The Podolsky generalized electrodynamics with higher derivatives is formulated in the first-order formalism. The first-order relativistic wave equation in the 20-dimensional matrix form is derived. We prove that the matrices of the equation obey the Petiau-Duffin-Kemmer algebra. The Hermitianizing matrix and Lagrangian in the first-order formalism are given. The projection operators extracting solutions of field equations for states with definite energy-momentum and spin projections are obtained, and we find the density matrix for the massive state. The $13\times 13$-matrix Schrodinger form of the equation is derived, and the Hamiltonian is obtained. Projection operators extracting the physical eigenvalues of the Hamiltonian are found.
We consider the self-interaction phenomenon in the framework of the Bopp-Podolsky electrodynamics. In the present paper, we obtain the self-interaction potential energy of a charge at rest for the spacetimes with topological defects of two types: for the axially symmetric spacetime of the straight cosmic string and the spherically symmetric global monopole spacetime. It is shown that the behavior of this expression depends essentially on the angular defect, in spite of the Bopp-Podolsky model parameter, which plays the role of a scale factor. In contrast with the usual Maxwell electrodynamics,…
For a Podolsky-axionic electrodynamics, we compute the interaction potential within the structure of the gauge-invariant but path-dependent variables formalism. The result is equivalent to that of axionic electrodynamics from a new noncommutative approach, up to first order in $θ$.
In this work we apply the Matsubara-Fradkin formalism and the Nakanishi's auxiliary field method to the quantization of the Podolsky electrodynamics in thermodynamic equilibrium. This approach allows us to write consistently the path integral representation for the partition function of gauge theories in a simple manner. Furthermore, we find the Dyson-Schwinger-Fradkin equations and the Ward-Fradkin-Takahashi identities for the Podolsky theory. We also write the most general form for the polarization tensor in thermodynamic equilibrium.
In this paper we demonstrate the arising of higher-derivative contributions to the effective action of electrodynamics on the base of generalized Julia-Toulouse mechanism and explicitly show that the complete effective action generated within this methodology is nonlocal.
In this paper we obtain the expression for the self-force in the model with the Lagrangian containing additional terms, quadratic in Maxwell tensor derivatives (so-called Bopp-Podolsky electrodynamics). Features of this force are analyzed for various limiting cases. When a charged particle moves along straight line with a uniform acceleration, an explicit formula is found. In the framework of the considered model, an observable renormalized particle mass is shown to depend on its acceleration. This dependence allows, in principle, to extract experimentally a value of the particle bare mass.
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 …
We confirm the stability of Podolsky's generalized electrodynamics by constructing a series of two-parametric bounded conserved quantities which includes the canonical energy-momentum tensors. In addition, we evaluate the transition-amplitude of this higher derivative system in BV antifield formalism and obtain the desirable generalized radiation gauge condition by choosing appropriate gauge-fixing fermion. Within the framework of Lagrangian BRST cohomology, we present the constructions of consistent interactions in Podolsky's model and when concentrating on the antighost number zero part of t…
We consider the interaction between a charged scalar boson and the Bopp-Podolsky gauge fields. The Bopp-Podolsky (BP) electrodynamics possesses both massive and massless propagation modes for the photon, while preserving gauge invariance. We obtain the propagator of all fields present in the model for the higher-order generalizations of the linear covariant, light-front and doubly transverse light-front gauges. Although BP's original model is described by a higher-order derivatives Lagrangian, it is possible to work with an equivalent reduced-order version by means of the introduction of an au…
In this work we will develop the canonical structure of Podolsky's generalized electrodynamics on the null-plane. This theory has second-order derivatives in the Lagrangian function and requires a closer study for the definition of the momenta and canonical Hamiltonian of the system. On the null-plane the field equations also demand a different analysis of the initial-boundary value problem and proper conditions must be chosen on the null-planes. We will show that the constraint structure, based on Dirac formalism, presents a set of second-class constraints, which are exclusive of the analysis…
In this work, we consider the generalized quantum electrodynamics proposed by Podolsky in Heisenberg picture via Kallen methodology. We investigate the effects of higher-order derivatives to understand the qualitative and quantitative aspects of vacuum polarization. In addition, the most general structure of induced current and polarization tensor that emerge naturally by a perturbative scheme "a la" Kallen is also obtained. Afterward, we discuss the physical implication of charge renormalization in the perspective of unitary and stable Podolsky theory.
