Choice Of Gauge Research Articles

Primordial black hole formation in a dust bouncing model

Linear scalar cosmological perturbations have increasing spectra in the contracting phase of bouncing models. We study the conditions for which these perturbations may collapse into primordial black holes and the hypothesis that these objects constitute a fraction of dark matter. We compute the critical density contrast that describes the collapse of matter perturbations in the flat-dust bounce model with a parametric solution, obtained from the Lemaitre-Tolman-Bondi metric that represents the spherical collapse. We discuss the inability of the Newtonian gauge to describe perturbations in contracting models as the perturbative hypothesis does not hold in such cases. We carry the calculations for a different Gauge choice and compute the perturbations' power spectra numerically. Finally, assuming a Gaussian distribution, we compute the primordial black hole abundance with the Press-Schechter formalism and compare it with observational constraints. From our analysis, we conclude that the primordial black hole formation in a dust-dominated contracting phase does not lead to a significant mass fraction of primordial black holes in dark matter today.

Detecting quantum vacuum fluctuations of the electromagnetic field

Abstract Quantum vacuum fluctuations of the electromagnetic field result in two signatures on a harmonically trapped charged particle: a shift from the natural trap frequency and generation of quantum coherences. We assess the role of the long-wavelength and rotating-wave approximations in estimating this frequency shift. We estimate the magnitude of the frequency shift using parameters from a single-electron cyclotron experiment and also demonstrate how the dependence of the frequency shift on the magnetic field of the cyclotron is tied to the rotating-wave approximation. We expect the frequency shift to be observable in future experiments. We also suggest a possible route to detecting vacuum-generated quantum coherences. These experiments should settle the debate on
the choice of approximations and gauge in capturing the effect of the quantum vacuum fluctuations.

Geometric theory of (extended) time-reversal symmetries in stochastic processes: I. Finite dimension

Abstract In this article, we analyze three classes of time-reversal of a Markov process with Gaussian noise on a manifold. We first unveil a commutativity constraint for the most general of these time-reversals to be well defined. Then we give a triad of necessary and sufficient conditions for the stochastic process to be time-reversible. While most reversibility conditions in the literature require knowledge of the stationary probability, our conditions do not, and therefore can be analytically checked in a systematic way. We then show that the mathematical objects whose cancellation is required by our reversibility conditions play the role of independent sources of entropy production. Furthermore, we give a geometric interpretation of the so-called irreversible cycle-affinity as the vorticity of a certain vector field for a Riemannian geometry given by the diffusion tensor. We also discuss the relation between the time-reversability of the stochastic process and that of an associated deterministic dynamics: its Stratonovitch average. Finally, we show that a suitable choice of a reference measure—that can be considered as a prior or a gauge, depending on the context—allows to study a stochastic process in a way that is both coordinate-free and independent of the prescription used to define stochastic integrals. When this reference measure plays the role of a gauge choice, we interpret our previous results through the lens of gauge theory and prove them to be gauge-invariant.

Three-component aerodynamic load cells

The article examines the effect of flow on models studied in wind tunnels. To determine the force effect of the flow on the model under study, a more accurate and reliable method of directly measuring forces and moments using aerodynamic strain gauge balances is proposed. When solving a plane problem for a symmetrical model at zero slip angle, a design of three-component scales is proposed that measures the lift force, the drag force and the pitching moment. To eliminate the interaction between the supporting devices and the model, which causes disturbances in the flow near the model, the scales are located outside the model and the working part of the wind tunnel. The components of the aerodynamic force and moment acting on the model are measured using resistance strain gauges, which convert the deformation of the elastic element into a change in electrical resistance, which is measured by an instrument connected to an appropriate measuring circuit. The choice of strain gauges as weight elements is due to their very small size and weight, the ability to measure very small relative deformations of elastic elements, low inertia, which makes it possible to measure not only static but also dynamic loads, and the possibility of remote measurements. To compensate for the influence of various sources of errors, increase sensitivity and ensure greater measurement accuracy, the strain gauges are connected via a bridge circuit and included in all four arms of the bridge. Deformation of the horizontal measuring beam causes a change in resistance not only in the strain gauges that measure the pitching moment, but also in the strain gauges designed to measure the lift force. Since the design of the scales does not allow for electrical separation of these components, the influence of the pitching moment on the magnitude of the lift force is determined during the calibration process and is assessed using a special influence graph constructed from the results of calibration data. In strain gauge measurements, the output values of forces and moments acting on the model under test are obtained in the form of corresponding readings from a device that measures electrical signals proportional to the applied forces. To convert instrument data into values of forces and moments, a joint calibration of scales and instruments is carried out in order to obtain calibration coefficients. Additional components of aerodynamic forces and moments created by the holder are determined by purging it in the presence of the model. Calculated dependencies for determining the components of the aerodynamic impact are given. The values of the coefficients of aerodynamic forces and moments are given in the flow coordinate system. The pledge has been given.

