Gauge Mode Research Articles

Yet Another Lattice Formulation of 2D U(1) Chiral Gauge Theory via Bosonization

Abstract Recently, lattice formulations of Abelian chiral gauge theory in two dimensions have been devised on the basis of the Abelian bosonization. A salient feature of these 2D lattice formulations is that the gauge invariance is exactly preserved for anomaly-free theories and thus is completely free from the question of the gauge mode decoupling. In the present paper, we propose yet another lattice formulation sharing this desired property. A particularly unique point in our formulation is that the vertex operator of the dual scalar field, which carries the vector charge of the fermion and the “magnetic charge” in the bosonization, is represented by a “hole” excised from the lattice; this is the excision method formulated recently by Abe et al. in a somewhat different context.

Final report on key comparison APMP.M.P-K7.3 in hydraulic gauge pressure from 10 MPa to 100 MPa

Main textThis report describes the results of a key comparison among hydraulic high pressure standards that have been maintained by seven National Metrology Institutes (NMIs: NIMT, NMIJ/AIST, NPLI, RCM-LIPI, NMIM, VMI and NMLPHIL). This comparison was carried out during the period March 2016 to October 2017 within the framework of the Asia-Pacific Metrology Programme (APMP) in order to determine their degrees of equivalence in the pressure range from 10 MPa to 100 MPa, gauge mode. The pilot institute was the National Institute of Metrology (Thailand) (NIMT). All participating institutes used hydraulic pressure balance as their pressure standards. In order to ensure reliability, two high precision pressure transducers were used as the transfer standard. The sensing element of the transducers was a precision quartz crystal resonator attached to a small Bourdon tube. During the comparison, the transfer standard was calibrated at the pilot institute two times, before and after circulating the transfer standard to participants. From the two NIMT calibration results, the transfer standard was sufficiently stable to meet the requirements of the comparison. The long-term instability obtained from the two calibration results was taken into account as the uncertainty of the transfer standard for all participants. As the matter of fact NPL India and NMIM participated in this comparison as one of the linkage institutes and participating institutes, respectively. However, it was found later that the systems of hydraulic pressure balance reference standards used in this comparison were not functioning. Therefore, the comparison results were withdrawn. The degrees of equivalence of each national measurement standard were expressed quantitatively by deviations from the key comparison reference value of the corresponding CCM key comparison, CCM.P-K7 through the linkage institute, NMIJ/AIST. In conclusion, the hydraulic pressure standards in the range 10 MPa to 100 MPa, gauge mode of the five participating NMIs were found to be equivalent within their claimed uncertainties.To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database https://www.bipm.org/kcdb/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

SIM key comparison in pneumatic gauge pressure for high accuracy pressure balances up to 120 kPa (SIM.M.P-K6)

Main textThis report describes the results of a pneumatic pressure standards key comparison among eleven SIM National Metrology Institutes to determine their degree of equivalence in the pressure range from 10 kPa to 120 kPa in gauge mode. The pilot laboratory was the Centro Nacional de Metrología (CENAM, Mexico). All participating institutes used pneumatic pressure balances as their pressure standard. The transfer standard was a complete system including a pressure balance with a free-deformation piston-cylinder assembly and a set of masses. Eleven participants completed their measurements and reported the pressure-dependent effective areas of the transfer standard at specified pressures with the associated uncertainties. NRC/Canada and BSJ/Jamaica withdrew the comparison by not sending their measurements. To link the results of the nine laboratories that sent their results to the CCM.P- NIST, the USA provided the reference values. To evaluate the compatibility of the results of the participants their relative deviations from those obtained by NIST results were analyzed. The results of six participating NMIs agree with the NIST reference values within their expanded uncertainties (k = 2) in the entire pressure range from 10 kPa to 120 kPa according to the normalized error equation method.To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database https://www.bipm.org/kcdb/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Monopole fluctuation of the CMB and its gauge invariance

The standard theoretical description $\mathrm{\ensuremath{\Theta}}(\stackrel{^}{n})$ of the observed cosmic microwave background (CMB) temperature anisotropies is gauge dependent. It is, however, well known that the gauge mode is limited to the monopole and that the higher angular multipoles ${\mathrm{\ensuremath{\Theta}}}_{l}$ ($l\ensuremath{\ge}1$) are gauge invariant. Several attempts have been made in the past to properly define the monopole fluctuation, but the resulting values of the monopole power ${C}_{0}$ are infinite due to the infrared divergences. The infrared divergences arise from the contribution of the uniform gravitational potential to the monopole fluctuation, in violation of the equivalence principle. Here we present the gauge-invariant theoretical description of the observed CMB temperature anisotropies and compute the monopole power ${C}_{0}=1.66\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ in a $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. While the gauge dependence in the standard calculations originates from the ambiguity in defining the hypersurface for the background CMB temperature $\overline{T}$ today, it is in fact well defined and one of the fundamental cosmological parameters. We argue that once the cosmological parameters are chosen, the monopole fluctuation can be unambiguously inferred from the angle average of the observed CMB temperature, making it a model-dependent ``observable.'' Adopting simple approximations for the anisotropy formation, we derive a gauge-invariant analytical expression for the observed CMB temperature anisotropies to study the CMB monopole fluctuation and the cancellation of the uniform gravitational potential contributions on large scales.

