Residual Gauge Invariance Research Articles

Stationary two-state system in optics using layered materials

In scenarios where electrons are confined to a flat surface, such as graphene, quantizing electrodynamics reveals intriguing insights. We find that one of Maxwell’s equations manifests as part of the Hamiltonian, leading to novel constraints on physical states due to residual gauge invariance. We identify two quantum states with zero energy expectation values: one replicates the scattering and absorption of light, a phenomenon familiar in classical optics, while the other is more fundamentally associated with photon creation. These states form an inseparable two-state system, giving a new formula for reflection and transmission coefficients with photon emission effects. Notably, there exists a special thickness of the surface where these states decouple, offering intriguing possibilities for exploring physics through symmetry-based perturbations involving concepts of parity, axial gauge fields, and surface deformation.

Residual Gauge Invariance in a Massive Lorentz-Violating Extension of QED

We reassess an alternative CPT-odd electrodynamics obtained from a Palatini-like procedure. Starting from a more general situation, we analyze the physical consistency of the model for different values of the parameter introduced in the mass tensor. We show that there is a residual gauge invariance in the model if the local transformation is taken to vary only in the direction of the Lorentz-breaking vector. This residual gauge invariance can be extended to all models whose only source of gauge symmetry breaking is such a mass term.

BMS algebra from residual gauge invariance in light-cone gravity

We analyze the residual gauge freedom in gravity, in four dimensions, in the light-cone gauge, in a formulation where unphysical fields are integrated out. By checking the invariance of the light-cone Hamiltonian, we obtain a set of residual gauge transformations, which satisfy the BMS algebra realized on the two physical fields in the theory. Hence, the BMS algebra appears as a consequence of residual gauge invariance in the bulk and not just at the asymptotic boundary. We highlight the key features of the light-cone BMS algebra and discuss its connection with the quadratic form structure of the Hamiltonian.

Loop quantization of a model for D = 1 + 2 (anti)de Sitter gravity coupled to topological matter

We present a complete quantization of Lorentzian gravity with cosmological constant, coupled to a set of topological matter fields. The approach of loop quantum gravity is used thanks to a partial gauge fixing leaving a residual gauge invariance under a compact semi-simple gauge group, namely Spin(4) = SU(2) × SU(2). A pair of quantum observables is constructed, which are non-trivial despite being gauge-equivalent to zero at the classical level. A semi-classical approximation based on appropriately defined coherent states shows non-vanishing expectation values for them, thus not reproducing their classical behaviour.

Three-dimensional dynamics of four-dimensional topological BF theory with boundary

We consider the four-dimensional (4D) abelian topological BF theory with a planar boundary, following Symanzik's method. We find the most general boundary conditions compatible with the field equations broken by the boundary. The residual gauge invariance is described by means of two Ward identities which generate a current algebra. We interpret this algebra as canonical commutation relations of fields, which we use to construct a 3D Lagrangian. As a remarkable by-product, we find a (unique) boundary condition which can be read as a duality relation between 3D dynamical variables.

Cosmological perturbations in Hořava-Lifshitz gravity

We study cosmological perturbations in Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz Gravity, a recently proposed potentially ultraviolet-complete quantum theory of gravity. We consider scalar metric fluctuations about a homogeneous and isotropic space-time. Starting from the most general metric, we work out the complete second order action for the perturbations. We then make use of the residual gauge invariance and of the constraint equations to reduce the number of dynamical degrees of freedom. At first glance, it appears that there is an extra scalar metric degree of freedom. However, introducing the Sasaki-Mukhanov variable, the combination of spatial metric fluctuation and matter inhomogeneity for which the action in general relativity has canonical form, we find that this variable has the standard time derivative term in the second order action, and that the extra degree of freedom is nondynamical. The limit $\ensuremath{\lambda}\ensuremath{\rightarrow}1$ is well behaved, unlike what is obtained when expanding about Minkowski space-time. Thus, there is no strong coupling problem for Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity when considering cosmological solutions. We also compute the spectrum of cosmological perturbations. If the potential in the action is taken to be of ``detailed balance'' form, we find a cancellation of the highest derivative terms in the action for the curvature fluctuations. As a consequence, the initial spectrum of perturbations will not be scale-invariant in a general space-time background, in contrast to what happens when considering Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz matter leaving the gravitational sector unperturbed. However, if we break the detailed balance condition, then the initial spectrum of curvature fluctuations is indeed scale-invariant on ultraviolet scales. As an application, we consider fluctuations in an inflationary background and draw connections with the ``trans-Planckian problem'' for cosmological perturbations. In the special case in which the potential term in the action is of detailed balance form and in which $\ensuremath{\lambda}=1$, the equation of motion for cosmological perturbations in the far UV takes the same form as in general relativity. However, in general the equation of motion is characterized by a modified dispersion relation.

CUBIC SUPERSYMMETRY AND ABELIAN GAUGE INVARIANCE

On the basis of recent results extending nontrivially the Poincaré symmetry, we investigate the properties of bosonic multiplets including 2-form gauge fields. Invariant-free Lagrangians are explicitly built which involve possibly 3- and 4-form fields. We also study in detail the interplay between this symmetry and a U (1) gauge symmetry, and in particular the implications of the automatic gauge-fixing of the latter corresponding to a residual gauge invariance, as well as the absence of self-interaction terms.

