We find the dual equivalent (gauge invariant) version of the Maxwell theory in D=4 with a Proca-like mass term by using the symplectic embedding method. The dual theory obtained (Maxwell-Podolsky) includes a higher-order derivative term and preserve the gauge symmetry. We also furnish an investigation of the pole structure of the vector propagator by the residue matrix which considers the eventual existence of the negative-norm of the theory.
We discuss an inherent Pauli-Villars regularization in Bopp-Podolsky's generalized electrodynamics. Introducing gauge-fixing terms for Bopp-Podolsky's generalized electrodynamic action, we realize a unique feature for the corresponding photon propagator with a built-in Pauli-Villars regularization independent of the gauge choice made in Maxwell's usual electromagnetism. According to our realization, the length dimensional parameter $a$ associated with Bopp-Podolsky's higher order derivatives corresponds to the inverse of the Pauli-Villars regularization mass scale $Λ$, i.e. $a = 1/Λ$. Solving …
The Symplectic Projector Method is applied to derive the local physical degrees of freedom and the physical Hamiltonian of the Maxwell-Chern-Simons theory in $d=1+2$. The results agree with the ones obtained in the literature through different approaches.
We examine Podolsky's electrodynamics, which is noninvariant under the usual duality transformation. We deduce a generalization of Hodge's star duality, which leads to a dual gauge field and restores to a certain extent the dual symmetry. The model becomes fully dual symmetric asymptotically when it reduces to the Maxwell theory. We argue that this strict dual symmetry directly implies the existence of the basic invariants of the electromagnetic fields.
We consider a vector-tensor gravitational model with terms quadratic in the Maxwell tensor derivatives, called the Bopp-Podolsky term. The gravitational field equations of the model and the equations describing the evolution of the vector field are obtained and their Newtonian limit is investigated. The cosmological implications of a Bopp-Podolsky type dark energy term are investigated for a Bianchi type I homogeneous and anisotropic geometry for two models, corresponding to the absence and presence of the self-interacting potential of the field, respectively. The time evolutions of the Hubble…
The constrained structure of the duality invariant form of Maxwell theory is considered in the Hamiltonian formulation of Dirac as well as from the symplectic viewpoint. Compared to the former the latter approach is found to be more economical and elegant. Distinctions from the constrained analysis of the usual Maxwell theory are pointed out and their implications are also discussed.
The aim of this work is to discuss some aspects of the reduction of order formalism in the context of the Fadeev-Jackiw symplectic formalism, both at the classical and the quantum level. We start by reviewing the symplectic analysis in a regular theory (a higher derivative massless scalar theory), both using the Ostrogradsky prescription and also by reducing the order of the Lagrangian with an auxiliary field, showing the equivalence of these two approaches. The interpretation of the degrees of freedom is discussed in some detail. Finally, we perform the similar analysis in a singular higher d…
Einstein-Maxwell theory is not only covariant under diffeomorphisms but also is under $U(1)$ gauge transformations. We introduce a combined transformation constructed out of diffeomorphism and $U(1)$ gauge transformation. We show that symplectic potential, which is defined in covariant phase space method, is not invariant under combined transformations. In order to deal with that problem, following Donnelly and Freidel proposal \cite{1}, we introduce new fields. In this way, phase space and consequently symplectic potential will be extended. We show that new fields produce edge modes. We consi…
We consider the holography of the Abelian Maxwell-Chern-Simons (MCS) system in Lorentzian three-dimensional asymptotically-AdS spacetimes, and discuss a broad class of boundary conditions consistent with conservation of the symplectic structure. As is well-known, the MCS theory contains a massive sector dual to a vector operator in the boundary theory, and a topological sector consisting of flat connections dual to U(1) chiral currents; the boundary conditions we examine include double-trace deformations in these two sectors, as well as a class of boundary conditions that mix the vector operat…
The theorem which says that helicity is the conserved quantity associated with the duality symmetry of the vacuum Maxwell equations is proved by viewing electromagnetism as an infinite dimensional symplectic system. In fact, it is shown that helicity is the moment map of duality acting as an $SO(2)$ group of canonical transformations on the symplectic space of all solutions of the vacuum Maxwell equations.
