Related papers: A note on non-Lorentzian duality symmetries
We expand on the known result that the Carroll algebra in $2+1$ dimensions admits two non-trivial central extensions by computing the associated Lie group, which we call extended Carroll group. The symplectic geometry associated to this…
We study magnetic monopoles in a Lorentz- and CPT-odd electrodynamical framework in (3+1) dimensions. This is the standard Maxwell model extended by means of a Chern-Simons-like term, $b_\mu\tilde{F}^{\mu\nu}A_\nu$ ($b_\mu$ constant), which…
For the free massless spin-one and spin-two field theories one may write the action in a form which is manifestly invariant under electric-magnetic duality. This is achieved by introducing new potentials through solving the constraints of…
In 1973, Le Bellac and Levy-Leblond (Nuovo Cimento B 14, 217-234) discovered that Maxwell's equations possess two non-relativistic Galilei-covariant limits, corresponding to E >> cB (electric limit) or E << cB (magnetic limit). Here, we…
We show how to obtain the dual of any lattice model with inhomogeneous local interactions based on an arbitrary Abelian group in any dimension and on lattices with arbitrary topology. It is shown that in general the dual theory contains…
The Carrollian limit ($c \to 0$) of General Relativity provides the geometric language for describing null hypersurfaces, such as black hole event horizons and null infinity. Motivated by the well-established electric and magnetic limits of…
Symmetries and conserved charges are investigated for linearised gravity and its dual formulation in terms of the dual graviton field. Conserved charges are constructed for the dual graviton theory as Noether charges associated with…
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…
Galilean and Carrollian algebras acting on two-dimensional Newton-Cartan and Carrollian manifolds are isomorphic. A consequence of this property is a duality correspondence between one-dimensional Galilean and Carrollian fluids. We describe…
We discuss the notion of duality and selfduality in the context of the dual projection operation that creates an internal space of potentials. Contrary to the prevailing algebraic or group theoretical methods, this technique is applicable…
We investigate two dimensional (2d) quantum field theories which exhibit Non- Lorentzian Ka\v{c}-Moody (NLKM) algebras as their underlying symmetry. Our investigations encompass both 2d Galilean (speed of light $c \rightarrow \infty$) and…
We revisit the question of whether classical general relativity obeys, beyond the linearised order, an analogue of the global U(1) electric-magnetic duality of Maxwell theory, with the Riemann tensor playing the role analogous to the field…
The development of relational electromagnetism after Gauss appears to stop around 1870. Maxwell recognised relational electromagnetism as mathematically equivalent to his own formulae and called for an explanation of why so different…
Modifications of the electromagnetic Maxwell Lagrangian in four dimensions have been considered by some authors. One may include an explicit massive term (Proca) and a topological but not Lorentz-invariant term within certain observational…
We demonstrate that an action proposed by A. Khoudeir and N. R. Pantoja in {\sl Phys. Rev.} {\bf D53}, 5974 (1996) for endowing Maxwell theory with manifest electric--magnetic duality symmetry contains, besides the Maxwell field, additional…
We propose two methods for obtaining the dual of non-linear relativity as previously formulated in momentum space. In the first we allow for the (dual) position space to acquire a non-linear representation of the Lorentz group independently…
We study how the coupling with gravity of theories with non-linearly realized space-time symmetries is modified when one changes the parametrization of the coset. As an example, we focus on the so-called Galileon duality: a…
It is shown that the canonical classical $r$-matrix arising from the Drinfel'd double structure underlying the two-fold centrally extended (2+1) Galilean and Newton-Hooke Lie algebras (with either zero or non-zero cosmological constant…
The Lagrangian and Hamiltonian formulations of electromagnetism are reviewed and the Maxwell equations are obtained from the Hamiltonian for a system of many electric charges. It is shown that three of the equations which were obtained from…
In this paper we investigate how electromagnetic duality survives derivative corrections to classical non-linear electrodynamics. In particular, we establish that electromagnetic selfduality is satisfied to all orders in $\alpha'$ for the…