In this work we study the Higgs mechanism and the Debye shielding for the Bopp-Podolsky theory of electrodynamics. We find that not only the massless sector of the Podolsky theory acquires a mass in both these phenomena, but also that its massive sector has its mass changed. Furthermore, we find a mathematical analogy in the way these masses change between these two mechanisms. Besides exploring the behaviour of the screened potentials, we find a temperature for which the presence of the generalized gauge field may be experimentally detected.
We develop the Hamilton-Jacobi formalism for Podolsky's electromagnetic theory on the null-plane. The main goal is to build the complete set of Hamiltonian generators of the system, as well as to study the canonical and gauge transformations of the theory.
In this article we study some classical aspects of Podolsky Electrodynamics in the static regime. We develop the multipole expansion for the theory in both the electrostatic and the magnetostatic cases. We also address the problem of consistently truncating the infinite series associated with the several kinds of multipoles, yielding approximations for the static Podolskian electromagnetic field to any degree of precision required. Moreover, we apply the general theory of multipole expansion to some specific physical problems. In those problems we identify the first terms of the series with th…
We perform the canonical and path integral quantizations of a lower-order derivatives model describing Podolsky's generalized electrodynamics. The physical content of the model shows an auxiliary massive vector field coupled to the usual electromagnetic field. The equivalence with Podolsky's original model is studied at classical and quantum levels. Concerning the dynamical time evolution we obtain a theory with two first-class and two second-class constraints in phase space. We calculate explicitly the corresponding Dirac brackets involving both vector fields. We use the Senjanovic procedure …
Extended Theories of Electrodynamics in $f(R)$ Gravity
Scuola Superiore Meridionale（南方高等学院）；INFN Sez. di Napoli（意大利国家核物理研究所那不勒斯分部）；Dipartimento di Fisica “E. Pancini（环境与空间物理化学实验室（LPC2E）, 法国国家科学研究中心（CNRS）, 奥尔良大学）；Laboratoire de Physique et Chimie de l’Environnement et de l’Espace (LPC2E) UMR 7328 Centre National de la Recherche Scientifique (CNRS), Université d’Orléans (UO)（中部地区宇宙科学观测站（OSUC）, 法国国家科学研究中心（CNRS）, 巴黎天文台, 巴黎文理研究大学）；Observatoire des Sciences de l’Univers en region Centre (OSUC) UMS 3116 Université d’Orléans (UO), Centre National de la Recherche Scientifique (CNRS) Observatoire de Paris (OP), Université Paris Sciences & Lettres (PSL)
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…
We consider the four dimensional topologically massive electrodynamics in which a gauge field is interacting with 2nd rank antisymmetric tensor field through a topological interaction. The photon becomes massive by eating the 2nd rank tensor field, which is dual to the Higgs mechanism. We explicitly demonstrate the nature of the mechanism by performing a canonical analysis of the theory and discuss various aspects of it.
The Scale Magnetic Effect (SME) is the generation of electric current due to conformal anomaly in external magnetic field in curved spacetime. The effect appears in a vacuum with electrically charged massless particles. Similarly to the Hall effect, the direction of the induced anomalous current is perpendicular to the direction of the external magnetic field $\bf B$ and to the gradient of the conformal factor $τ$, while the strength of the current is proportional to the beta function of the theory. In massive electrodynamics the SME remains valid, but the value of the induced current differs …
We discuss the Heisenberg-Wigner phase-space formalism in quantum electrodynamics as well as scalar quantum electrodynamics with respect to transverse fields. In regard to the special characteristics of such field types we derive modified transport equations such that particle momenta perpendicular to the propagation direction of the waves show up as external parameters only. In case of spatially oscillating fields we further demonstrate how to transform momentum derivative operators of infinite order into simple coupling terms.
In this paper, we construct a single Lagrangian for both limits of Galilean electrodynamics. The framework relies on a covariant formalism used in describing Newton-Cartan geometry. We write down the Galilean conformal algebra and its representation in this formalism. We also show that the Lagrangian is invariant under the Galilean conformal algebra in d = 4 and calculate the energy-momentum tensor.
