Gauge-invariant Theory Research Articles

Double copy of 3D Chern-Simons theory and 6D Kodaira-Spencer gravity

We apply an algebraic double copy construction of gravity from gauge theory to three-dimensional (3D) Chern-Simons theory. The kinematic algebra K is the 3D de Rham complex of forms equipped, for a choice of metric, with a graded Lie algebra that is equivalent to the Schouten-Nijenhuis bracket on polyvector fields. The double copied gravity is defined on a subspace of K⊗K¯ and yields a topological double field theory for a generalized metric perturbation and two 2-forms. This local and gauge invariant theory is non-Lagrangian but can be rendered Lagrangian by abandoning locality. Upon fixing a gauge this reduces to the double copy of Chern-Simons theory previously proposed by Ben-Shahar and Johansson. Furthermore, using complex coordinates in C3 this theory is related to six-dimensional (6D) Kodaira-Spencer gravity in that truncating the two 2-forms and one equation yields the Kodaira-Spencer equations on a 3D real slice of C3. The full 6D Kodaira-Spencer theory can instead be obtained as a consistent truncation of a chiral double copy. Published by the American Physical Society 2024

Even- and odd-parity stabilities of black holes in Einstein-Aether gravity

In Einstein-Aether theories with a timelike unit vector field, we study the linear stability of static and spherically symmetric black holes against both even- and odd-parity perturbations.For this purpose, we formulate a gauge-invariant black hole perturbation theory in the background Aether-orthogonal frame where the spacelike property of hypersurfaces orthogonal to the timelike Aether field is always maintained even inside the metric horizon. Using a short-wavelength approximation with large radial and angular momenta, we show that, in general, there are three dynamical degreesof freedom arising from the even-parity sector besides two propagating degrees of freedom present in the odd-parity sector. The propagation speeds of even-parity perturbations and their no-ghost conditions coincide with those of tensor, vector, and scalar perturbations on the Minkowski background, while the odd sector contains tensor and vector modes with the same propagation speeds as those in the even-parity sector (and hence as those on the Minkowski background).Thus, the consistent study of black hole perturbations in the Aether-orthogonal frame on static and spherically symmetric backgrounds does not add new small-scale stability conditions to those known for the Minkowski background in the literature.

Effective Abelian lattice gauge field theories for scalar-matter-monopole interactions

We present a gauge and Lorentz invariant effective field theory model for the interaction of a charged scalar matter field with a magnetic monopole source, described by an external magnetic current. The quantum fluctuations of the monopole field are described effectively by a strongly coupled “dual” Ud(1) gauge field, which is independent of the electromagnetic Uem(1) gauge field. The effective interactions of the charged matter with the monopole source are described by a gauge invariant mixed Chern-Simons-like (Pontryagin-density) term between the two U(1) gauge fields. The latter interaction coupling is left free, and a lattice study of the system is performed with the aim of determining the phase structure of this effective theory. Our study shows that, in the spontaneously broken-symmetry phase, the monopole source triggers, via the mixed Chern-Simons term, which is nontrivial in its presence, the generation of a dynamical singular configuration (magnetic-monopolelike) for the respective gauge fields. The scalar field also behaves in the broken phase in a way similar to that of the scalar sector of the ’t Hooft-Polyakov monopole. Moreover, we show that the modest size of the lattices involved does not have significant effects on the main conclusions of our analysis. Published by the American Physical Society 2024

A basic examination of the gauged model of the Floreanini-Jackiw chiral boson within the framework of BRST symmetry

We consider the gauged model of Floreanini-Jackiw chiral boson which is generated from the chiral boson with parameter-free Faddeevian anomaly. This model does not have a manifestly Lorentz co-variant structure. However, it is exactly solvable and has a physical subspace that is precisely Lorentz invariant. The recommendation of Mitra and Rajaraman makes this model gauge invariant in the usual phasespace. Additionally, Wess-Zumino terms for this model are constructed to make it gauge-invariant which allows BRST embedding of the resulting gauge-invariant theory. Despite the strange structural appearance of the models when viewed in terms of Lorentz covariance BRST invariant reformulation has been found possible. Additionally, it has been observed that being supplemented with BRST symmetry, anti-BRST symmetry plays a crucial role in pinpointing the specific symmetric physical states.

