are discussed. Local causality are kinematical constraints dynamically implemented via solutions of the field equations, but in…
Dense distributions of string-like objects in material media are considered in terms of continuum field theory. The strings are assumed to carry a quantized abelian topological charge, such as the Burgers vector of dislocations in solids or…
Gauge theory is a theory with constraints and, for that reason, the space of physical states is not a manifold but a stratified space (orbifold) with singularities. The classification of strata for smooth (and generalized) connections is…
A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…
We study manifolds arising as spaces of sections of complex manifolds fibering over the projective line with normal bundle of each section isomorphic to several copies of O(k). Such manifolds provide a natural setting for certain integrable…
This article serves as a pedagogical introduction to the problem of motion in classical field theories. The primary focus is on self-interaction: How does an object's own field affect its motion? General laws governing the self-force and…
A new geometrical setting for classical field theories is introduced. This description is strongly inspired in the one due to Skinner and Rusk for singular lagrangians systems. For a singular field theory a constraint algorithm is developed…
Motivated by the search for a Hamiltonian formulation of Einstein equations of gravity which depends in a minimal way on choices of coordinates, nor on a choice of gauge, we develop a multisymplectic formulation on the total space of the…
The most general gauge-invariant marginal deformation of four-dimensional abelian BF-type topological field theory is studied. It is shown that the deformed quantum field theory is topological and that its observables compute, in addition…
We present a brief introduction to the relativistic kinetic theory of gases with emphasis on the underlying geometric and Hamiltonian structure of the theory. Our formalism starts with a discussion on the tangent bundle of a Lorentzian…
We show that there exists a natural Tulczyjew triple in the dynamics of objects for which the standard kinematic configuration space $TM$, i.e. the tangent bundle, is replaced with its $n$-th exterior power, i.e. the bundle of tangent…
The theory of twistors on foliated manifolds is developed and the twistor space of the normal bundle is constructed. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate…
The paper presents a general geometric approach to energy-momentum tensors in Lagrangian field theories, based on a Hilbert-type definition. The approach is consistent with the ones defining energy-momentum tensors in terms of hypermomentum…
We consider classical gauge theory with spontaneous symmetry breaking on a principal bundle $P\to X$ whose structure group $G$ is reducible to a closed subgroup $H$, and sections of the quotient bundle $P/H\to X$ are treated as classical…
We present a topological quantization of free massive bosonic fields as the first example of a classical field theory with a quantum counterpart to be studied under this formalism. First, we identify certain harmonic map as a geometric…
In this article I give a rigorous construction of the classical and quantum photon field on non-compact manifolds with boundary and in possibly inhomogeneous media. Such a construction is complicated by the presence of zero-modes that may…
The dynamics of a classical branelike object in a curved background is derived from the covariant stress-energy conservation of the brane matter. The world sheet equations and boundary conditions are obtained in the pole-dipole…
Quantum field theory is discussed in M\"obius corner kaleidoscopes using the method of images. The vacuum average of the stress-energy tensor of a free field is derived and is shown to be a simple sum of straight cosmic string expressions,…
We classify almost all classical string configurations, considered in the framework of the semi-classical limit of the string/gauge theory duality. Then, we describe a procedure for obtaining the conserved quantities and the exact classical…