We formulate axion-electrodynamics and magnetohydrodynamics (MHD) in the cosmological context assuming weak gravity. The two formulations are made for a general scalar field with general $f(ϕ)$-coupling, and an axion as a massive scalar field with $ϕ^2$-coupling, with the helical electromagnetic field. The $α$-dynamo term appears naturally from the helical coupling in the MHD formulation. In the presence of the electromagnetic coupling, however, the Schrödinger and hydrodynamic formulations of the coherently oscillating axion are {\it not} available for the conventional $ϕ$ coupling; instead, $ϕ^2$ coupling allows successful formulations preserving the dark matter nature of the axion to nonlinear order. In the MHD formulation, direct couplings between the scalar and electromagnetic fields appear only for non-ideal MHD. We study gravitational and magnetic instabilities of the scalar field and axion MHDs.
A general scheme for axion electrodynamics is given, in which a surrounding medium of constant permittivity and permeability is assumed. Then, as an application we give simple numerical estimates for the electromagnetic current density produced by the electrically neutral time-dependent axions $a=a(t)$ in a strong magnetic field. As is known, the assumption $a=a(t)$ is common under astrophysical conditions. In the third part of the paper, we consider the implications by assuming instead an axion amplitude $a(z)$ depending on one coordinate $z$ only. If such an axion field is contained within t…
Within the dual symmetric point of view, the theory for seeking axion dark matter via haloscope experiments is derived by exactly solving the dual symmetric axion electrodynamics equation. Notwithstanding that the conventional theory of axion electrodynamics presented in [Phys. Rev. Lett. 51, 1415 (1983) and J. Phys. A: Math. Gen. 19, L33 (1986)] is more commonly used in haloscope theory, we show that the dual symmetric axion electrodynamics has more advantages to apply to haloscope theory. First, the dual symmetric and conventional perspectives of axion electrodynamics coincide under long-wav…
We study higher-form symmetries and a higher group in the low energy limit of a $(3+1)$-dimensional axion electrodynamics with a massive axion and a massive photon. A topological field theory describing topological excitations with the axion-photon coupling, which we call a topological axion electrodynamics, is obtained in the low energy limit. Higher-form symmetries of the topological axion electrodynamics are specified by equations of motion and Bianchi identities. We find that there are induced anyons on the intersections of symmetry generators. By a link of worldlines of the anyons, we sho…
We study non-invertible global symmetries in $(3+1)$-dimensional axion electrodynamics with a massless axion and a massless photon. In addition to a previously known non-invertible 0-form shift symmetry of the axion, we find a non-invertible 1-form symmetry associated with the equation of motion for the photon. Correlation functions of non-invertible symmetry defects lead to invertible 1- and 2-form symmetry defects associated with Bianchi identities for the axion and photon. In terms of the correlation functions, we discuss several phenomena for extended objects, such as induced fractional el…
In this contribution, we re-assess some aspects of axionic electrodynamics by coupling non-linear electromagnetic effects to axion physics. We present a number of motivations to justify the coupling of the axion to the photon in terms of a general non-linear extension of the electromagnetic sector. Our emphasis in the paper relies on the investigation of the constitutive permittivity and permeability tensors, for which the axion contributes by introducing dependence on the frequency and wave vector of the propagating radiation. Also, we point out how the axion mass and the axion-photon-photon …
Axion electrodynamics is based upon the Lagrangian of the electromagnetic (EM) field plus its interaction with the axions, and is accordingly a physically open system. It means that the four-divergence of the EM energy-momentum tensor is different from zero, implying in turn that the total EM energy and momentum (when integrated over all space) do not constitute a four-vector. The EM force is in principle accessible to experimental detection, just analogous to what is the case in ordinary electrodynamics. In the first half of this paper the energy-momentum aspects of axion electrodynamics are …
The new nonlinear axionically extended version of the general relativistic magnetohydrodynamics is formulated. The self-consistent formalism of this theory is based on the introduction into the Lagrangian of the new unified scalar invariant, which is quadratic in the Maxwell tensor, and contains two periodic functions of the pseudoscalar (axion) field. The constructed unified invariant and the elaborated nonlinear theory as a whole, are invariant with respect to two symmetries: first, the discrete symmetry associated with the properties of the axion field; second, the Jackson's SO(2) type symm…
Energy-momentum conservation of classical axion-electrodynamics is carefully analyzed in the Hamiltonian formulation of the theory. The term responsible for the energy transfer between the electromagnetic and the axion sectors is identified. As a special application the axion-to-light Primakoff-process in the background of a static magnetic field is worked out and the radiative self-damping of the axion oscillations is characterized quantitatively. The damping time turns out comparable to the age of the Universe in the preferred axion mass range.