We consider the master Lagrangian of Deser and Jackiw, interpolating between the self-dual and the Maxwell-Chern-Simons Lagrangian, and quantize it following the symplectic approach, as well as the traditional Dirac scheme. We demonstrate the equivalence of these procedures in the subspace of the second-class constraints. We then proceed to embed this mixed first- and second-class system into an extended first-class system within the framework of both approaches, and construct the corresponding generator for this extended gauge symmetry in both formulations.
We have conclusively established the duality between noncommutative Maxwell-Chern-Simons theory and Self-Dual model, the latter in ordinary spacetime, to the first non-trivial order in the noncommutativity parameter $θ^{μν}$, with $θ^{0i}=0$. This shows that the former theory is free for marginally noncommutative spacetimes. A $θ$-generalized covariant mapping between the variables of the two models in question has been derived explicitly, that converts one model to the other, including the symplectic structure and action.
The construction of an alternative electromagnetic theory that preserves Lorentz and gauge symmetries, is considered. We start off by building up Maxwell electrodynamics in (3+1)D from the assumption that the associated Lagrangian is a gauge-invariant functional that depends on the electron and photon fields and their first derivatives only. In this scenario, as well-known, it is not possible to set up a Lorentz invariant gauge theory containing a massive photon. We show nevertheless that there exist two radically different electrodynamics, namely, the Chern-Simons and the Podolsky formulation…
In this work we have shown that it is possible to construct non-Abelian field theories employing, in a systematic way, the Faddeev-Jackiw symplectic formalism. This approach follows two steps. In the first step, the original Abelian fields are modified in order to introduce the non-Abelian algebra. After that, the Faddeev-Jackiw method is implemented and the gauge symmetry relative to some non-Abelian symmetry group, is introduced through the zero-mode of the symplectic matrix. We construct the SU(2) and SU(2)xU(1) Yang-Mills theories having as starting point the U(1) Maxwell electromagnetic t…
In this work we show that we can obtain dual equivalent actions following the symplectic formalism with the introduction of extra variables which enlarge the phase space. We show that the results are equal as the one obtained with the recently developed gauging iterative Noether dualization method (NDM). We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method (SEM) is more profound since it can reveal a whole family of dual equivalent actions. We illustrate the method demonstrating that the gauge-invariance of the electromagnetic Maxwell Lagrangian br…
A "Master" gauge theory is constructed in 2+1-dimensions through which various gauge invariant and gauge non-invariant theories can be studied. In particular, Maxwell-Chern-Simons, Maxwell-Proca and Maxwell-Chern-Simons -Proca models are considered here. The Master theory in an enlarged phase space is constructed both in Lagrangian (Stuckelberg) and Hamiltonian (Batalin-Tyutin) frameworks, the latter being the more general one, which includes the former as a special case. Subsequently, BRST quantization of the latter is performed. Lastly, the master Lagrangian, constructed by Deser and Jackiw …
In 4-dimensional supergravity theories, covariant under symplectic electric-magnetic duality rotations, a significant role is played by the symplectic matrix M(ϕ), related to the coupling of scalars ϕ to vector field-strengths. In particular, this matrix enters the twisted self-duality condition for 2-form field strengths in the symplectic formulation of generalized Maxwell equations in the presence of scalar fields. In this investigation, we compute several properties of this matrix in relation to the attractor mechanism of extremal (asymptotically flat) black holes. At the attractor points w…
We give the global mathematical formulation of a class of generalized four-dimensional theories of gravity coupled to scalar matter and to Abelian gauge fields. In such theories, the scalar fields are described by a section of a surjective pseudo-Riemannian submersion $π$ over space-time, whose total space carries a Lorentzian metric making the fibers into totally-geodesic connected Riemannian submanifolds. In particular, $π$ is a fiber bundle endowed with a complete Ehresmann connection whose transport acts through isometries between the fibers. In turn, the Abelian gauge fields are "twisted"…
The interactions between gluons are important in theories such as quantum chromodynamics. Therefore, to rediscover new features of well known methods in order to investigate the SU(3) gauge group can be a new way to deal with Yang-Mills theories. In this work we analyzed YM theories through the well known Faddeev-Jackiw formalism for constrained systems. Besides, we showed precisely that having U(1) Maxwell electromagnetic theory as a starting point we can construct SU(3)-like and SU(3) X SU(2) X U(1) non-Abelian theories.