Study of characteristics elementary atomic processes in the neon-like multicharged ions plasma within an energy approach

We present the theoretical foundations of an advanced relativistic approach to computing the main energy, spectral characteristics of radiative-collisional processes in the plasma (in particular, the Debye plasma) of atomic as the example, neon-like) ions with simultaneous, quantitatively consistent consideration of the complex relativistic, interelectron exchange-correlation and plasma environment effects. The approach is based on the combination of a relativistic energy approach (S-matrix Gell-Mann and Low formalism), the relativistic gauge-invariant many-body perturbation theory with optimized Dirac-Fock-Sturm and Debye-Hückel approximations with accounting for the plasma environment effects with possible generalization on the presence of an additional external electromagnetic field. The fundamental point of our approach is the selection of the optimized Dirac-Fock-Sturm zeroth approximation and application of the consistent procedure for constructing a one-quasiparticle representation (basis’s of relativistic wave functions) in compliance with the principle of gauge invariance, in particular, by minimizing a gauge-noninvariant contributions to the radiative widths of the atomic (ionic) levels due to the complex exchange-correlation effects. The electron-ion collision strength and the dioelect5ron capture rate etc are determined within the presented theory.

Collisional broadening and shift of the hyperfine lines for complex atomic systems in atmosphere of the buffer inert gases

An effective approach to determination of the collisional hyperfine lines shift and broadening in a buffer gas medium is presented and based on the generalized kinetic theory of spectral lines, the exchange perturbation theory and relativistic gauge-invariant perturbation theory with the optimized model potential approximation for computing the optimized basises of the relativistic wave functions.The results of calculating the shift and broadening of the hyperfine structure spectral lines due to collisions for complex atoms (here thallium is considered) in an atmosphere of inert gases (Kr, Xe) are presented and compared with other available alternative theoretical and experimental data. It is shown that the ratio of an adiabaticbroadening to a collisional shift for the pair of Tl–Kr (Га/р)/ fр is ~1/75 and for the pair of Tl- Xe(Га/р)/fр ~1/60.These estimates testify to a violation of well-known Foley relationship, which is, as a rule, inviolable in the standard atomic spectroscopy.

MOG as symmetry breaking in scalar–vector–tensor gravity

ABSTRACT The Modified Gravity Model (MOG) has been proposed as a solution to the dark matter problem, but it does not meet the gauge invariant condition. The aim of this work is to propose a gauge-invariant theory, which suggests that symmetry can break at a low temperature in the Universe, leading to the MOG theory. This theory has the potential to alter the dynamics of the early and late Universe and naturally produce cosmological inflation.

Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity

In this paper, we discuss on the phenomenological footprints of gauge invariant theories of gravity where the gravitational effects are due not only to spacetime curvature, but also to vectorial nonmetricity. We explore the possibility that vectorial nonmetricity and gauge symmetry may survive after $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ (electroweak) symmetry breaking, so that these may have impact on the explanation of certain cosmological puzzles, such as the nature of the dark matter and of the dark energy. We show that this is possible only for theories with gradient nonmetricity, i.e., when the vectorial nonmetricity amounts to a gradient of a scalar. The possibility that vectorial nonmetricity may have played a role in the quantum epoch is not ruled out. We also present an alternative interpretation of gauge invariance of theories with vectorial nonmetricity, which we call the ``many-worlds'' interpretation due to its overall similitude with the known interpretation of quantum physics.

(Non-)unitarity of strictly and partially massless fermions on de Sitter space

We present the dictionary between the one-particle Hilbert spaces of totally symmetric tensor-spinor fields of spin s = 3/2, 5/2 with any mass parameter on D-dimensional (D ≥ 3) de Sitter space (dSD) and Unitary Irreducible Representations (UIR’s) of the de Sitter algebra spin(D, 1). Our approach is based on expressing the eigenmodes on global dSD in terms of eigenmodes of the Dirac operator on the (D − 1)-sphere, which provides a natural way to identify the corresponding representations with known UIR’s under the decomposition spin(D, 1) ⊃ spin(D). Remarkably, we find that four- dimensional de Sitter space plays a distinguished role in the case of the gauge-invariant theories. In particular, the strictly massless spin-3/2 field, as well as the strictly and partially massless spin-5/2 fields on dSD, are not unitary unless D = 4.

Quantum scale invariance in gauge theories and applications to muon production

We discuss quantum scale invariance in (scale invariant) gauge theories with both ultraviolet (UV) and infrared (IR) divergences. Firstly, their BRST invariance is checked in two apparently unrelated approaches using a scale invariant regularisation (SIR). These approaches are then shown to be equivalent. Secondly, for the Abelian case we discuss both UV and IR quantum corrections present in such theories. We present the Feynman rules in a form suitable for offshell Green functions calculations, together with their one-loop renormalisation. This information is then used for the muon production cross section at one-loop in a quantum scale invariant theory. Such a theory contains not only new UV poles but also IR poles. While the UV poles bring new quantum corrections (in the form of counterterms), finite or divergent, that we compute, it is shown that the IR poles do not bring new physics. The IR quantum corrections, both finite and divergent, cancel out similarly to the way the IR poles themselves cancel in the traditional approach to IR divergences (in the cross section, after summing over virtual and real corrections). Hence, the evanescent interactions induced by the scale-invariant analytical continuation of the SIR scheme do not affect IR physics, as illustrated at one-loop for the muon production ($e^+ e^- \to \mu^+\mu^-$) cross section.

