Gauge Invariant Field Research Articles

Gauge-invariant quantum fields

Gauge-invariant quantum fields are constructed in an Abelian power-counting renormalizable gauge theory with both scalar, vector and fermionic matter content. This extends previous results already obtained for the gauge-invariant description of the Higgs mode via a propagating gauge-invariant field. The renormalization of the model is studied in the Algebraic Renormalization approach. The decomposition of Slavnov–Taylor identities into separately invariant sectors is analyzed. We also comment on some non-renormalizable extensions of the model whose 1-PI Green’s functions are the flows of certain differential equations of the homogeneous Euler type, exactly resumming the dependence on a certain set of dim. 6 and dim. 8 derivative operators. The latter are identified uniquely by the condition that they span the mass and kinetic terms in the gauge-invariant dynamical fields. The construction can be extended to non-Abelian gauge groups.

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

Order parameters for gauge invariant condensation far from equilibrium

Nuclear collisions at sufficiently high energies are expected to produce far-from-equilibrium matter with a high density of gluons at early times. We show gauge condensation, which occurs as a consequence of the large density of gluons. To identify this condensation phenomenon, we construct two local gauge invariant observables that carry the macroscopic zero mode of the gauge condensate. The first order parameter for gauge condensation investigated here is the correlator of the spatial Polyakov loop. We also consider, for the first time, the correlator of the gauge invariant scalar field, associated with the exponent of the Polyakov loop. Using real-time lattice simulations of classical-statistical SU(2) gauge theory, we find gauge condensation on a system-size-dependent timescale tcond∼L1/ζ with a universal scaling exponent ζ. Furthermore, we suggest an effective theory formulation describing the dynamics using one of the order parameters identified. The formation of a condensate at early times may have intriguing implications for the early stages in heavy-ion collisions. Published by the American Physical Society 2024

New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space

We present new infinitesimal ‘conformal-like’ symmetries for the field equations of strictly massless spin-s ≥ 3/2 totally symmetric tensor-spinors (i.e. gauge potentials) on 4-dimensional de Sitter spacetime (dS4). The corresponding symmetry transformations are generated by the five closed conformal Killing vectors of dS4, but they are not conventional conformal transformations. We show that the algebra generated by the ten de Sitter (dS) symmetries and the five conformal-like symmetries closes on the conformal-like algebra so(2, 4) up to gauge transformations of the gauge potentials. The transformations of the gauge-invariant field strength tensor-spinors under the conformal-like symmetries are given by the product of γ5 times a usual infinitesimal conformal transformation of the field strengths. Furthermore, we demonstrate that the two sets of physical mode solutions, corresponding to the two helicities ±s of the strictly massless theories, form a direct sum of Unitary Irreducible Representations (UIRs) of the conformal-like algebra. We also fill a gap in the literature by explaining how these physical modes form a direct sum of Discrete Series UIRs of the dS algebra so(1, 4).

Off-shell fields and conserved currents

We study interactions of higher-spin massless fields φ with conserved currents multilinear in the off-shell matter fields ϕ. Specifically, we focus on the 3d case where a slight modification of the σ−-cohomology technique developed earlier is directly applicable to control nontriviality of the interaction vertices at the convention that the vertices removable by a local field redefinition of a higher-spin field or having schematic form F(φ)G(ϕ), where F(φ) is a gauge invariant field strength of a free higher-spin field, are called deformationally trivial. It is demonstrated how the σ−-cohomology approach can be applied to the analysis of nonlinear vertices. Generally, deformationally trivial vertices are not σ−-closed while the deformationally non-trivial ones must be in H(σ−). It is shown that, at least in the 3d case, the relevant cohomology group H1(σ−)=0 and, hence, no deformationally non-trivial off-shell vertices exist. On the other hand, there exists an infinite class of deformationally trivial vertices, that includes the vertex recently proposed for spin three. Our analysis goes beyond the higher-spin vertices allowing to show that, at least in three dimensions, nonlinear combinations of the off-shell scalar fields and their derivatives cannot obey non-trivial equations.