O(9, 25) symmetry of heterotic string theory at orders α′, α′2

In a recent study, we have observed that by imposing a truncated T-duality transformation on the circular reduction of the bosonic couplings in the heterotic theory at four- and six-derivative orders, we can calculate these couplings in a particular YM gauge where the YM potential vanishes but its field strength remains non-zero. Importantly, the coupling constants are independent of the gauge choice, so these results are valid across different YM gauge choices.In this work, we explore the cosmological reduction of these couplings when the YM gauge fields belong to the Cartan subalgebra of SO(32) or E8 × E8. We demonstrate that after applying appropriate one-dimensional field redefinitions and total derivative terms, the couplings can be expressed in a proposed O(9, 25)-invariant canonical form, which is the extension of the canonical O(9, 9)-invariant form for just the NS-NS fields proposed by Hohm and Zwiebach. This O(9, 25)-invariant expression is in terms of the trace of the first time derivative of the generalized metric, which encompasses both the YM field and the NS-NS fields.

Quantum states and spectra of small cylindrical and toroidal lattices

Abstract We examine the spectrum and quantum states of small lattices with cylindrical and toroidal topology subject to a scalar gauge potential that introduces a position dependent phase in the inter-site coupling. Equivalency of gauges assumed in infinite lattices is generally lost due to the periodic boundary conditions, and conditions that restore it are identified. We trace the impact of various system parameters including gauge choice, boundary conditions and inter-site coupling strengths, and an additional axial field. We find gauge dependent appearance of avoided crossings and persistent degeneracies, and we show their impact on the associated eigenstates. Smaller lattices develop prominent gaps in spectral lines associated with edge states, which are suppressed in the thermodynamic limit. Toroidal lattices have counterparts of most of the features observed in cylindrical lattices, but notably they display a transition from localization to delocalization determined by the relation between the field parameter and the number of lattice sites.

Path integral and conformal instability in nonlocal quantum gravity

We introduce the Lorentzian path integral of nonlocal quantum gravity. After introducing the functional measure, the Faddeev-Popov sector and the field correlators, we move to perturbation theory and describe Efimov analytic continuation of scattering amplitudes to Euclidean momenta and back to Lorentzian. We show that the conformal instability problem in the Euclidean path integral is solved by suitable gauge choices at the perturbative level. The three examples of Einstein gravity, Stelle gravity and nonlocal quantum gravity are given.

Can a radiation gauge be horizon-locking?

In this short Note, I answer the titular question: yes, a radiation gauge can be horizon-locking. Radiation gauges are very common in black hole perturbation theory. It’s also very convenient if a gauge choice is horizon-locking, i.e. the location of the horizon is not moved by a linear metric perturbation. Therefore it is doubly convenient that a radiation gauge can be horizon-locking, when some simple criteria are satisfied. Though the calculation is straightforward, it seemed useful enough to warrant writing this Note. Finally I show an example: the ℓ vector of the Hartle–Hawking tetrad in Kerr satisfies all the conditions for ingoing radiation gauge to keep the future horizon fixed.

Toward a covariant framework for post-Newtonian expansions for radiative sources

We consider the classic problem of a compact fluid source that behaves nonrelativistically and that radiates gravitational waves. The problem consists of determining the metric close to the source as well as far away from it. The nonrelativistic nature of the source leads to a separation of scales resulting in an overlap region where both the 1/c and (multipolar) G expansions are valid. Standard approaches to this problem (the Blanchet-Damour and the DIRE approach) use the harmonic gauge. We define a “post-Newtonian” class of gauges that admit a Newtonian regime in inertial coordinates. In this paper we set up a formalism to solve for the metric for any post-Newtonian gauge choice. Our methods are based on previous work on the covariant theory of nonrelativistic gravity (a 1/c expansion of general relativity that uses post-Newton-Cartan variables). At the order of interest in the 1/c and G expansions we split the variables into two sets: transverse and longitudinal. We show that for the transverse variables the problem can be reduced to inverting Laplacian and d’Alembertian operators on their respective domains subject to appropriate boundary conditions. The latter are regularity in the interior and asymptotic flatness with a Sommerfeld no-incoming radiation condition imposed at past null infinity. The longitudinal variables follow from the gauge choice. The full solution is then obtained by the method of matched asymptotic expansion. We show that our methods reproduce existing results in harmonic gauge to 2.5PN order. Published by the American Physical Society 2024

Gauge fixing for sequence-function relationships.