Modular Bosonic Subsystem Codes.

We introduce a framework to decompose a bosonic mode into two virtual subsystems-a logical qubit and a gauge mode. This framework allows the entire toolkit of qubit-based quantum information to be applied in the continuous-variable setting. We give a detailed example based on a modular decomposition of the position basis and apply it in two situations. First, we decompose Gottesman-Kitaev-Preskill grid states and find that the encoded logical state can be damaged due to entanglement with the gauge mode. Second, we identify and disentangle qubit cluster states hidden inside of Gaussian continuous-variable cluster states.

Supplementary pressure comparison from 10 MPa to 100 MPa in hydraulic media at gauge mode

The regional supplementary comparison EURAMET.M.P-S13 for pressure measurements in liquid media from 10 MPa to 100 MPa was piloted by the TÜBİTAK UME Pressure Laboratory, Turkey. The transfer standard was a digital pressure gauge, serial number 116321, manufactured by Paroscientific Inc. Eighteen laboratories participated in this comparison. Fourteen laboratories are from EURAMET region; namely UME, MKEH, BoM, DPM, DMDM, MBM, GUM, IMT, HMI/FSB-LPM, VSL, VTT MIKES, FORCE Technology, IMBIH, NSAI NML. VMC is from COOMET and QAF, EMI, SASO NMCC are from GULFMET region.Main textTo reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Supplementary pressure comparison from (0.7 to 7) MPa in gas media at gauge mode

This report gives the results of a comparison of pressure standards of three National Metrology institutes in the range of 0.7 MPa to 7 MPa. This comparison was piloted by UME and was carried out from February 2017 to March 2019. This work is a part of the GULFMET project and is registered as a supplementary comparison GULFMET.M.P-S1. The transfer standard used was a digital pressure gauge, model 745-1K, serial number 114944, manufactured by Paroscientific Inc, with a resolution of 1 hPa. The reference values have been determined from the weighted mean of the deviations which is a measurement error of the test instrument reported by the participants for each specified pressure.Main textTo reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Final report on supplementary comparison APMP.M.P-S9 in gas gauge pressure from 2 MPa to 20 MPa

This report describes the results of a supplementary comparison of gas pressure standards at three National Metrology Institutes - National Institute of Metrology (Thailand) (NIMT), Physikalisch-Technische Bundesanstalt (PTB) and National Metrology Laboratory of the Philippines (NMLPHIL) - carried out within the framework of Asia-Pacific Metrology Programme (APMP) in order to determine their degrees of equivalence at pressures in the range from 2 MPa to 20 MPa for gauge mode. The pilot institute was NIMT. The measurements were carried out from February 2016 to July 2016. All participating institutes used pressure balances as their pressure standards. A reference pressure monitor was used as a transfer standard. Characteristics of the transfer standard were evaluated at the pilot institute and then used for uncertainty estimations. After completing the comparison measurements, the transfer standard showed a less stable behaviour than expected, resulting in a significant contribution to the uncertainties of the results. The degrees of equivalence that were evaluated in terms of differences of the participant's results and the comparison reference values divided by their expanded uncertainties (k=2) are all within the unity. This demonstrates equivalence of the compared standards on the uncertainty level, which is unfortunately dominated by the uncertainty of the transfer standard.Main textTo reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Scalar-metric-affine theories: Can we get ghost-free theories from symmetry?

We reveal the existence of a certain hidden symmetry in general ghost-free scalar-tensor theories which can only be seen when generalizing the geometry of the spacetime from Riemannian. For this purpose, we study scalar-tensor theories in the metric-affine (Palatini) formalism of gravity, which we call scalar-metric-affine theories for short, where the metric and the connection are independent. We show that the projective symmetry, a local symmetry under a shift of the connection, can provide a ghost-free structure of scalar-metric-affine theories. The ghostly sector of the second-order derivative of the scalar is absorbed into the projective gauge mode when the unitary gauge can be imposed. Incidentally, the connection does not have the kinetic term in these theories and then it is just an auxiliary field. We can thus (at least in principle) integrate the connection out and obtain a form of scalar-tensor theories in the Riemannian geometry. The projective symmetry then hides in the ghost-free scalar-tensor theories. As an explicit example, we show the relationship between the quadratic order scalar-metric-affine theory and the quadratic U-degenerate theory. The explicit correspondence between the metric-affine (Palatini) formalism and the metric one could be also useful for analyzing phenomenology such as inflation.

