scholarly journals Deformations of the exterior algebra of differential forms

2016 ◽  
Vol 57 (4) ◽  
pp. 771-787
Author(s):  
Ariel Molinuevo
Keyword(s):  
Differential Forms ◽  
Exterior Algebra

scholarly journals Exterior Algebra with Differential Forms on Manifolds

2012 ◽  
Vol 60 (2) ◽  
pp. 247-252
Author(s):  
Md. Showkat Ali ◽  
K.M. Ahmed ◽  
M.R. Khan ◽  
Md. Mirazul Islam
Keyword(s):  
Differential Geometry ◽  
Differential Equations ◽  
Differential Forms ◽  
Exterior Algebra ◽  
Linear Spaces ◽  
Exterior Differentiation

The concept of an exterior algebra was originally introduced by H. Grassman for the purpose of studying linear spaces. Subsequently Elie Cartan developed the theory of exterior differentiation and successfully applied it to the study of differential geometry [8], [9] or differential equations. More recently, exterior algebra has become powerful and irreplaceable tools in the study of differential manifolds with differential forms and we develop theorems on exterior algebra with examples.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11528 Dhaka Univ. J. Sci. 60(2): 247-252, 2012 (July)

scholarly journals Homogeneous and Inhomogeneous Maxwell’s Equations in Terms of Hodge Star Operator

2018 ◽  
Vol 37 ◽  
pp. 15-27
Author(s):  
Zakir Hossine ◽  
Md Showkat Ali
Keyword(s):  
Riemannian Manifolds ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Differential Forms ◽  
Flat Space ◽  
Space Time ◽  
Exterior Algebra ◽  
Important Ingredient ◽  
Maxwell’S Equation ◽  
Hodge Star Operator

The main purpose of this work is to provide application of differential forms in physics. For this purpose, we describe differential forms, exterior algebra in details and then we express Maxwell’s equations by using differential forms. In the theory of pseudo-Riemannian manifolds there will be an important operator, called Hodge Star Operator. Hodge Star Operator arises in the coordinate free formulation of Maxwell’s equation in flat space-time. This operator is an important ingredient in the formulation of Stoke’stheorem.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 15-27

scholarly journals Multisymplectic structures and the variational bicomplex

2009 ◽  
Vol 148 (1) ◽  
pp. 159-178 ◽  
Author(s):  
THOMAS J. BRIDGES ◽  
PETER E. HYDON ◽  
JEFFREY K. LAWSON
Keyword(s):  
Riemannian Manifold ◽  
Differential Forms ◽  
Relative Equilibria ◽  
Exterior Algebra ◽  
Variational Bicomplex ◽  
Main Observation ◽  
Hamiltonian Pdes ◽  
Definition Of ◽  
New View

AbstractMultisymplecticity and the variational bicomplex are two subjects which have developed independently. Our main observation is that re-analysis of multisymplectic systems from the view of the variational bicomplex not only is natural but also generates new fundamental ideas about multisymplectic Hamiltonian PDEs. The variational bicomplex provides a natural grading of differential forms according to their base and fibre components, and this structure generates a new relation between the geometry of the base, covariant multisymplectic PDEs and the conservation of symplecticity. Our formulation also suggests a new view of Noether theory for multisymplectic systems, leading to a definition of multimomentum maps that we apply to give a coordinate-free description of multisymplectic relative equilibria. Our principal example is the class of multisymplectic systems on the total exterior algebra bundle over a Riemannian manifold.

scholarly journals Matter coupling in Minimal Massive 3D Gravity and spinor-matter interactions in exterior algebra formalism

2021 ◽  
Author(s):  
Hakan Cebeci
Keyword(s):  
Field Equation ◽  
Source Term ◽  
Differential Forms ◽  
Exterior Algebra ◽  
Consistency Relation ◽  
Matter Coupling ◽  
Spinor Matter ◽  
3D Gravity

Abstract In this work, by employing the exterior algebra formalism, we study the matter coupling in Minimal Massive 3D Gravity (MMG) by first considering that the matter Lagrangian is connection-independent and then considering that the matter coupling is connection-dependent. The matter coupling in MMG has been previously investigated in the work \cite{arvanitakis_2} in tensorial notation where the matter Lagrangian is considered to be connection-independent. In the first part of the present paper, we revisit the connection-independent matter coupling by using the language of differential forms. We derive the MMG field equation and construct the related source 2-form. We also obtain the consistency relation within this formalism. Next, we examine the case where the matter Lagrangian is connection-dependent. In particular, we concentrate on the spinor-matter coupling and obtain the MMG field equation by explicitly constructing the source term. We also get the consistency relation that the source term should satisfy in order that spinor-matter coupled MMG equation be consistent.

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