相关论文: A mathematical base for Fibre bundle formulation o…

Reparametrization invariant Lagrangian theories with higher derivatives are considered. We investigate the geometric structures behind these theories and construct the Hamiltonian formalism in a geometric way. The Legendre transformation…

Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…

Finsler geometry motivates a generalization of the Riemannian structure of spacetime to include dependence of the spacetime metric and associated invariant tensor fields on the four-velocity coordinates as well as the spacetime coordinates…

We give a new construction of strict deformation quantization of symplectic manifolds equipped with a proper Lagrangian fiber bundle structure, whose representation spaces are the quantum Hilbert spaces obtained by geometric quantization.…

Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…

Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…

Field theoretical models with first order Lagrangean can be formulated in a covariant Hamiltonian formalism. In this article, the geometrical construction of the Gerstenhaber structure that encodes the equations of motion is explained for…

We define quantum field theory by taking the Lagrangian action to be given as a sequence of mathematically well-defined functionals written in terms of operator fields fulfilling given \hbox{local} commutation relations. The renormalized…

For scalar field theories, such as those EFTs describing the Higgs, it is well-known that the 2-derivative Lagrangian is captured by geometry. That is, the set of operators with exactly 2 derivatives can be obtained by pulling back a metric…

In classical field theory, the composite fibred manifolds Y -> Z -> X provides the adequate mathematical formulation of gauge models with broken symmetries, e.g., the gauge gravitation theory. This work is devoted to connections on…

We propose a distinction between the physical and the mathematical parts of gauge field theories. The main problem we face is to uphold a strong and meaningful criterion of what is physical. We like to call it "Field's dilemma", referring…

The paper introduces the approach to construction of the Lagrangian of the field (fields). This approach is based solely on the metric function of the Finsler space: the Lagrangian is constructed as the unit divided by the volume swept by…

The standard formulation of gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic qunantum theoretical access in the spirit of Wigner's representation theory shows that…

A quantum field theory approach is put forward to generalize the concept of classical spatial light beams carrying orbital angular momentum to the single-photon level. This quantization framework is carried out both in the paraxial and…

Jet formalism provides the adequate mathematical formulation of classical field theory, reviewed in hep-th/0612182v1. A formulation of QFT compatible with this classical one is discussed. We are based on the fact that an algebra of…

Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and…

A fibre bundle viewpoint of gauge field theories is reviewed with focus on a possible quantum interpretation. The fundamental quantum properties of non-separability of state spaces is considered in the context of defining the connection on…

Building on the Utiyama principle we formulate an approach to Lagrangian field theory in which exterior covariant differentials of vector-valued forms replace partial derivatives, in the sense that they take up the role played by the latter…

Algebraic quantum field theory is a general mathematical framework for relativistic quantum physics, based on the theory of operator algebras. It comprises all observable and operational aspects of a theory. In its framework the entire…

The bundles suitable for a description of higher-spin fields can be built in terms of a 2-spinor bundle as the basic `building block'. This allows a clear, direct view of geometric constructions aimed at a theory of such fields on a curved…