Electric field-based quantization of the gauge invariant Proca theory

We consider the gauge invariant version of the Proca theory, where besides the real vector field there is also the real scalar field. We quantize the theory such that the commutator of the scalar field operator and the electric field operator is given by a predefined three-dimensional vector field, say $\cal E$ up to a global prefactor. This happens when the field operators of the gauge invariant Proca theory satisfy the proper gauge constraint. In particular, we show that $\cal E$ given by the classical Coulomb field leads to the Coulomb gauge constraint making the vector field operator divergenceless. We also show that physically unreadable gauge constraints can have a strikingly simple $\cal E$-representation in our formalism. This leads to the discussion of Debye, Yukawa, etc. gauges. In general terms, we explore the mapping between classical vector fields and gauge constraints imposed on the operators of the studied theory.

Anomalies from an effective field theory perspective

The path-integral measure of a gauge-invariant fermion theory is transformed under the chiral transformation and leads to an elegant derivation of the anomalous chiral Ward-Takahashi identities, as we know from the seminal work of Fujikawa. We present in this work an alternative and illuminating way to calculate the Jacobian in the path-integral measure from the covariant derivative expansion technique used in effective field theory. We present several ways to customize the crucial regularization such that the anomaly is located in the desired current, which is unprecedented within the path integral approach. We are then able to derive, in a transparent and unified way, the covariant, consistent, gravitational, and scale anomalies.

Gauge-invariant theory of truncated quantum light-matter interactions in arbitrary media

The loss of gauge invariance in models of light-matter interaction which arises from material and photonic space truncation can pose significant challenges to conventional quantum optical models when matter and light strongly hybridize. In structured photonic environments, necessary in practice to achieve strong light-matter coupling, a rigorous model of field quantization within the medium is also needed. Here we use the framework of macroscopic QED by quantizing the fields in an arbitrary material system, with a spatially dependent dispersive and absorptive dielectric, starting from a fundamental light-matter action. We truncate the material and mode degrees of freedom while respecting the gauge principle by imposing a partial gauge-fixing constraint during canonical quantization, which admits a large number of gauges including the Coulomb and multipolar gauges commonly used in quantum optics. We also consider gauge conditions with explicit time dependence, enabling us to unambiguously introduce additional phenomenologically time-dependent light-matter interactions in any gauge. Our results allow one to derive rigorous nonrelativistic models of ultrastrong light-matter interactions in structured photonic environments with no gauge ambiguity. Results for two-level systems and the dipole approximation are discussed, as well as how to go beyond the dipole approximation for effective single-particle models. By comparing with the limiting case of an inhomogeneous dielectric, where dispersion and absorption can be neglected and the fields can be expanded in terms of the generalized transverse eigenfunctions of the dielectric, we show how lossy systems can introduce an additional gauge ambiguity, which we resolve and predict to have fundamental implications for open quantum system models. Finally, we show how observables in mode-truncated systems can be calculated without ambiguity by using a simple gauge-invariant model of photodetection.

Gauge-invariant semidiscrete Wigner theory

A gauge-invariant Wigner quantum mechanical theory is obtained by applying the Weyl-Stratonovich transform to the von Neumann equation for the density matrix. The transform reduces to the Weyl transform in the electrostatic limit, when the vector potential and thus the magnetic field are zero. Both cases involve a center-of-mass transform followed by a Fourier integral on the relative coordinate introducing the momentum variable. The latter is continuous if the limits of the integral are infinite or, equivalently, the coherence length is infinite. However, the quantum theory involves Fourier transforms of the electromagnetic field components, which imposes conditions on their behavior at infinity. Conversely, quantum systems are bounded and often very small, as is, for instance, the case in modern nanoelectronics. This implies a finite coherence length, which avoids the need to regularize non-converging Fourier integrals. Accordingly, the momentum space becomes discrete, giving rise to momentum quantization and to a semi-discrete gauge-invariant Wigner equation. To gain insights into the peculiarities of this theory one needs to analyze the equation for specific electromagnetic conditions. We derive the evolution equation for the linear electromagnetic case and show that it significantly simplifies for a limit dictated by the long coherence length behavior, which involves momentum derivatives. In the discrete momentum picture these derivatives are presented by finite difference quantities which, together with further approximations, allow to develop a computationally feasible model that offers physical insights into the involved quantum processes. In particular, a Fredholm integral equation of the second kind is obtained, where the "power" of the kernel components, measuring their rate of modification of the quantum evolution, can be evaluated.