We study higher-form global symmetries and a higher-group structure of a low-energy limit of $(3+1)$-dimensional axion electrodynamics in a gapped phase described by a topological action. We argue that the higher-form symmetries should have a semi-strict 4-group (3-crossed module) structure by consistency conditions of couplings of the topological action to background gauge fields for the higher-form symmetries. We find possible 't Hooft anomalies for the 4-group global symmetry, and discuss physical consequences.
We investigate a higher-group structure of massless axion electrodynamics in $(3+1)$ dimensions. By using the background gauging method, we show that the higher-form symmetries necessarily have a global semistrict 3-group (2-crossed module) structure, and exhibit 't Hooft anomalies of the 3-group. In particular, we find a cubic mixed 't Hooft anomaly between 0-form and 1-form symmetries, which is specific to the higher-group structure.
We study higher-form symmetries in a low-energy effective theory of a massless axion coupled with a photon in $(3+1)$ dimensions. It is shown that the higher-form symmetries of this system are accompanied by a semistrict 3-group (2-crossed module) structure, which can be found by the correlation functions of symmetry generators of the higher-form symmetries. We argue that the Witten effect and anomalous Hall effect in the axion electrodynamics can be described in terms of 3-group transformations.
We present the extended electrodynamics in the presence of the axion and dark photon. We derive the extended versions of Maxwell's equations and dark Maxwell's equations (for both massive and massless dark photons) as well as the wave equations. We discuss the implications of this extended electrodynamics including the enhanced effects in the particle conversions under the external magnetic or dark magnetic field. We also discuss the recently reported anomaly in the redshifted 21cm spectrum using the extended electrodynamics.
The most sensitive haloscopes that search for axion dark matter through the two photon electromagnetic anomaly, convert axions into photons through the mixing of axions with a large DC magnetic field. In this work we apply Poynting theorem to the resulting axion modified electrodynamics and identify two possible Poynting vectors, one similar to the Abraham Poynting vector and the other to the Minkowski Poynting vector in electrodynamics. The latter picks up the extra non-conservative terms while the former does not. To understand the source of energy conversion and power flow in the detection …
We study the Casimir effect in axion electrodynamics. A finite $θ$-term affects the energy dispersion relation of photon if $θ$ is time and/or space dependent. We focus on a special case with linearly inhomogeneous $θ$ along the $z$-axis. Then we demonstrate that the Casimir force between two parallel plates perpendicular to the $z$-axis can be either attractive or repulsive, dependent on the gradient of $θ$. We call this repulsive component in the Casimir force induced by inhomogeneous $θ$ the anomalous Casimir effect.