On the direct quantization of Proca gauge invariant field

In this study, we use the generalized integration constants method “GCI” [1,2] to quantize two fields with constraints. Indeed, Proca field, that describes a massive boson is studied first, based on a Lagrangian without gauge symmetry, in order to determine the necessary brackets for its canonical quantization. Then, another gauge invariant version of this field, obtained by adding an additional scalar field in the mass term, is quantized after fixing this gauge.”

SO(1,3) Yang-Mills solutions on Minkowski space via cosets

We present a novel family of Yang-Mills solutions, with gauge group SO(1,3), on Minkowski space that are geometrically distinguished into two classes, viz. interior and exterior of the lightcone. We achieve this by foliating the former with SO(1,3)/SO(3) cosets and the latter with SO(1,3)/SO(1,2) cosets and analytically solving the Yang-Mills equation of an SO(1,3)-invariant gauge field. The resulting fields and their stress-energy tensor, when translated to the Minkowski space, diverge at the lightcone, but we demonstrate how this stress-energy tensor could be regularised due to its unique algebraic structure.

Purely virtual extension of quantum field theory for gauge invariant fields: quantum gravity

Quantum gravity is extended to include purely virtual “cloud sectors”, which allow us to define a complete set of point-dependent observables, including a gauge invariant metric and gauge invariant matter fields, and calculate their off-shell correlation functions perturbatively. The ordinary on-shell correlation functions and the S matrix elements are unaffected. Each extra sector is made of a cloud field, its anticommuting partner, a “cloud-fixing” function and a cloud Faddeev-Popov determinant. The additional fields are purely virtual, to ensure that no ghosts propagate. The extension is unitary. In particular, the off-shell, diagrammatic version of the optical theorem holds. The one-loop two-point functions of dressed scalars, vectors and gravitons are calculated. Their absorptive parts are positive, cloud independent and gauge independent, while they are unphysical if non purely virtual clouds are used. We illustrate the differences between our approach to the problem of finding a complete set of observables in quantum gravity and other approaches available in the literature.

The Gauge-Relativity of Quantum Light, Matter, and Information

We describe the physical relativity of light and matter quantum subsystems, their correlations, and energy exchanges. We examine the most commonly adopted definitions of atoms and photons, noting the significant difference in their localisation properties when expressed in terms of primitive manifestly gauge-invariant and local fields. As a result, different behaviours for entanglement generation and energy exchange occur for different definitions. We explore such differences in detail using toy models of a single photonic mode interacting with one and two dipoles.

A massive gauge theory à la Utiyama

Utiyama’s method is a deductive approach of building gauge theories for semi-simple groups of local transformations, including the Abelian U(1) case, the non-Abelian SU(N) group, and the gravitational interaction. Gauge theories à la Utiyama typically predict a massless gauge potential. This work brings a mass generation mechanism and Utiyama’s method together thus giving mass to the interaction boson without breaking the gauge symmetry. Herein we devote our attention to the Abelian case. Two gauge potentials are introduced: a vetor field A μ and a scalar field B. The associated gauge-invariant field strengths F μ ν and G μ are built from Utiyama’s technique. Gauge invariance requirement upon the total Lagrangian (including matter fields and gauge fields) yields the conserved currents. Finally, we study the simplest type of Lagrangian involving the field strengths and obtain the related field equation. By imposing appropriate constraints on this particular example, Stueckelberg model is recovered.

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.

