Related papers: Spinor fields in general Newton-Cartan backgrounds

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…

A geometric approach to the standard model in terms of the Clifford algebra Cl_7 is advanced. A key feature of the model is its use of an algebraic spinor for one generation of leptons and quarks. Spinor transformations separate into…

Conformal extensions of Levy-Leblond's Carroll group, based on geometric properties analogous to those of Newton-Cartan space-time are proposed. The extensions are labelled by an integer $k$. This framework includes and extends our recent…

The first-order L\'evy-Leblond differential equations (LLEs) are the non-relativistic analogous of the Dirac equation: they are the "square roots" of the Schr\"odinger equation in ($1+d$) dimensions and admit spinor solutions. In this paper…

The gravitating matter is studied within the framework of the non-commutative geometry. The non-commutative Einstein-Hilbert action on the product of a four dimensional manifold with a discrete space gives the models of matter fields…

We show that the torsion of a Cartan geometry can be associated to two spin-2 fields. This structure allows a new approach to deal with the proposal of geometrization of spin-2 fields besides the traditional one dealt with in General…

We deal with Lagrangians which are not the standard scalar ones. We present a short review of tensor Lagrangians, which generate massless free fields and the Dirac field, as well as vector and pseudovector Lagrangians for the electric and…

We construct a class of Abelian and non-Abelian local gauge theories that consist only of matter fields of fermions. The Lagrangian is compact and local without containing an auxiliary vector field nor a subsidiary condition on the matter…

Using the recently advanced Galilean gauge theory (GGT) we give a comprehensive construction of torsional Newton Cartan geometry. The coupling of a Galilean symmetric model with background NC geometry following GGT is illustrated by a free…

We investigate the Lagrangian formulation of the double-copy correspondence between gauge theories and gravity, up to the cubic order. Building on the definition of the double-copy field as a convolution of two vectors, we obtain free…

We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields…

We study the quantum properties of a Galilean-invariant abelian gauge theory coupled to a Schr\"odinger scalar in 2+1 dimensions. At the classical level, the theory with minimal coupling is obtained from a null-reduction of relativistic…

We present a Lagrangian theory of gravitation that develops some ideas proposed several years ago. It is formulated on the 10-dimensional space $\mathcal{S}$ of the local Lorentz frames (tetrads) and it is covariant under the symplectic…

We show how implementing invariance under divergence-free gauge transformations leads to a remarkably simple Lagrangian description of massless bosons of any spin. Our construction covers both flat and (A)dS backgrounds and extends to…

We present an improvement to the Classical Effective Theory approach to the non-relativistic or Post-Newtonian approximation of General Relativity. The "potential metric field" is decomposed through a temporal Kaluza-Klein ansatz into three…

A covariant Hamiltonian formulation generalizing De Donder-Weyl mechanics is constructed with field strengths as velocity fields. Since the teleparallel equivalents to general relativity are quadratic in field strengths, the field-strength…

In this note we show that a "dynamical" interaction for arbitrary spin can be constructed in a straightforward way if gauge and Lorentz transformations are placed on the same foundation. As Lorentz transformations act on space-time…

We argue that higher spin fields originate from Hamiltonian mechanics and play a role of gauge fields ensuring covariance of geometric observables such as length and volume with respect to canonical transformations in the same way as a…

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…

Here we perform the Kaluza-Klein dimensional reduction from $D+1$ to $D$ dimensions of massless Lagrangians described by a symmetric rank-2 tensor and invariant under transverse differmorphisms (TDiff). They include the linearized…