Related papers: Graded Geometry and Tensor Gauge Theories
This article is expository in nature, outlining some of the many still incompletely understood features of higher spin field theory. We are mainly considering higher spin gauge fields in their own right as free-standing theoretical…
We present the general formulation of non-covariant Lagrangian of self-dual gauge theory. After specifying the parameters therein the previous Lagrangian in the decomposition of spacetime into $6=D_1+D_2$ and $6=D_1+D_2+D_3$ can be…
It is proved that there exist a vector representation of Dirac's spinor field and in one sense it is equivalent to biquaternion (i.e. complexified quaternion) representation. This can be considered as a generalization of Cartan's idea of…
A local gauge invariant interaction Lagrangian for two gauge fields of spin $\ell$ and $\ell-2$ $(\ell>2)$ and the scalar field is defined. It gives rise to one-loop corrections to the gauge field propagator. The loop function contains the…
It is shown that Connes' generalized gauge field in non-commutative geometry is derived by simply requiring that Dirac lagrangian be invariant under local transformations of the unitary elements of the algebra, which define the gauge group.…
We present a tensor calculus for exceptional generalised geometry. Expressions for connections, torsion and curvature are given a unified formulation for different exceptional groups E_n(n). We then consider "tensor gauge fields" coupled to…
In this paper, for massive fields of spins 2 and 3 with non-canonical Lagrangians, we build Hamiltonians and full systems of constraints and show that the use of derivatives in a redefinition of fields can give rise to a change of number of…
By consireding representation theory for non-associative algebras we construct the fundamental and adjoint representations of the octonion algebra. We then show how these representations by associative matrices allow a consistent octonionic…
Higher-spin theories are most commonly modelled on the example of spin 2. While this is appropriate for the description of free irreducible spin-s particles, alternative options could be equally interesting. In particular Maxwell's…
This is the second in a series of papers that aim to develop rigorous and most encompassing foundations for field theory, where in the first installment, we laid out the natural formulation of bosonic variational field theory via the…
We consider the general free field theory such that system of equations of motion includes a subsystem with a special property. If the subsystem is considered by itself, it would be a topological field theory having no local degrees of…
We discuss the formulation of cosmological topologically massive (simple) supergravity theory in three-dimensional Riemann-Cartan space-times. We use the language of exterior differential forms and the properties of Majorana spinors on…
We examine the variational and conformal structures of higher order theories of gravity which are derived from a metric-connection Lagrangian that is an arbitrary function of the curvature invariants. We show that the constrained first…
We study Lagrangians with the minimal amount of gauge symmetry required to propagate spin-two particles without ghosts or tachyons. In general, these Lagrangians also have a scalar mode in their spectrum. We find that, in two cases, the…
The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be…
We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general…
This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are…
We introduce a doubled formalism for the bosonic sector of the maximal supergravities, in which a Hodge dual potential is introduced for each bosonic field (except for the metric). The equations of motion can then be formulated as a twisted…
We apply the BRST approach, developed for higher spin field theories, to Lagrangian construction for totally antisymmetric massive fermionic fields in AdS_d space. As well as generic higher spin massive theories, the obtained Lagrangian…
Quadratic, second-order, non-local actions for tensor gauge fields transforming in arbitrary irreducible representations of the general linear group in D-dimensional Minkowski space are explicitly written in a compact form by making use of…