• Corpus ID: 115160125

Fibre Bundles, Jet Manifolds and Lagrangian Theory. Lectures for Theoreticians

  title={Fibre Bundles, Jet Manifolds and Lagrangian Theory. Lectures for Theoreticians},
In contrast with QFT, classical field theory can be formulated in a strict mathematical way by treating classical fields as sections of smooth fibre bundles. Addressing to the theoreticians, these Lectures aim to compile the relevant material on fibre bundles, jet manifolds, connections, graded manifolds and Lagrangian theory. They follow the perennial course of lectures on geometric methods in field theory at the Department of Theoretical Physics of Moscow State University. 

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Elements of supergeometry are an ingredient in many contemporary classical and quantum field models involving odd fields. For instance, this is the case of SUSY field theory, BRST theory,

The Profinite Dimensional Manifold Structure of Formal Solution Spaces of Formally Integrable PDEs

In this paper, we study the formal solution space of a nonlinear PDE in a fiber bundle. To this end, we start with foundational material and introduce the notion of a pfd structure to build up a new

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  • A. László
  • Mathematics
    Classical and Quantum Gravity
  • 2022
It is widely accepted that the Feynman integral is one of the most promising methodologies for defining a generally covariant formulation of nonperturbative interacting quantum field theories (QFTs)

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The inverse Higgs phenomenon, which plays an important rôle in physical systems with Goldstone bosons (such as the phonons in a crystal) involves nonholonomic mechanical constraints. By formulating

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The following questions are germane to our understanding of gauge-(in)variant quantities and physical possibility: in which ways are gauge transformations and spacetime diffeomorphisms similar, and



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Fibre bundles, an integral part of differential geometry, are also important to physics. This text, a succint introduction to fibre bundles, includes such topics as differentiable manifolds and

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Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in a very general setting. The cohomology of the variational bicomplex on an arbitrary graded manifold and

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I The Geometric Setting Introduction.- 1. Fiber Bundles.- 2. Jet Bundles.- 3. Principal Bundles and Connections.- 4. Natural Bundles.- 5. Gauge Natural Bundles.- II The Variational Structure of Field

The Geometry of Jet Bundles

Introduction 1. Bundles 2. Linear bundles 3. Linear operations on general bundles 4. First-order jet bundles 5. Second-order jet bundles 6. Higher-order jet bundles 7. Infinite jet bundles

On the notion of gauge symmetries of generic Lagrangian field theory

General Lagrangian theory of even and odd fields on an arbitrary smooth manifold is considered. Its non-trivial reducible gauge symmetries and their algebra are defined in this very general setting

The KT-BRST Complex of a Degenerate Lagrangian System

Quantization of a Lagrangian field system essentially depends on its degeneracy and implies its BRST extension defined by sets of non-trivial Noether and higher-stage Noether identities. However, one