The geometry that is defined by the scalars in couplings of Einstein-Maxwell theories in N=2 supergravity in 4 dimensions is denoted as special Kaehler geometry. There are several equivalent definitions, the most elegant ones involve the symplectic duality group. The original construction used conformal symmetry, which immediately clarifies the symplectic structure and provides a way to make connections to quaternionic geometry and Sasakian manifolds.
Mass dimension one quantum fields, constructed upon eigenspinors of the charge conjugation operator with dual helicity (ELKO), are prime candidates to describe dark matter. Their interaction with the photon and the proton, in scattering processes, are here explored and discussed, using both the standard QFT with a Maxwell gauge field and a generalized QFT also involving a Podolsky gauge sector. Renormalization and radiative corrections are analyzed in the ELKO setup, in the context of a generalized spinor dual and the twisted conjugation, both yielding unitarity. Several applications are scrut…
In this thesis the generally covariant locality principle for bosonic free fields has been thoroughly analyzed devoting particular attention to the case of spin 1 fields on curved spacetimes (Proca and Maxwell fields). This has been obtained in two steps: In the first place the preliminary study of the corresponding field equations led to the construction of a symplectic space of solutions describing the classical theories of the considered fields. Secondly the locally covariant quantum theory of the field under consideration has been obtained through the assignment of the Weyl algebra associa…
We give a global formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields for the generalized situation when the "duality structure" of the Abelian gauge theory is described by a flat symplectic vector bundle $(\mathcal{S},D,ω)$ defined over the scalar manifold $\mathcal{M}$. The construction uses a taming of $(\mathcal{S}, ω)$, which encodes globally the inverse gauge couplings and theta angles of the "twisted" Abelian gauge theory in a manner that makes no use of duality frames. We show that global solutions of the equations of motion of such models give cl…
In this paper, the analog of Maxwell electromagnetism for hydrodynamic turbulence, the metafluid dynamics, is extended in order to reformulate the metafluid dynamics as a gauge field theory. That analogy opens up the possibility to investigate this theory as a constrained system. Having this possibility in mind, we propose a Lagrangian to describe this new theory of turbulence and, subsequently, analyze it from the symplectic point of view. From this analysis, a hidden gauge symmetry is revealed, providing a clear interpretation and meaning of the physics behind the metafluid theory. Further, …
We study the canonical Hamiltonian analysis of gauge theories in the presence of boundaries. While the implementation of Dirac's program in the presence of boundaries, as put forward by Regge and Teitelboim, is not new, there are some instances in which this formalism is incomplete. Here we propose an extension to the Dirac formalism --together with the Regge-Teitelboim strategy,-- that includes generic cases of field theories. We see that there are two possible scenarios, one where there is no contribution from the boundary to the symplectic structure and the other case in which there is one,…
We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime with a fixed time-flow vector. For existence of a well-defined Hamiltonian variational principle taking into account a spatial boundary, it is necessary to modify the standard Arnowitt-Deser-Misner Hamiltonian by adding a boundary term whose form depends on the spatial boundary conditions for the gravitational field. The most general mathematically allowed boundary conditions and corresponding boundary terms are shown to be determined by solving a certain equation obta…
We implement the Dirac-Schwinger-Zwanziger integrality condition on four-dimensional classical ungauged supergravity and use it to obtain its duality-covariant, gauge-theoretic, differential-geometric model on an oriented four-manifold $M$ of arbitrary topology. Classical bosonic supergravity is completely determined by a submersion $π$ over $M$ equipped with a complete Ehresmann connection, a vertical euclidean metric, and a vertically-polarized flat symplectic vector bundle $Ξ$. Building on these structures, we implement the Dirac-Schwinger-Zwanziger integrality condition through the choice …
