GRADED LAGRANGIAN FORMALISM

2013 ◽  
Vol 10 (05) ◽  
pp. 1350016 ◽  
Author(s):  
G. SARDANASHVILY
Keyword(s):  
Classical Field Theory ◽  
General Setting ◽  
Classical Field ◽  
Lagrangian Formalism ◽  
Lagrangian Systems ◽  
Comprehensive Description ◽  
Variational Bicomplex ◽  
Gauge Symmetries ◽  
Degenerate Lagrangian ◽  
Graded Manifolds

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 reducible degenerate Lagrangian systems, characterized by hierarchies of non-trivial higher-order Noether identities and gauge symmetries. This is a general case of classical field theory and Lagrangian non-relativistic mechanics.

scholarly journals CLASSICAL FIELD THEORY: ADVANCED MATHEMATICAL FORMULATION

2008 ◽  
Vol 05 (07) ◽  
pp. 1163-1189 ◽  
Author(s):  
G. SARDANASHVILY
Keyword(s):  
Field Theory ◽  
Mathematical Formulation ◽  
Classical Field Theory ◽  
Classical Field ◽  
Fibre Bundles ◽  
Graded Manifolds

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 this classical field theory by means of ghosts and antifields for the purpose of its quantization.

scholarly journals Scalar field radiation emitted by an accelerated scalar point source: A classical field theory approach

2019 ◽  
Vol 65 (2 Jul-Dec) ◽  
pp. 105
Author(s):  
D. P. Meira Filho ◽  
G. Dos Santos de Sausa ◽  
L. Helena Silva de Souza ◽  
R. De Silva Sales ◽  
J. Kysnney Santos Kamassury ◽  
...  
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Point Source ◽  
Scalar Potential ◽  
Classical Field Theory ◽  
Minkowski Spacetime ◽  
Classical Field ◽  
Lagrangian Formalism ◽  
Theory Approach ◽  
Massive Scalar Field

In this paper we will use classical field theory to address the interaction of an accelerated point source with a non-massive Klein-Gordon-Fock (KGF) field in Minkowski spacetime. For this, initially, we obtain the KGF equation for the non-massive scalar field via lagrangian formalism and the scalar potential through Green's function formalism. Finally, we reach the expression of the power radiated by a point scalar source under the influence of this field and its covariant generalization.

scholarly journals CONFORMAL INVARIANCE IN CLASSICAL FIELD THEORY

1994 ◽  
Vol 09 (03) ◽  
pp. 225-239
Author(s):  
D.R. GRIGORE
Keyword(s):  
Field Theory ◽  
Classical Field Theory ◽  
Classical Field ◽  
Lagrangian Formalism ◽  
Conformal Transformations ◽  
Action Functional ◽  
First Order ◽  
Conformally Invariant ◽  
Conformal Field ◽  
Chern Simons

A geometric generalization of the first order Lagrangian formalism is used to analyze a conformal field theory for an arbitrary primary field. We require that the global conformal transformations are Noetherian symmetries and we prove that the action functional can be taken strictly invariant with respect to these transformations. In other words, there does not exist a “Chern-Simons” type Lagrangian for a conformally invariant Lagrangian theory.

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