# Graded Infinite Order Jet Manifolds

@article{Sardanashvily2007GradedIO, title={Graded Infinite Order Jet Manifolds}, author={Gennadi A Sardanashvily}, journal={International Journal of Geometric Methods in Modern Physics}, year={2007}, volume={04}, pages={1335-1362} }

The relevant material on differential calculus on graded infinite order jet manifolds and its cohomology is summarized. This mathematics provides the adequate formulation of Lagrangian theories of even and odd variables on smooth manifolds in terms of the Grassmann-graded variational bicomplex.

## 21 Citations

### Grassmann-graded Lagrangian theory of even and odd variables

- Mathematics
- 2012

Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of…

### GRADED LAGRANGIAN FORMALISM

- Physics
- 2013

Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of…

### ADVANCED MATHEMATICAL FORMULATION

- Mathematics

In contrast with QFT, classical field theory can be formulated in strict mathematical terms of fibre bundles, graded manifolds and jet manifolds. Second Noether theorems provide BRST extension of…

### On incompleteness of classical field theory

- Mathematics
- 2009

Classical field theory is adequately formulated as Lagrangian theory on fibre bundles and graded manifolds. One however observes that non-trivial higher stage Noether identities and gauge symmetries…

### Classical Field Theory: Advanced Mathematical Formulation

- Mathematics
- 2008

In contrast with QFT, classical field theory can be formulated in strict mathematical terms of fibre bundles, graded manifolds and jet manifolds. Second Noether theorems provide BRST extension of…

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

- Mathematics
- 2009

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…

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

- Mathematics
- 2009

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…

### SUSY gauge theory on graded manifolds

- Mathematics
- 2014

Lagrangian classical field theory of even and odd fields is adequately formulated in terms of fibre bundles and graded manifolds. In particular, conventional Yang-Mills gauge theory is theory of…

### Differential Calculus on -Graded Manifolds

- Mathematics
- 2017

The differential calculus, including formalism of linear differential operators and the Chevalley–Eilenberg differential calculus, over -graded commutative rings and on -graded manifolds is…

### The differential calculus on N-graded manifolds

- Mathematics
- 2016

The differential calculus, including formalism of linear differential operators and the Chevalley–Eilenberg differential calculus, over N-graded commutative rings and onN-graded manifolds is…

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The iterated BRST cohomology is studied by computing cohomology of the variational complex on the infinite order jet space of a smooth fibre bundle. This computation also provides a solution of the…

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