We study quantum electrodynamics on the noncommutative Minkowski space in the Yang-Feldman formalism. Local observables are defined by using covariant coordinates. We compute the two-point function of the interacting field strength to second order and find the infrared divergent terms already known from computations using the so-called modified Feynman rules. It is shown that these lead to nonlocal renormalization ambiguities. Also new nonlocal divergences stemming from the covariant coordinates are found. Furthermore, we study the supersymmetric extension of the model. For this, the supersymm…
In this work we study the so-called ModMax nonlinear electrodynamics, which is a novel model designed to preserve duality rotations and conformal transformations, such as the Maxwell's equations do. This model allows to study diverse gravitational phenomena when is coupled to General Relativity, in particular charged black holes and gravitational waves. In the present work we focus in the dynamics and Hamiltonian analysis of the model. Specifically, we analyze the propagation of the discontinuities of the field and obtain the corresponding dispersion relations. To perform the Hamiltonian analy…
Magnetized neutron stars constitute a special class of compact objects harbouring gravitational fields that deviate strongly from the Newtonian weak field limit. Moreover strong electromagnetic fields anchored into the star give rise to non-linear corrections to Maxwell equations described by quantum electrodynamics (QED). Electromagnetic fields close to or above the critical value of $\BQ=4.4\times10^9$~T are probably present in some pulsars and for most of the magnetars. To account properly for emission emanating from the neutron star surface like for instance thermal radiation and its polar…
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.
The basics of the premetric approach are discussed, including the essential details of the formalism and some of its beautiful consequences. We demonstrate how the classical electrodynamics can be developed without a metric in a quite straightforward way: Maxwell's equations, together with the general response law for material media, admit a consistent premetric formulation. Furthermore, we show that in relativistic theories of gravity, the premetric program leads to a better understanding of the interdependence between topological, affine, and metric concepts.
We develop a quaternionic electrodynamics and show that it naturally supports the existence of magnetic monopoles. We obtained the field equations, the continuity equation, the electrodynamic force law, the Poynting vector, the energy conservation and the stress-energy tensor. The formalism also enabled us to generalize the Dirac monopole and the charge quantization rule.
We introduce an effective field theory approach that describes the motion of finite size objects under the influence of electromagnetic fields. We prove that leading order effects due to the finite radius $R$ of a spherically symmetric charge is order $R^2$ rather than order $R$ in any physical model, as widely claimed in the literature. This scaling arises as a consequence of Poincaré and gauge symmetries, which can be shown to exclude linear corrections. We use the formalism to calculate the leading order finite size correction to the Abraham-Lorentz-Dirac force.
In this paper we compute the high-temperature effective Lagrangian for the quantum electrodynamics defined in the framework of Very Special Relativity (VSR). The main aspect of the VSR setting is that it modifies the gauge invariance, admitting now different types of interactions appearing in a nonlocal form. In order to explore the richness of these new couplings, we employ the usual Matsubara imaginary-time formalism to evaluate the effective Lagrangian at one and two-loop order. We illustrate the leading VSR Lorentz violation modifications by computing high-temperature internal energy densi…
We study Barut's covariant equations describing the electromagnetic interactions between N spin-1/2 particles. In the covariant formulation each particle is described by a Dirac spinor. It is assumed that the interactions between the particles are not mediated by a bosonic field (direct interactions). Within this formulation, using the Lagrangian formalism, we derive the approximate (semirelativistic) Breit equation for two interacting spin-1/2 particles.
The Maxwell electromagnetic and the Lorentz type force equations are derived in the framework of the R. Feynman proper time paradigm and the related vacuum field theory approach. The electron inertia problem is analyzed within the Lagrangian and Hamiltonian formalisms and the related pressure-energy compensation principle. The modified Abraham- Lorentz damping radiation force is derived, the electromagnetic electron mass origin is argued.
High order harmonic generation by extremely intense, interacting, electromagnetic waves in the quantum vacuum is investigated within the framework of the Heisenberg-Euler formalism. Two intersecting plane waves of finite duration are considered in the case of general polarizations. Detailed finite expressions are obtained for the case where only the first Poincaré invariant does not vanish. Yields of high harmonics in this case are most effective.
Using the recently developed formalism of braided noncommutative field theory, we construct an explicit example of braided electrodynamics, that is, a noncommutative $U(1)$ gauge theory coupled to a Dirac fermion. We construct the braided $L_\infty$-algebra of this field theory and apply the formalism to obtain the braided equations of motion, action functional and conserved matter current. The braided deformation leads to a modification of the charge conservation. Finally, the Feynman integral appearing in the one-loop contribution to the vacuum polarization diagram is calculated. There are n…
