Gauge Condition Research Articles

Well-posed formulation of Einstein-Maxwell effective field theory

We consider the well-posedness of the initial value problem for Einstein-Maxwell theory modified by higher derivative effective field theory corrections. Field redefinitions can be used to bring the leading parity-symmetric 4-derivative corrections to a form which gives second order equations of motion. We show that a recently introduced "modified harmonic" gauge condition can be used to obtain a formulation of these theories which admits a well-posed initial value problem when the higher derivative corrections to the equations of motion are small.

On the teleparallel frame problem

The role played by the congruence in the prediction of the gravitational energy in the teleparallel equivalent of general relativity is discussed. It is shown that some congruences yield unphysical predictions. It is also shown that the energy–momentum tensor density predicted by the proper reference frame of an arbitrary accelerated observer vanishes along the observer’s worldline, regardless of its acceleration. The latter result is discussed and arguments both against and in favor of the use of this type of frame to describe the gravitational energy are presented; arguments against the belief that the principle of equivalence is incompatible with the localization of the gravitational energy are also presented. A gauge condition is applied to the teleparallel frame and its consistence is discussed: using three different tetrads for the pp-wave spacetimes, it is shown that the most consistent prediction comes from the tetrad that satisfies this gauge. The possibility of having a well-defined concept of absolute vacuum is also discussed.

Quantum symmetries and conserved charges of the cosmological Friedmann-Robertson-Walker model

We discuss both the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the cosmological Friedmann-Robertson-Walker (FRW) model with a differential gauge condition in the extended phase space. In this discussion, the presence of anti-BRST symmetry provides the complete geometrical description of BRST within the ambit of the supervariable approach. We derive the conserved (anti-)BRST charges for the FRW model using the celebrated Noether theorem and show the nilpotency and absolute anti-commutativity properties of these conserved charges within the realm of BRST formalism. Finally, we prove the sanctity of (anti-)BRST symmetries through the derivation of these symmetry transformations within the framework of the (anti-)chiral supervariable approach (ACSA) to BRST formalism.

Second-order energy-momentum tensor of a scalar field

We investigate the second-order effective energy-momentum tensor (2EMT) constructed by the quadratic terms of the linear scalar cosmological perturbations while the universe is dominated by a scalar field. We show that 2EMT is gauge dependent. We then study 2EMT in three (longitudinal, spatially flat, and comoving) gauge conditions in the slow-roll stage of inflation. We find that 2EMT exhibits an effective fluid of $w=\ensuremath{-}1/3$ on superhorizon scales in all of those gauge conditions.

Metric Gravity in the Hamiltonian Form—Canonical Transformations—Dirac’s Modifications of the Hamilton Method and Integral Invariants of the Metric Gravity

Two different Hamiltonian formulations of the metric gravity are discussed and applied to describe a free gravitational field in the d dimensional Riemann space-time. Theory of canonical transformations, which relates equivalent Hamiltonian formulations of the metric gravity, is investigated in detail. In particular, we have formulated the conditions of canonicity for transformation between the two sets of dynamical variables used in our Hamiltonian formulations of the metric gravity. Such conditions include the ordinary condition of canonicity known in classical Hamilton mechanics, i.e., the exact coincidence of the Poisson (or Laplace) brackets which are determined for both the new and old dynamical Hamiltonian variables. However, in addition to this, any true canonical transformations defined in the metric gravity, which is a constrained dynamical system, must also guarantee the exact conservation of the total Hamiltonians Ht (in both formulations) and preservation of the algebra of first-class constraints. We show that Dirac’s modifications of the classical Hamilton method contain a number of crucial advantages, which provide an obvious superiority of this method in order to develop various non-contradictory Hamiltonian theories of many physical fields, when a number of gauge conditions are also important. Theory of integral invariants and its applications to the Hamiltonian metric gravity are also discussed. For Hamiltonian dynamical systems with first-class constraints this theory leads to a number of peculiarities some of which have been investigated.

Second-order gauge-invariant formalism for the cosmological observables: complete verification of their gauge-invariance

Accounting for all the relativistic effects, we have developed the fully nonlinear gauge-invariant formalism for describing the cosmological observables and presented the second-order perturbative expressions associated with light propagation and observations without choosing a gauge condition. For the first time, we have performed a complete verification of the validity of our second-order expressions by comparing their gauge-transformation properties from two independent methods: one directly obtained from their expressions in terms of metric perturbations and the other expected from their nonlinear relations. The expressions for the cosmological observables such as galaxy clustering and the luminosity distance are invariant under diffeomorphism and gauge-invariant at the observed position. We compare our results to the previous work and discuss the differences in the perturbative expressions. Our second-order gauge-invariant formalism constitutes a major step forward in the era of precision cosmology and its applications in the future will play a crucial role for going beyond the power spectrum and probing the early universe.