Gauge invariant derivation of zeroth and first laws of black hole thermodynamics

In gauge invariant theories, like Einstein-Maxwell theory, physical observables should be gauge invariant. In particular, mass, entropy, angular momentum, electric charge and their respective chemical potentials, temperature, horizon angular velocity and electric potential which appear in the laws of black hole thermodynamics should be gauge invariant. In the usual construction of the laws of black hole thermodynamics, gauge invariance of the intensive quantities is subtle; here we remedy this and provide a gauge invariant derivation and the proof of the zeroth and first laws of black hole thermodynamics.

Perturbations of a class of locally rotationally symmetric cosmologies with applications to dissipative fluids

A gauge invariant perturbation theory, based on the covariant split of spacetime, is used to study first order perturbations on a class of anisotropic cosmological backgrounds. The perturbations as well as the energy-momentum tensor are kept general, giving a system of equations on which different physical situations may be imposed. Through a harmonic decomposition, the system is then transformed to evolution equations in time and algebraic constraints. This result is then applied to dissipative one-component fluids, and on using the simplified acausal Eckart theory the system is reduced to two closed subsystems, governed by four and eight harmonic coefficients for the odd and even sectors respectively. The system is also seen to close in a simplified causal theory. It is then demonstrated, within the Eckart theory, how vorticity can be generated from viscosity.

M5 branes on ℝ1,1×Taub-NUT

We study M5 branes on ℝ1,1×Taub-NUT that we view as a singular fibration. Reducing the M5 branes along the fiber gives 5d SYM. Due to the singularity, this 5d theory has a gauge anomaly and it is not supersymmetric. To cure these problems we add a supersymmetric gauged chiral WZW theory on the 2d submanifold where the circle fiber vanishes. In addition we add a mass term for the five scalar fields located on this submanifold. With all this, we obtain a fully supersymmetric and gauge invariant theory.

OPTIMIZED RELATIVISTIC MANY-BODY PERTURBATION THEORY IN CALCULATIONS OF ATOMIC SPECTRAL AND RADIATION CHARACTERISTICS: Eu ATOM

The new formalism of the relativistic gauge-invariant perturbation theory (RMBPT-ODF) with the optimized Dirac-Fock approximation and a generalized energy approach is applied to the study of energy, radiation, and spectroscopic characteristics of a group of heavy atomic systems, in particular, energy levels and transition probabilities and oscillator strengths of the transitions 4f7(8S)6s2 8S7/2 4f7(8S)6s6p 8P5/2,7.2,9.2, 4f7(8S)6s7p 8P5/2,7\2, 4f7(8S)6s8p 8P9/2,7\2 in spectrum of the europium atom Eu I. It is shown that the required formalism, in comparison with the standard non-optimized relativistic Hartree-Fock and Dirac-Fock methods, allows obtaining more accurate data both on energies and amplitudes and probabilities of radiative transitions, which is due to the use of the optimized zero ODF approximation, a fairly complete and effective account of complex many-body exchange-correlation effects. The contribution due to the polarization of the core reaches 30% of the value of the oscillator strength; the value of the calibration-invariant contribution to the radiation width is fractions of a percent, in contrast to all existing methods of modern atomic spectroscopy, for which the contribution reaches 5-50%.

Quantum wires, Chern-Simons theory, and dualities in the quantum Hall system

Over the years, many theoretical frameworks have been developed to understand the remarkable physics of the quantum Hall system. In this work we discuss the interplay among quantum wires, Chern-Simons theory, bosonization, and particle-vortex duality, which enable a unified approach for the Laughlin states of the fractional quantum Hall system. Starting from the so-called quantum wires system, which is a semi-microscopic description in terms of 1+1 dimensional theories, we discuss the emergence of 2+1 dimensional low-energy effective field theories by using different maps connecting the microscopic degrees of freedom with the macroscopic ones. We show the origin of these maps by embedding the bosonized version of the original quantum wires model in a gauge invariant theory and using particle vortex-duality.

Consistency of the dual formulation of axion solutions to the strong CP problem

An exact duality between axion with arbitrary potential and antisymmetric form-field has been derived some time ago. Using this duality, the axion solution to strong-CP problem has been formulated as a gauge invariant theory of forms. In this description, the QCD axion is represented by a Kalb-Ramond field which is eaten-up by the Chern-Simons $3$-form of QCD, thereby making it massive. This ensures the CP-invariance of the vacuum. Although viewed as an effective low energy theory, this formulation accomplishes the same goal as ordinary Peccei-Quinn mechanism, due to its gauge invariance, it is protected against unwanted UV-corrections. In the previous work it has been shown that dual formulation is insensitive to UV-physics in the sense that the corrections to CP-conserving vacuum from arbitrary massive sources are strictly zero. By going carefully through duality transformations and source-resolution, we reproduce this curious result and give some further consistency checks. We apply similar analysis to other approaches to naturalness problems based on form fields and axions, such as cosmological relaxation of the standard model Higgs boson mass via the attractor mechanism.