A Supersymmetric Extension of Axionic Electrodynamics: From Axions and Photons to Axinos and Photinos
Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Instituto Federal do Espírito Santo（圣埃斯皮里图联邦学院）；Centro Federal de Educação Tecnológica C. S. da Fonseca（C.S.达丰塞卡联邦技术教育中心）
Simulating Axion Electrodynamics in Magnetized Plasmas: Energy transfer in the inhomogeneous and strongly varying limit
Dipartimento di Fisica, “Sapienza” Università di Roma & Sezione INFN Roma1（罗马大学物理系及INFN罗马第一分部）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Instituto de Física Corpuscular (IFIC), University of Valencia-CSIC（瓦伦西亚大学-CSIC粒子物理研究所）；CENTRA, Departamento de Fisica, Instituto Superior Técnico – IST, Universidade de Lisboa – UL（里斯本大学技术学院物理系CENTRA中心）；Department of Theoretical Physics, CERN（欧洲核子研究中心理论物理部）；Department of Particle Physics and Astrophysics, Weizmann Institute of Science（魏茨曼科学研究所粒子物理与天体物理系）；Rudolf Peierls Centre for Theoretical Physics, University of Oxford（牛津大学鲁道夫·派尔斯理论物理中心）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器研究所）；II. Institute of Theoretical Physics, Universität Hamburg（汉堡大学第二理论物理研究所）
One of the intriguing properties characteristic to three-dimensional topological materials is the topological magnetoelectric phenomena arising from a topological term called the $θ$ term. Such magnetoelectric phenomena are often termed the axion electrodynamics, since the $θ$ term has exactly the same form as the action describing the coupling between a hypothetical elementary particle, axion, and a photon. The axion was proposed about forty years ago to solve the so-called strong CP problem in quantum chromodynamics, and is now considered as a candidate for dark matter. In this tutorial, we …
In a recent publication, Tobar, McAllister, and Goryachev claim that using an alternative definition of the Poynting vector can dramatically enhance the sensitivity of their proposed axion dark matter detector. While the choice of Poynting vector is indeed ambiguous, it cannot affect physical results, such as the reading on a voltmeter, as long as the same definition is used consistently. I explain this point in detail, and locate the specific errors in their calculation.
The overcritical regime of axion-electrodynamics (AED) is investigated. For magnetic fields larger than the characteristic scale linked to AED, quantum vacuum fluctuations due to axion-like fields can dominate over those associated with the electron-positron fields. This hypothetical regime of the dominance of AED over QED is predicted to induce strong birefringence and screening effects. We show that, if the magnetic field lines are curved, extraordinary photons could be canalized along the field direction. It is also shown that the running QED coupling depends on the magnetic field strength,…
We investigate $2n$-dimensional axion electrodynamics for the purpose of exploring a higher-group structure underlying it. This is manifested as a Green-Schwarz transformation of the background gauge fields that couple minimally to the conserved currents. The $n=3$ case is studied most intensively. We derive the identities of correlation functions among the global symmetry generators by using a gauge transformation that maps two correlation functions with each other. A key ingredient in this computation is given by the Green-Schwarz transformation and the 't Hooft anomalies associated with the…
We present a reformulation of axion modified electrodynamics with all modifications redefined within the constitutive relations between the D,H,B and E fields. This allows the interpretation of the axion induced background bound charge, polarization current and background polarization and magnetization satisfying the charge-current continuity equation. This representation is of similar form to photon sector odd-parity Lorentz invariance violating background fields. We show that when a DC B-field is applied an oscillating background polarization is induced at a frequency equivalent to the axion…
An axion background field induces tiny oscillating electric and magnetic fields in an external static magnetic field. This signature is used to search for axion dark matter. We use standard quantum field theory techniques to obtain an expression for a transition amplitude, from which we identify the classical electromagnetic fields induced by the background axion field. We confirm previous results, that if the spatial size $R$ of the applied static magnetic field is small compared to the axion Compton wavelength $λ$, the induced electric and magnetic fields are parametrically suppressed by the…
School of Basic and Applied Sciences, K. R. Mangalam University（K.R.曼加拉姆大学基础与应用科学学院）；Saha Institute of Nuclear Physics（萨哈核物理研究所）；Homi Bhabha National Institute（霍米·巴巴国立学院）
本文构建了Carrollian轴子电动力学理论，通过$c \ o 0$展开得到电型和磁型两类，发现磁型理论中存在Witten效应的Carrollian类比，但线性磁电效应消失。
We provide a statistical mechanical derivation of relativistic magnetohydrodynamics on the basis of the $(3+1)$-dimensional quantum electrodynamics; the system endowed with the magnetic one-form symmetry. The conservation laws and the constitutive relations are presented in a manifestly covariant way with respect to the general coordinate transformation. The method of the local Gibbs ensemble (or nonequilibrium statistical operator) combined with the path-integral formula for the thermodynamic functional enables us to obtain an exact form of the constitutive relations. Applying the derivative …
We show for the classical Maxwell equations, including the axion electromagnetic anomaly source term, that a cosmic axion field induces an oscillating electric N-moment for any static magnetic N-moment. This is a straightforward result, accessible to anyone who has taken a first year graduate course in electrodynamics.
Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
Recently there has been a surge of new experimental proposals to search for ultra-light axion dark matter with axion mass, $m_a\lesssim1\,μ$eV. Many of these proposals search for small oscillating magnetic fields induced in or around a large static magnetic field. Lately, there has been interest in alternate detection schemes which search for oscillating electric fields in a similar setup. In this paper, we explicitly solve Maxwell's equations in a simplified geometry and demonstrate that in this mass range, the axion induced electric fields are heavily suppressed by boundary conditions. Unfor…
Axion Hair and Pulsar Electrodynamics: modelling, discharge dynamics, and particle-in-cell simulations
Rudolf Peierls Centre for Theoretical Physics, University of Oxford（牛津大学鲁道夫·派尔斯理论物理中心）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器中心）；II. Institute of Theoretical Physics, Universität Hamburg（汉堡大学第二理论物理研究所）；Department of Theoretical Physics, CERN（欧洲核子研究中心理论物理部）；Dipartimento di Fisica, “Sapienza” Università di Roma & Sezione INFN Roma1（罗马第一大学物理系及INFN罗马一分部）；Weizmann Institute of Science（魏茨曼科学研究所）；Institut de Física d’Altes Energies (IFAE) and Barcelona Institute of Science and Technology (BIST)（高等能源物理研究所及巴塞罗那科学与技术研究院）；Institute for Advanced Study, Princeton（普林斯顿高等研究院）；University of Maryland（马里兰大学）；Johns Hopkins University（约翰斯·霍普金斯大学）
A consistent renormalization of a quantum theory of axion-electrodynamics requires terms beyond the minimal coupling of two photons to a neutral pseudoscalar field. This procedure is used to determine the self-energy operators of the electromagnetic and the axion fields with an accuracy of second-order in the axion-diphoton coupling. The resulting polarization tensor is utilized for establishing the axion-modified Coulomb potential of a static pointlike charge. In connection, the plausible distortion of the Lamb-shift in hydrogenlike atoms is established and the scopes for searching axionlike …
We study the dynamics of a plasma of charged relativistic fermions at very high temperature $T\gg m$, where $m$ is the fermion mass, coupled to the electromagnetic field. In particular, we derive a magneto-hydrodynamical description of the evolution of such a plasma. We show that, as compared to conventional MHD for a plasma of non-relativistic particles, the hydrodynamical description of the relativistic plasma involves new degrees of freedom described by a pseudo-scalar field originating in a local asymmetry in the densities of left-handed and right-handed fermions. This field can be interpr…
In a constant and homogeneous magnetic background, quantum vacuum fluctuations due to axion-like fields can dominate over those associated with the electron-positron fields. Considering the framework of axion-electrodynamics, the self-energy operator for the electromagnetic field is determined with an accuracy to second-order in the axion-diphoton coupling. This outcome is utilized for establishing modifications to the propagation characteristics of photons and to the Coulomb potential of a static pointlike charge. Notably, in the magnetosphere of a neutron star, the effect of photon capture b…
This dissertation studies the quantum anomalous effects on the description of high energy electrodynamics. We argue that on the temperatures comparable to the electroweak scale, characteristic for the early Universe and objects like neutron stars, the description of electromagnetic fields in conductive plasmas needs to be extended to include the effects of chiral anomaly. It is demonstrated that chiral effects can have a significant influence on the evolution of magnetic fields, tending to produce exponential amplification, creation of magnetic helicity from initially non-helical fields, and c…