Attenuated Gravitational Radiation

The hypothesis of an alternative way of obtaining gravitational waves is the physical motivation of this article. Using the linear field approximation and a symmetry transformation of the affine connection, new field equations and new gauge conditions have been obtained. Solutions to these field equations have been considered in the empty space and in the wave zone, and in both of them the oscillation amplitudes of their solutions are attenuated exponentially. We expect that these solutions can be useful for building more sophisticated gravitational wave models, and also as an impulse for researching further symmetry transformations of general relativity.

Nonlinear Radiation Gauge for Near Kerr Spacetimes

In this paper, we introduce and explore the properties of a new gauge choice for the vacuum Einstein equation inspired by the ingoing and outgoing radiation gauges (IRG, ORG) for the linearized vacuum Einstein equation introduced by Chrzanowski in his work on metric reconstruction (Chrzanowski in Phys Rev D 11:2042–2062, 1975) on the Kerr background. It has been shown by Price et al. (Class Quantum Gravity 24:2367–2388, 2007) that the IRG/ORG are consistent gauges for the linearized vacuum Einstein equation on Petrov type II backgrounds. In (Andersson et al. Stability for linearized gravity on the Kerr spacetime, 2019), the ORG was used in proving linearized stability for the Kerr spacetime, and the new non-linear radiation gauge introduced here is a direct generalization of that gauge condition, and is intended to be used to study the stability of Kerr black holes under the evolution generated by the vacuum Einstein equation.

ADM formulation and Hamiltonian analysis of f(Q) gravity

$f(Q)$ gravity is an extension of the symmetric teleparallel equivalent to general relativity. We demonstrate the Hamiltonian analysis of $f(Q)$ gravity with fixing the coincident gauge condition. Using the standard Dirac-Bergmann algorithm, we show that $f(Q)$ gravity has 8 physical degrees of freedom. This result reflects that the diffeomorphism symmetry of $f(Q)$ gravity is completely broken due to the gauge fixing. Moreover, in terms of the perturbations, we discuss the possible mode decomposition of these degrees of freedom.

On the Decomposition Theorem for Gluons

Recently, the problem of spin and orbital angular momentum (AM) separation has widely been discussed. Nowadays, all discussions about the possibility to separate the spin AM from the orbital AM in the gauge invariant manner are based on the ansatz that the gluon field can be presented in form of the decomposition where the physical gluon components are additive to the pure gauge gluon components, i.e. $A_\mu = A_\mu^{\text{phys}}+A_\mu^{\text{pure}}$. In the present paper, we show that in the non-Abelian gauge theory this gluon decomposition has a strong mathematical evidence in the frame of the contour gauge conception. In other words, we reformulate the gluon decomposition ansatz as a theorem on decomposition and, then, we use the contour gauge to prove this theorem. In the first time, we also demonstrate that the contour gauge possesses the special kind of residual gauge related to the boundary field configurations and expressed in terms of the pure gauge fields. As a result, the trivial boundary conditions lead to the inference that the decomposition includes the physical gluon configurations only provided the contour gauge condition.

Note on the strong hyperbolicity of f(R) gravity with dynamical shifts

The well-posedness of the gravitational equations of $f(R)$ gravity are studied in this paper. Three formulations of the $f(R)$ gravity with dynamical shifts (which are all based on the Arnowitt-Deser-Misner (ADM) formalism of the equations) are investigated. These three formulations are all proved to be strongly hyperbolic by pseudodifferential reduction. The first one is the Baumagarte-Shapiro-Shibata-Nakamura (BSSN) formulation with the so-called "hyperbolic $K$-driver" condition and the "hyperbolic Gamma driver" condition. The second one is the ADM formulation with modified harmonic gauge conditions. We find that the equations are not strong hyperbolic in traditional Z4 formulation for $f(R)$ gravity. So, in the third formulation, we improve the Z4 formulation, and show these equations are strong hyperbolic with modified harmonic gauge conditions.

Neveu-Schwarz-Ramond open superstring in the proper-time gauge: Free field theory

We study the Neveu-Schwarz-Ramond (NSR) open super-string theory in the proper-time gauge. The string field action is obtained by evaluating the Polyakov string path integral. In this study, we focus on the open-string free-field action, which corresponds to the string path integral on a strip. Depending on the periodicity of the fermion fields, the open super-string has two sectors: The Neveu-Schwarz (NS) and Ramond (R) sectors. We can impose the gauge conditions to fix the (super-) reparametrization invariance on the two-dimensional metric and its super-partner on the string world sheet to secure the covariance, in contrast to the light-cone gauge condition. Accordingly, the proper-time emerges in the NS sector and both proper-time and its super-partner appear in the R-sector. Integration leads to free-string field actions in both sectors.

