Related papers: Stress theory for classical fields
We attempt a clarification of geometric aspects of quantum field theory by using the notion of smoothness introduced by Fr\"olicher and exploited by several authors in the study of functional bundles. A discussion of momentum and position…
In this note, we consider how the bundle geometry of field space interplays with the covariant phase space methods so as to allow to write results of some generality on the presymplectic structure of invariant gauge theories coupled to…
We derive a generic identity which holds for the metric (i.e. variational) energy-momentum tensor under any field transformation in any generally covariant classical Lagrangian field theory. The identity determines the conditions under…
The ordinary formalism for classical field theory is applied to dynamical group field theories. Focusing first on a local group field theory over one copy of SU(2) and, then, on more involved nonlocal theories (colored and non colored)…
The classical theory of gravity is formulated as a gauge theory on a frame bundle with spontaneous symmetry breaking caused by the existence of Dirac fermionic fields. The pseudo-Riemannian metric (tetrad field) is the corresponding Higgs…
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…
We study the dynamics of classical and quantum particles with spin and dipole moments in external fields within the framework of the general approach by making use of the projection technique. Applications include the neutrino physics in…
We consider arbitrary preexisting residual stress states in arbitrarily shaped, unloaded bodies. These stresses must be self-equilibrating and traction free. Common treatments of the topic tend to focus on either the mechanical origins of…
We review the concept of a graded bundle, which is a generalisation of a vector bundle, its linearisation, and a double structure of this kind. We then present applications of these structures in geometric mechanics including systems with…
We discuss the physical meaning and the geometric interpretation of causality implementation in classical field theories. Causality is normally implemented through kinematical constraints on fields but we show that in a zero-distance limit…
The transmission of stress through a marginally stable granular pile in two dimensions is exactly formulated in terms of a vector field of loop forces, and thence in terms of a single scalar potential. The loop force formulation leads to a…
The structure of topological quantum field theories on the compact Kahler manifold is interpreted. The BRST transformations of fields are derived from universal bundle and the observables are found from the second Chern class of universal…
Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
The Standard Model of the theory of elementary particles is based on the $U(1)\times SU(2)\times SU(3)$ symmetry. In the presence of a gravitation field, i. e. in a non-flat space-time manifold, this symmetry is implemented through three…
I consider configuration spaces for $N$-body problems, gauge theories and for GR in both geometrodynamical and Ashtekar variables forms, including minisuperspace and inhomogeneous perturbations thereabout in the former case. These examples…
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…
The definitions and some basic properties of the linear transports along paths in vector bundles and the normal frames for them are recalled. The formalism is specified on line bundles and applied to a geometrical description of the…
We take advantage of the principal bundle geometry of the space of connections to obtain general results on the presymplectic structure of two classes of (pure) gauge theories: invariant theories, and non-invariant theories satisfying two…
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…