相关论文: Geometric Structures in Field Theory

Tangent category theory is a well-established categorical framework for differential geometry. A long list of fundamental geometric constructions, such as the tangent bundle functor, vector fields, Euclidean spaces, and vector bundles have…

Motivated by the study of physical models associated with General Relativity, we review some finite-dimensional, geometric and covariant formulations that allow us to characterize in a simple manner the symmetries for classical field theory…

We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended…

Most modern theoretical considerations of the physical world suggest that nature is: (1) field-theoretic, (2) smooth, (3) local, (4) gauged, (5) containing fermions, and (6) non-perturbative. Tautologous as this may sound to experts, it is…

We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed…

We formulate a kinematical extension of Double Field Theory on a $2d$-dimensional para-Hermitian manifold $(\mathcal{P},\eta,\omega)$ where the $O(d,d)$ metric $\eta$ is supplemented by an almost symplectic two-form $\omega$. Together…

I construct a global version of the local polysymplectic approach to covariant Hamiltonian field theory pioneered by C. Gunther. Beginning with the geometric framework of the theory, I specialize to vertical vector fields to construct the…

The k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic formulation of…

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…

We state the intrinsic form of the Hamiltonian equations of first-order Classical Field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar…

Geometric structures on manifolds became popular when Thurston used them in his work on the geometrization conjecture. They were studied by many people and they play an important role in higher Teichm\"uller theory. Geometric structures on…

This set of lecture notes first gives an introduction to the geometry of principal bundles. Next, it demonstrates how they can be used to formalize the concept of gauge theories arising in physics. A basic familiarity with the differential…

This is the second in a series of papers that aim to develop rigorous and most encompassing foundations for field theory, where in the first installment, we laid out the natural formulation of bosonic variational field theory via the…

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…

In this review the foundations of Geometric Quantization are explained and discussed. In particular, we want to clarify the mathematical aspects related to the geometrical structures involved in this theory: complex line bundles, hermitian…

In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian to Hamiltonian classical field theories, and then we…

In gauge theory, Higgs fields are responsible for spontaneous symmetry breaking. In classical gauge theory on a principal bundle P, a symmetry breaking is defined as the reduction of a structure group of this principal bundle to a subgroup…

We investigate G-invariant symplectic structures on the cotangent bundle T*P of a principal G-bundle P(M,G) which are canonically related to automorphisms of the tangent bundle TP covering the identity map of P and commuting with the action…

In a class of generalized gravity theories with general couplings between the scalar field and the scalar curvature in the Lagrangian, we describe the quantum generation and the classical evolution processes of both the scalar and tensor…

Multisymplectic geometry - which originates from the well known de Donder-Weyl theory - is a natural framework for the study of classical field theories. Recently, two algebraic structures have been put forward to encode a given theory…