Quantum theory of Weyl-invariant scalar-tensor gravity

We perform a manifestly covariant quantization of a Weyl-invariant (i.e., a locally scale-invariant) scalar-tensor gravity in the extended de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance and a new scalar gauge for Weyl invariance within the framework of the BRST formalism. We show that choral symmetry, which is a Poincar\'e-like $IOSp(8|8)$ supersymmetry in the case of Einstein gravity, is extended to a Poincar\'e-like $IOSp(10|10)$ supersymmetry. We point out that there is a gravitational conformal symmetry in quantum gravity and account for how conventional conformal symmetry in a flat Minkowski space-time is related to the gravitational conformal symmetry. Moreover, we examine the mechanism of the spontaneous symmetry breaking of the choral symmetry, and show that the gravitational conformal symmetry is spontaneously broken to the Poincar\'e symmetry and the corresponding massless Nambu-Goldstone bosons are the graviton and the dilaton. We also prove the unitarity of the physical $S$ matrix on the basis of the BRST quartet mechanism.

General Couplings Conditions of Four-Dimensional Maxwell-Klein-Gordon System

In this paper, we investigate the conditions for the Maxwell Klein Gordon system’s general gauge couplings in (3 + 1)-dimensional Minkowski spacetime. For the multi-interaction of photons and charged spin-0 particle, we begin with the Lagrangian with the general coupling turned on. The equation of motion is then derived in the form of a nonlinear wave equation. We obtained the general solution for the vector potential using the spherical means method. By considering the Coulomb gauge condition, we get the constraint for the couplings, which are critical in proving the global well-posedness of the solution.

Modelling credit spreads on commercial mortgage loans

PurposeThis paper offers empirical evidence on factors influencing credit spreads on commercial mortgage loans. It extends existing work on the pricing of commercial mortgage loans. The authors examine the relative significance of a range of factors on loan pricing that are lender, asset and loan specific. The research explores and quantifies the sources of spread differentials among commercial mortgage loans. The paper contributes to a limited literature on the subject and serves the purpose of price discovery in commercial property lending. It offers a framework to compare actual pricing with fundamental-based estimates of loan spreads.Design/methodology/approachPanel analysis is deployed to examine the cross-section and time-series determinants of commercial mortgage loan margins and credit spreads. Using an exclusive database of loan portfolios in the United Kingdom (UK), the panel analysis enables the authors to analyse and quantify the impact of a number of theory-consistent and plausible factors determining the cost of lending to commercial real estate (CRE), including type and origin of lender, loan size, loan to value (LTV) and characteristics of asset financed – type, location and grade.FindingsSpreads on commercial mortgages and, therefore, loan pricing differ by the type of lender – bank, insurance company and debt fund. The property sector is another significant risk factor lenders price in. The LTV ratio has increased in importance since 2012. Prior to global financial crisis (GFC), lenders made little distinction in pricing different LTVs. Loans secured in secondary assets command a higher premium of 50–60bps. The analysis establishes an average premium of 35bps for loans advanced in regions compared to London. London is particularly seen a less risky region for loan advancements in the post-GFC era.Research limitations/implicationsThe study considers the role of lender characteristics and the changing regulation in the pricing of commercial mortgage loans and provides a framework to study spreads or pricing in this market that can include additional fundamental influences, such as terms of individual loans. The ultimate aim of such research is to assess whether mortgage loans are correctly priced and spotting risks emanating from actual loan spreads being lower than fundamental-based spreads pointing to tight pricing and over-lending.Practical implicationsThe analysis provides evidence on lender criteria that determine the cost of loans. The study confirms that differences in regulation affect loan pricing. The regulatory impact is most visible in the increased significance of LTV. In that sense, regulation has been effective in restricting lending at high LTV levels.Originality/valueThe paper exploits a database of a commercial mortgage loan portfolio to make loan pricing more transparent to the different types of lender and borrowers. Lenders can use the estimates to assess whether commercial loans are fairly priced. Borrowers better understand the relative significance of risk factors affecting margins and the price they are charged. The results of this paper are of value to regulators as they can assist to understand the determinants of loan margins and gauge conditions in the lending market.