Black hole perturbations in Maxwell-Horndeski theories

We study the linear stability of black holes in Maxwell-Horndeski theories where a $U(1)$ gauge-invariant vector field is coupled to a scalar field with the Lagrangian of full Horndeski theories. The perturbations on a static and spherically symmetric background can be decomposed into odd- and even-parity modes under the expansion of spherical harmonics with multipoles $l$. For $l\ensuremath{\ge}2$, the odd-parity sector contains two propagating degrees of freedom associated with the gravitational and vector field perturbations. In the even-parity sector, there are three dynamical perturbations arising from the scalar field besides the gravitational and vector field perturbations. For these five propagating degrees of freedom, we derive conditions for the absence of ghost/Laplacian stabilities along the radial and angular directions. We also discuss the stability of black holes for $l=0$ and $l=1$, in which case no additional conditions are imposed to those obtained for $l\ensuremath{\ge}2$. We apply our general results to Einstein-Maxwell-dilaton-Gauss-Bonnet theory and Einstein-Born-Infeld-dilaton gravity and show that hairy black hole solutions present in these theories can be consistent with all the linear stability conditions. In regularized four-dimensional Einstein-Gauss-Bonnet gravity with a Maxwell field, however, exact charged black hole solutions known in the literature are prone to instabilities of even-parity perturbations besides a strong coupling problem with a vanishing kinetic term of the radion mode.

Flux-based three-dimensional electrodynamic modeling approach to superconducting circuits and materials

Modeling the behavior of superconducting electronic circuits containing Josephson junctions is crucial for the design of superconducting information processors and devices. In this paper, we introduce DEC-QED, a computational approach for modeling the electrodynamics of superconducting electronic circuits containing Josephson junctions in arbitrary three-dimensional electromagnetic environments. DEC-QED captures the nonlinear response and induced currents in BCS superconductors and accurately captures phenomena such as the Meissner effect, flux quantization, and Josephson effects. Using a spatial coarse-graining formulation based on discrete exterior calculus (DEC), DEC-QED can accurately simulate transient and long-time dynamics in superconductors. The expression of the entire electrodynamic problem in terms of the gauge-invariant flux field and charges makes the resulting classical field theory suitable for second quantization.

Renormalizable extension of the Abelian Higgs-Kibble model with a dimension-six operator

A deformation of the Abelian Higgs Kibble model induced by a dimension 6 derivative operator is studied. A novel differential equation is established fixing the dependence of the vertex functional on the coupling $z$ of the dim.6 operator in terms of amplitudes at $z = 0$ (those of the power-counting renormalizable Higgs-Kibble model). The latter equation holds in a formalism where the physical mode is described by a gauge-invariant field. The functional identities of the theory in this formalism are studied. In particular we show that the Slavnov-Taylor identities separately hold true at each order in the number of internal propagators of the gauge-invariant scalar. Despite being non-power-counting renormalizable, the model at $z \neq 0$ depends on a finite number of physical parameters.

Quantum Yang-Mills theory in de Sitter ambient space formalism

We present the quantum Yang-Mills theory in the four-dimensional de Sitter ambient space formalism. In accordance with the SU(3) gauge symmetry the interaction Lagrangian is formulated in terms of interacting color charged fields in curved space-time. The gauge-invariant field equations are obtained in an independent coordinate description, and their corresponding color conserved currents are computed. It is shown that the Faddeev-Popov ghost fields appear similarly to their Minkowskian counterparts. We obtain that the free ghost fields are massless minimally coupled scalar fields. The problems of the vacuum state, namely the breaking of de Sitter invariance, and the appearance of infrared divergence in its quantization procedure, are discussed. The existence of an axiomatic quantum Yang-Mills theory within the framework of the Krein space quantization is examined. The infrared divergence regularization of the interaction between the gauge vector fields and the ghost fields is studied in the one-loop approximation. Two different regularization methods are discussed: cut-off regularization and Krein space regularization. A mass term for the gauge vector fields is obtained, which may explain the mass gap and the color confinement problems at the quantum level in de Sitter background. The large curvature limit at the early universe or inflationary epoch is considered.

Double field theory as the double copy of Yang-Mills theory

We show that double field theory arises from the color-kinematic double copy of Yang-Mills theory. A precise double copy prescription for the Yang-Mills action at quadratic and cubic order is provided that yields the double field theory action in which the duality invariant dilaton has been integrated out. More precisely, at quadratic order this yields the gauge invariant double field theory, while at cubic order it yields the cubic double field theory action subject to a gauge condition that originates from Siegel gauge in string field theory.