Propagators with the Mandelstam-Leibbrandt prescription in the light-cone gauge

We show that the Feynman propagator in the light-cone gauge with the Mandelstam-Leibbrandt prescription has a logarithmic growth for large $\stackrel{\texttildelow{}}{n}\ifmmode\cdot\else\textperiodcentered\fi{}x$ which is related to the presence of a residual gauge invariance. Furthermore, we show that the retarded propagator for the $\stackrel{\texttildelow{}}{n}\ifmmode\cdot\else\textperiodcentered\fi{}A$ component of the gauge field develops a coordinate dependent mass. We argue that this feature is unphysical and may be eliminated by fixing the residual gauge degrees of freedom.

Some observations on interpolating gauges and non-covariant gauges

We discuss the viability of using interpolating gauges to define the non-covariant gauges starting from the covariant ones. We draw attention to the need for a very careful treatment of boundary condition defining term. We show that the boundary condition needed to maintain gauge-invariance as the interpolating parameter θ varies, depends very sensitively on the parameter variation. We do this with a gauge used by Doust. We also consider the Lagrangian path-integrals in Minkowski space for gauges with a residual gauge-invariance. We point out the necessity of inclusion of an e-term (even) in theformal treatments, without which one may reach incorrect conclusions. We, further, point out that the e-termcan contribute to the BRST WT-identities in a non-trivial way (even as e → 0). We point out that these contributions lead to additional constraints on Green's function that arenot normally taken into account in the BRST formalism that ignores the e-term, and that they are characteristic of the way the singularities in propagators are handled. We argue that a prescription, in general, will require renormalization; if at all it is to be viable.

ADDITIONAL CONSIDERATIONS IN THE DEFINITION AND RENORMALIZATION OF NON-COVARIANT GAUGES

In this work, we pursue further consequences of a general formalism for non-covariant gauges developed in an earlier work (hep-th/0205042). We carry out further analysis of the additional restrictions on renormalizations noted in that work. We use the example of the axial gauge A3 = 0. We find that if multiplicative renormalization together with ghost-decoupling is to hold, the "prescription-term" (that defines a prescription) cannot be chosen arbitrarily but has to satisfy certain nontrivial conditions (over and above those implied by the validity of power counting) arising from the WT identitites associated with the residual gauge invariance. We also give a restricted class of solutions to these conditions.

SOME OBSERVATIONS ON NONCOVARIANT GAUGES AND THE ε-TERM

We consider the Lagrangian path-integrals in Minkowski space for gauges with a residual gauge-invariance. From rather elementary considerations, we demonstrate the necessity of inclusion of an ε-term (even) in the formal treatments, without which one may reach incorrect conclusions. We show, further, that the ε-term can contribute to the BRST WT-identities in a nontrivial way (even as ε → 0). We also show that the (expectation value of the) correct ε-term satisfies an algebraic condition. We show by considering (a commonly used) example of a simple local quadratic ε-term, that lead to additional constraints on Green's function that are not normally taken into account in the BRST formalism which ignores the ε-term, and that they are characteristic of the way the singularities in propagators are handled. We argue that for a subclass of these gauges, the Minkowski path-integral could not be obtained by a Wick rotation from a Euclidean path-integral.

Remarks on the reduced phase space of -dimensional gravity on a torus in the Ashtekar formulation

We examine the reduced phase space of the Barbero-Varadarajan solutions of the Ashtekar formulation of (2 + 1)-dimensional general relativity on a torus. We show that it is a finite-dimensional space due to the existence of an infinite-dimensional residual gauge invariance which reduces the infinite-dimensional space of solutions to a finite-dimensional space of gauge-inequivalent solutions. This is in agreement with general arguments which imply that the number of physical degrees of freedom for (2 + 1)-dimensional Ashtekar gravity on a torus is finite.

Gauge theory description of D-brane black holes: Emergence of the effective SCFT and Hawking radiation

We study the hypermultiplet moduli space of an N = 4, U( Q 1) × U( Q 5) gauge theory in 1 + 1 dimensions to extract the effective SCFT description of near extremal 5-dimensional black holes modelled by a collection of D1- and D5-branes. On the moduli space, excitations with fractional momenta arise due to a residual discrete gauge invariance. It is argued that, in the infra-red, the lowest energy excitations are described by an effective c = 6, N = 4 SCFT on T 4, also valid in the large black hole regime. The “effective string tension” is obtained using T-duality covariance. While at the microscopic level, minimal scalars do not couple to (1, 5) strings, in the effective theory a coupling is induced by (1, 1) and (5, 5) strings, leading to Hawking radiation. These considerations imply that, at least for such black holes, the calculation of the Hawking decay rate for minimal scalars has a sound foundation in string theory and statistical mechanics and, hence, there is no information loss.

Hamiltonian lattice gauge theories and the role of longitudinal modes

The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. The role of the longitudinal gluon is discussed in both Lagrangian and Hamiltonian lattice gauge theories.

Residual gauge invariance of Hamiltonian lattice gauge theories

The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegenbauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically.

Supersymmetric S-covariant R ξ gauge

We present here a supersymmetric extension of a class of non-linear gauges which respect the residual gauge invariance of spontaneously broken gauge theories.

Residual invariance in axial gauge

There remains a residual gauge freedom after the axialgauge fixation. We investigate how gauge theories satisfy the residual gauge invariance. It is found that the generator of the residual gauge transformation sandwiched by eigenstates of the total Hamiltonian automatically vanishes. The «constraint» that the generator annihilates physical states does not work.

Remarks on the implementation of Gauss's law in theA0=0gauge

A naive implementation of the residual gauge invariance of (continuum) QED in the A = 0 gauge leads to charged-particle nonpropagation in space. It is shown that the Ward-Takahashi identities leading to this result are false. Rather, Gauss's law supplants these false identities, and implies that it is only the longitudinal modes of the Maxwell field that are rendered immobile by gauge invariance. Analogous results are conjectured to hold in quantum chromodynamics.