Quantitative models of sequence-function relationships are ubiquitous in computational biology, e.g., for modeling the DNA binding of transcription factors or the fitness landscapes of proteins. Interpreting these models, however, is complicated by the fact that the values of model parameters can often be changed without affecting model predictions. Before the values of model parameters can be meaningfully interpreted, one must remove these degrees of freedom (called "gauge freedoms" in physics) by imposing additional constraints (a process called "fixing the gauge"). However, strategies for fixing the gauge of sequence-function relationships have received little attention. Here we derive an analytically tractable family of gauges for a large class of sequence-function relationships. These gauges are derived in the context of models with all-order interactions, but an important subset of these gauges can be applied to diverse types of models, including additive models, pairwise-interaction models, and models with higher-order interactions. Many commonly used gauges are special cases of gauges within this family. We demonstrate the utility of this family of gauges by showing how different choices of gauge can be used both to explore complex activity landscapes and to reveal simplified models that are approximately correct within localized regions of sequence space. The results provide practical gauge-fixing strategies and demonstrate the utility of gauge-fixing for model exploration and interpretation.

On the evaluation of the Ray-Singer torsion path integral

There are very few explicit evaluations of path integrals for topological gauge theories in more than 3 dimensions. Here we provide such a calculation for the path integral representation of the Ray-Singer Torsion of a flat connection on a vector bundle on base manifolds that are themselves S1 bundles of any dimension. The calculation relies on a suitable algebraic choice of gauge which leads to a convenient factorisation of the path integral into horizontal and vertical parts.

Quantum Circuits with Multiterminal Josephson-Andreev Junctions

We explore superconducting quantum circuits where several leads are simultaneously connected beyond the tunneling regime, such that the fermionic structure of Andreev bound states in the resulting multiterminal Josephson junction influences the states of the full circuit. Using a simple model of single-channel contacts and a single level in the middle region, we discuss different circuit configurations where the leads are islands with finite capacitance and/or form loops with finite inductance. We find situations of practical interest where the circuits can be used to define noise-protected qubits, which map to the bifluxon and 0−π qubits in the tunneling regime. We also point out the subtleties of the gauge choice for a proper description of these quantum circuit dynamics. Published by the American Physical Society 2024

The classical double copy in curved spacetimes: perturbative Yang-Mills from the bi-adjoint scalar

We formulate a version of the double copy for classical fields in curved spacetimes. We provide a correspondence between perturbative solutions to the bi-adjoint scalar equations and those of the Yang-Mills equations in position space. At the linear level, we show that there exists a map between these solutions for maximally symmetric spacetime backgrounds, that provides every Yang-Mills solution by the action of an appropriate differential operator on a bi-adjoint scalar solution. Given the existence of a linearized map, we show that it is possible to cast the solutions of the Yang-Mills equations at arbitrary perturbation order in terms of the corresponding bi-adjoint scalar solutions. This all-order map is reminiscent of the flat space BCJ double copy, and works for any curved spacetime where the perturbative expansion holds. We show that these results have the right flat space limit, and that the correspondence is agnostic to the choice of gauge.

DPSV trick for spherically symmetric backgrounds

We discuss the approach suggested by Deffayet et al. (DPSV) to analysing the linearized perturbations in Horndeski theory in the case of a static, spherically symmetric background. In L3 subclass of Horndeski theories we prove the validity of the DPSV approach by showing that the original method corresponds to a specific gauge choice in the quadratic action for perturbations. We also show that in the case of a spherically symmetric background the DPSV trick does not work in a more general L4 Horndeski theory.

Spontaneous Emergence of a Causal Time Axis in Euclidean Space from a Gauged Rotational Symmetry Theory

We demonstrate the emergence of an effective “time” axis in the ground state of a gauged rotational symmetry theory in four-dimensional Euclidean space. In so doing, we remove the necessity of Wick rotation to Lorentz spacetime, an arbitrary and sometimes ill-defined procedure, especially for gravity-related theories. We begin by adapting the Cho-Duan-Ge decomposition to the gauge theory of the four-dimensional rotational symmetry group SO(4), where it identifies the maximal Abelian subgroup SO(2)⊗SO(2) in a gauge covariant manner. We then find the one-loop effective theory to have a stable condensate of monopoles corresponding to the reduction of SO(4) symmetry to SO(2)⊗SO(2). The construction of the condensate ensures that the four-dimensional spatial direction of its field strength must coincide with that of this embedding, and that a magnetic potential must be worked against to divert a trajectory away from this direction. Indeed, movement along this direction represents minimal potential energy. We take it to be the time direction. The gauge-dependent nature of the condensate is such that different gauge choices may lead to different time axes and we show on very general grounds that these different coordinate systems must be relatable by transformations of Lorentz form.