Extended superconformal higher-spin gauge theories in four dimensions

Using the off-shell formulation for mathcal{N} = 2 conformal supergravity in four dimensions, we describe superconformal higher-spin multiplets of conserved currents in a curved background and present their associated unconstrained gauge prepotentials. The latter are used to construct locally superconformal chiral actions, which are demonstrated to be gauge invariant in arbitrary conformally flat backgrounds. The main mathcal{N} = 2 results are then generalised to the mathcal{N} -extended case. We also present the gauge-invariant field strengths for on-shell massless higher-spin mathcal{N} = 2 supermultiplets in anti-de Sitter space. These field strengths prove to furnish representations of the mathcal{N} = 2 superconformal group.

Reformulation of gauge theories in terms of gauge invariant fields

We present a reformulation of gauge theories in terms of gauge invariant fields. Focusing on abelian theories, we show that the gauge and matter covariant fields can be recombined to introduce new gauge invariant degrees of freedom. Starting from the (1+1) dimensional case on the lattice, with both periodic and open boundary conditions, we then generalize to higher dimensions and to the continuum limit. To show explicit and physically relevant examples of the reformulation, we apply it to the Hamiltonian of a single particle in a (static) magnetic field, to pure abelian lattice gauge theories, to the Lagrangian of quantum electrodynamics in (3+1) dimensions and to the Hamiltonian of the 2d and the 3d Hofstadter model. In the latter, we show that the particular construction used to eliminate the gauge covariant fields enters the definition of the magnetic Brillouin zone. Finally, we briefly comment on relevance of the presented reformulation to the study of interacting gauge theories.

Higher spin analogs of linearized topologically massive gravity and linearized new massive gravity

We suggest a new spin-4 self-dual model (parity singlet) and a new spin-4 parity doublet in $D=2+1$. They are of higher order in derivatives and are described by a totally symmetric rank-4 tensor without extra auxiliary fields. Despite the higher derivatives they are ghost free. We find gauge invariant field combinations which allow us to show that the canonical structure of the spin-4 (spin-3) models follows the same pattern of its spin-2 (spin-1) counterpart after field redefinitions. For $s=1$, 2, 3, 4, the spin-$s$ self-dual models of order $2s\ensuremath{-}1$ and the doublet models of order $2s$ can be written in terms of three gauge invariants. The cases $s=3$ and $s=4$ suggest a restricted conformal higher spin symmetry as a principle for defining linearized topologically massive gravity and linearized ``new massive gravity'' for arbitrary integer spins. A key role in our approach is played by the fact that the Cotton tensor in $D=2+1$ has only two independent components for any integer spin.

The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms

Here we perform the Kaluza–Klein dimensional reduction from D+1 to D dimensions of massless Lagrangians described by a symmetric rank-2 tensor and invariant under transverse differmorphisms (TDiff). They include the linearized Einstein–Hilbert theory, linearized unimodular gravity and scalar tensor models. We obtain simple expressions in terms of gauge invariant field combinations and show that unitarity is preserved in all cases. After fixing a gauge, the reduced model becomes a massive scalar tensor theory. We show that the diffeomorphism (Diff) symmetry, instead of TDiff, is a general feature of the massless sector of consistent massive scalar tensor models. We discuss some subtleties when eliminating Stückelberg fields directly at action level as gauge conditions. A non local connection between the massless sector of the scalar tensor theory and the pure tensor TDiff model leads to a parametrization of the non conserved source which naturally separates spin-0 and spin-2 contributions in the pure tensor theory. The case of curved backgrounds is also investigated. If we truncate the non minimal couplings to linear terms in the curvature, vector and scalar constraints require Einstein spaces as in the Diff and WTDiff (Weyl plus Diff) cases. We prove that our linearized massive scalar tensor models admit those curved background extensions.