Histories and observables in covariant field theory

@article{Paugam2011HistoriesAO,
  title={Histories and observables in covariant field theory},
  author={Fr{\'e}d{\'e}ric Paugam},
  journal={Journal of Geometry and Physics},
  year={2011},
  volume={61},
  pages={1675-1702}
}
Abstract Motivated by DeWitt’s viewpoint of covariant field theory, we define a general notion of a non-local classical observable that applies to many physical Lagrangian systems (with bosonic and fermionic variables), by using methods that are now standard in algebraic geometry. We review the methods of local functional calculus, as they are presented by Beilinson and Drinfeld, and relate them to our construction. We partially explain the relation of these with Vinogradov’s secondary calculus… Expand
Homotopical Poisson reduction of gauge theories
The classical Poisson reduction of a given Lagrangian system with (local) gauge symmetries has to be done before its quantization. We propose here a coordinate free and self-contained mathematicalExpand
Gauge Theories and Their Homotopical Poisson Reduction
In this chapter, we define general gauge theories and study their classical aspects. These may also be called local variational problems, because their action functional is a local functional. TheExpand
Model categorical Koszul-Tate resolution for algebras over differential operators
Derived D-Geometry is considered as a convenient language for a coordinate-free investigation of nonlinear partial differential equations up to symmetries. One of the first issues one meets in theExpand
On four Koszul-Tate resolutions
We suggest a D-geometric de nition of a Koszul-Tate (KT) resolution for a DGDAmorphism (thought of as the projection onto an on-shell function algebra). Here DGDA denotes the category of di erentialExpand
Algebraic Analysis of Non-linear Partial Differential Equations
This chapter introduces the necessary tools for a differential algebraic coordinate-free study of non-linear partial differential equations in general, and of Lagrangian mechanics in particular. WeExpand
Model structure on differential graded commutative algebras over the ring of differential operators
We construct a cofibrantly generated model structure on the category of differential non-negatively graded quasi-coherent commutative DX-algebras, where DX is the sheaf of differential operators of aExpand
Model structure on di erential graded commutative algebras over the ring of di erential operators
We construct a co brantly generated model structure on the category of di erential non-negatively graded quasi-coherent commutative DX -algebras, where DX is the sheaf of di erential operators of aExpand
Homotopical algebraic context over differential operators
Building on our previous work, we show that the category of non-negatively graded chain complexes of $$\mathcal {D}_X$$DX-modules – where X is a smooth affine algebraic variety over an algebraicallyExpand
Koszul–Tate resolutions as cofibrant replacements of algebras over differential operators
Homotopical geometry over differential operators is a convenient setting for a coordinate-free investigation of nonlinear partial differential equations modulo symmetries. One of the first issues oneExpand

References

SHOWING 1-10 OF 40 REFERENCES
Quantization of Gauge Systems
This is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classicalExpand
The (Secret?) homological algebra of the Batalin-Vilkovisky approach
This is a survey of `Cohomological Physics', a phrase that first appeared in the context of anomalies in gauge theory. Differential forms were implicit in physics at least as far back as Gauss (1833)Expand
Homological perturbation theory and the algebraic structure of the antifield-antibracket formalism for gauge theories
The algebraic structure of the antifield-antibracket formalism for both reducible and irreducible gauge theories is clarified. This is done by using the methods of Homological Perturbation TheoryExpand
Renormalization and Effective Field Theory
This book tells mathematicians about an amazing subject invented by physicists and it tells physicists how a master mathematician must proceed in order to understand it. Physicists who know quantumExpand
Homotopical Algebraic Geometry II: Geometric Stacks and Applications
This is the second part of a series of papers devoted to develop Homotopical Algebraic Geometry. We start by defining and studying generalizations of standard notions of linear and commutativeExpand
Symplectic reduction, BRS cohomology, and infinite-dimensional Clifford algebras
Abstract This paper gives the mathematical foundations for the BRS quantization procedure. We first discuss the classical finite dimensional BRS procedure and relate it to Marsden-WeinsteinExpand
Noether's variational theorem II and the BV formalism
We review the basics of the Lagrangian approach to field theory and recast Noether's Second Theorem formulated in her language of dependencies using a slight modernization of terminology andExpand
Poisson sigma models and deformation quantization
This is a review aimed at the physics audience on the relation between Poisson sigma models on surfaces with boundary and deformation quantization. These models are topological open string theories.Expand
Au-dessous de SpecZ .
In this article we use the theories of relative algebraic geometry and of homotopical algebraic geometry (cf. [HAGII]) to construct some categories of schemes defined under Spec ℤ. We define theExpand
The Global Approach to Quantum Field Theory
I: CLASSICAL DYNAMICAL THEORY II: THE HEURISTIC ROAD TO QUANTIZATION. THE QUANTUM FORMALISM AND ITS INTERPRETATION III: EVALUATION AND APPROXIMATION OF FEYNMAN FUNCTIONAL INTEGRALS IV: LINEAR SYSTEMSExpand
...
1
2
3
4
...