Equivalence between the gauge n ⋅ ∂n ⋅ A = 0 and the axial gauge

Singularity of the gauge condition n⋅∂n⋅A=0 at n⋅k=0 is studied here. Such singularity is different from that in axial gauge and can not be regularized through analytical continuation method. It is proved that construction of continuous and well defined gauge links is obstructed by the Gribov ambiguity. Thus continuous gauge conditions which are free from the Gribov ambiguity are essential in studies on nonlocal gauge invariant objects. The Faddeev-Popov determinant of the gauge n⋅∂n⋅A=0, which is solved explicitly here, behaves like a δ-functional of gauge potentials once singularities in the functional integral is neglected and the length of the space along nμ direction tends to infinity. As a sequence, perturbation series in the gauge n⋅∂n⋅A=0 are equivalent to those in axial gauge for objects which are free from these singularities. However, the equivalence between the gauge n⋅∂n⋅A=0 and axial gauge is nontrivial for objects suffering from these singularities. It is also demonstrated through explicit calculations that the equivalence for long distance objects is not the case in general, especially lattice calculations show significant distinctions among the axial gauge n⋅A=0, the Landau gauge ∂⋅A=0 and the gauge n⋅∂n⋅A=0 for long distance objects.

The Influence of Gauge Conditions on Process and Result of Solving 3-D Problems of Computational Electromagnetism by the Finite Element Method

This article discusses the properties of the practical application results of the Coulomb and the “tree-cotree” gauge conditions for problems based on massive finite element 3-D-meshes (up to 12 million tetrahedrons) and with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${A}$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}$ </tex-math></inline-formula> formulation of the magnetic potential. The influence of the sort of gauging of the magnetic vector potential on the accuracy of the calculated solution of systems of linear algebraic equations (SLAEs) is shown by the example of magnetostatics and quasi-static (frequency domain) benchmark problems. The study was carried out for the cases of solving problems by iterative methods of the Krylov subspace and by direct methods. Iterative methods have shown the complexity of achieving the required solution accuracy with an increase in the number of finite elements and deterioration of the properties of the SLAE. The analysis of the dependence of the iterative process convergence and the required solution accuracy on the number of elements in the mesh and the type of gauging applied is accomplished. For direct methods for solving SLAEs, an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> estimate of the dependence of the value of the relative forward error on the presence and type of the gauge condition is performed. The possibility and efficiency of using block low-rank (BLR) factorization for solving SLAEs in the presence and absence of gauge conditions are considered. The conditions for using the gauging of the magnetic vector potential are shown, which are suitable for simplifying the process of preparing and solving numerical problems and increasing the accuracy of the calculated values of the magnetic vector potential in the frequency domain.

Optimized integrating factor technique for Schrödinger-like equations

The integrating factor technique is widely used to solve numerically (in particular) the Schrödinger equation in the context of spectral methods. Here, we present an improvement of this method exploiting the freedom provided by the gauge condition of the potential. Optimal gauge conditions are derived considering the equation and the temporal numerical resolution with an adaptive embedded scheme of arbitrary order. We illustrate this approach with the nonlinear Schrödinger (NLS) and with the Schrödinger–Newton (SN) equations. We show that this optimization increases significantly the overall computational speed, sometimes by a factor five or more. This gain is crucial for long time simulations, as, with larger time steps, less computations are performed and the overall accumulation of round-off errors is reduced.

Generalized Yang-Mills theory under rotor mechanism

This paper follows the previous work on generalized abelian gauge field theory of higher-order derivatives under rotor model and extends the study to the most generalized non-abelian case. We find that the rotor mechanism from the abelian case applies nicely to the non-abelian case under the Lorentz gauge condition. Under the rotor mechanism, the gauge field transforms as Tμa→□nTμa. When the order of field derivative is n=0, this restores back to the original Yang-Mills action. Our work gives an extensive generalization of the Yang-Mills theory with higher-order field derivatives. We also compute the equation of motion and Noether's current of the generalized non-abelian gauge field theory. Finally, we study the dynamic instability issue of the theory by the Ostrogradsky construction and the analysis of the 00-component of the energy-momentum tensor.

Critical gravitational collapse of a nonminimally coupled scalar field

We study the critical gravitational collapse of a massless scalar field non-minimally coupled to gravity, using a quadratic coupling function with a strength parameter $\xi$. We concentrate on critical phenomena of type II, and determine with an accuracy of at least $10^{-12}$ the value of the critical amplitude for collapse to a black hole, as well as the values of the critical and echoing exponents. Obtaining such high accuracy in the critical amplitude requires us to do a coordinate radial transformation that effectively increases resolution near the central regions by a factor of at least $10^3$. As expected, we find that for the case of small coupling the critical behaviour is very similar to that of a minimally coupled scalar field. On the other hand, for high coupling the dynamics become so violent that we need to introduce a special slicing condition, known as the shock-avoiding slicing condition, in order to avoid gauge pathologies that would otherwise cause our simulations to fail. With this new gauge condition we are able to perform high accuracy simulations even in the strong coupling regime, where we find that the critical and echoing exponents become significantly smaller, and that the echoing behavior is richer and can not be modelled by a single harmonic.