Gauge choice for organizing infrared singularities in QCD

Gauge choice for organizing infrared singularities in QCD

Local well-posedness of the Einstein-Yang-Mills system in constant mean extrinsic curvature spatial harmonic generalized Coulomb gauge

We study the local well-posedness of the Einstein-Yang-Mills equations in constant mean extrinsic curvature spatial harmonic generalized Coulomb gauge. In this choice of gauge, the complete Einstein-Yang-Mills equations reduce to a coupled elliptic-hyperbolic system. We establish the existence of a unique, local, continuous-in-time solution to this coupled system. This yields an “in time” continuation criteria of the solutions which are to be used in the potential future proof of improved continuation criteria for this coupled system utilizing Moncrief’s light cone estimate technique.

A Discrete-Variable Local Diabatic Representation of Conical Intersection Dynamics.

Conical intersections (CIs) are ubiquitous in polyatomic molecules and are responsible for a wide range of phenomena in photochemistry and photophysics. Modeling the conical intersection dynamics with adiabatic electronic states is hindered by the divergence of the first- and second-order derivative couplings at CIs due to electronic degeneracy. We introduce and implement a novel diabatic representation for exact correlated electron-nuclear wave packet dynamics through conical intersections. It directly employs the adiabatic electronic states but avoids the singular first- and second-order derivative couplings and is robust to different gauge choices of the electronic wave function phases. The reference nuclear geometries defining the adiabatic electronic states are determined by a discrete-variable representation of the nuclear coordinates. The nonadiabatic effects are accounted for by the electronic overlap matrix instead of derivative couplings as in the adiabatic representation. Illustrated by a two-mode conical intersection model, this representation captures all nonadiabatic effects, including electronic transitions, electronic coherence, and geometric phases. Thus, this representation provides a singularity-free framework for modeling ab initio conical intersection wave packet dynamics.

Switching quantum reference frames in the N-body problem and the absence of global relational perspectives

Given the importance of quantum reference frames (QRFs) to both quantum and gravitational physics, it is pertinent to develop a systematic method for switching between the descriptions of physics relative to different choices of QRFs, which is valid in both fields. Here we continue with such a unifying approach, begun in [Quantum 4, 225 (2020)], whose key ingredient is a symmetry principle, which enforces physics to be relational. Thanks to gauge related redundancies, this leads to a perspective-neutral structure which contains all frame choices at once and via which frame perspectives can be consistently switched. Formulated in the language of constrained systems, the perspective-neutral structure is the constraint surface classically and the gauge invariant Hilbert space in the Dirac quantized theory. By contrast, a perspective relative to a specific frame corresponds to a gauge choice and the associated reduced phase and Hilbert space. QRF changes thus amount to a gauge transformation. We show that they take the form of `quantum coordinate changes'. We illustrate this in a general mechanical model, namely the relational N-body problem in 3D space with rotational and translational symmetry. This model is especially interesting because it features the Gribov problem so that globally valid gauge fixing conditions, and hence relational frame perspectives, are absent. The constraint surface is topologically non-trivial and foliated by 3-, 5- and 6-dimensional gauge orbits, where the lower dimensional orbits are a set of measure zero. The N-body problem also does not admit globally valid canonically conjugate pairs of Dirac observables. These challenges notwithstanding, we exhibit how one can construct the QRF transformations for the 3-body problem. Our construction also sheds new light on the generic inequivalence of Dirac and reduced quantization through its interplay with QRF perspectives.

Purely virtual extension of quantum field theory for gauge invariant fields: Yang–Mills theory

We extend quantum field theory by including purely virtual “cloud” sectors, to define physical off-shell correlation functions of gauge invariant quark and gluon fields, without affecting the S matrix amplitudes. The extension is made of certain cloud bosons, plus their anticommuting partners. Both are quantized as purely virtual, to ensure that they do not propagate ghosts. The extended theory is renormalizable and unitary. In particular, the off-shell, diagrammatic version of the optical theorem holds. We calculate the one-loop two-point functions of dressed quarks and gluons, and show that their absorptive parts are gauge independent, cloud independent and positive (while they are generically unphysical if the cloud sectors are not purely virtual). A gauge/cloud duality simplifies the computations and shows that the gauge choice is just a particular cloud. It is possible to dress every field insertion with a different cloud. We compare the purely virtual extension to previous approaches to similar problems.