Gravitational dressing of 3D conformal Galileon

Could a conformal Galileon be describing a gauge mode of a broader diffeomorphism invariant theory? We answer this question affirmatively in 3D by using a coset construction for a nonlinearly realized conformal symmetry. In particular, we show that the conformal Galileon emerges as a Stückelberg field of a local Weyl symmetry. The coset construction gives us a diffeomorphism and Weyl invariant 3D theory containing first, second, and third powers of the curvatures, their couplings to certain tensors made of the Galileon and its derivatives, and the conformal Galileon terms. In a theory with a boundary additional surface terms are required for the boundary Weyl anomaly cancellation. When gravity is switched off, the theory reduces to the conformal Galileon plus a boundary term. On the other hand, it reduces to a generalization of “New Massive Gravity” by A. Sinha, if the Weyl symmetry is gauge-fixed in a particular way. Last but not least, there exists a parameter space for which the theory has no propagating ghosts. Thus we show by an explicit construction that “New Massive Gravity” (and its generalization) is a unique scalar ghost free low energy effective field theory non-linearly realizing conformal symmetry in 3D.

Development and characterisation of a low pressure transfer standard in the range 1 Pa to 10 kPa

We describe a transfer standard for low absolute and gauge pressure in the range 1 Pa to 10 kPa. This transfer standard is composed of three differential capacitance diaphragm gauges (CDGs) of full-scale 130 Pa, 1.3 kPa and 13 kPa respectively and one absolute 130 kPa resonant silicon gauge (RSG). The objective for the relative uncertainty contribution (<em>k</em>=1) of this standard during a comparison is a few tens of ppm at 10 kPa to a few hundred ppm at 1 Pa. It relies on a good long-term stability of the calibration slope of the RSG used, between 5 kPa and 10 kPa, disseminated to CDGs in absolute mode and subsequently in gauge mode. The methods to assess such uncertainty and the preliminary characterisation of the transfer standard are presented.

Final report on comparison of hydraulic pressure balance effective area determination in the range up to 80 MPa

Bilateral comparison was organized between the laboratory for process measurement of the Croatian Metrology Institute (HMI/FSB-LPM) and the pressure laboratory of the Directorate of Measures and Precious Metals of the Republic of Serbia (DMDM). Laboratory for process measurement of HMI acted as the pilot laboratory. The aim of the comparison was to evaluate the degree of equivalence in the determination of effective area and elastic distortion coefficient, considering respective uncertainties of the two laboratories. Measurements were done on the pressure balance in gauge mode, with oil as transmitting medium, in the gauge pressure range 10–80 MPa. The results of the comparison successfully demonstrated that the hydraulic gauge pressure standards are equivalent within their claimed uncertainties.Main textTo reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Higher-spin Witten effect and two-dimensional fracton phases

We study the role of "$\theta$ terms" in the action for three-dimensional $U(1)$ symmetric tensor gauge theories, describing quantum phases of matter hosting gapless higher-spin gauge modes and gapped subdimensional particle excitations, such as fractons. In Maxwell theory, the $\theta$ term is a total derivative which has no effect on the gapless photon, but has two important, closely related consequences: attaching electric charge to magnetic monopoles (the Witten effect) and leading to a Chern-Simons theory on the boundary. We will find that a similar story holds in the higher-spin $U(1)$ gauge theories. These theories admit generalized $\theta$ terms which have no effect on the gapless gauge mode, but which bind together electric and magnetic charges (both of which are generally subdimensional) in specific combinations, in a higher-spin manifestation of the Witten effect. We derive the corresponding Witten quantization condition. We find that, as in Maxwell theory, imposing time-reversal invariance restricts $\theta$ to certain discrete values. We also find that these new $\theta$ terms imply a non-trivial boundary structure. The boundaries host fracton excitations coupled to a tensor $U(1)$ gauge field with a Chern-Simons-like action, in both chiral and non-chiral varieties. These boundary theories open a door to the study of $U(1)$ fracton phases described by tensor Chern-Simons theories, not only on boundaries of three-dimensional systems, but also in strictly two spatial dimensions. We explicitly work through three examples of bulk and boundary theories, the principles of which can be readily extended to arbitrary higher-spin theories.

Final report on supplementary comparison APMP.M.P-S7.TRI in hydraulic gauge pressure from 40 MPa to 200 MPa

This report describes the results of a supplementary comparison of hydraulic high-pressure standards at three national metrology institutes (NMIs); National Metrology Institute of Japan, AIST (NMIJ/AIST), National Institute of Standards and Technology (NIST), USA and National Institute for Standards (NIS), Egypt, which was carried out at NIST during the period May 2001 to September 2001 within the framework of the Asia-Pacific Metrology Programme (APMP) in order to evaluate their degrees of equivalence at pressures in the range 40 MPa to 200 MPa for gauge mode. The pilot institute was NMIJ/AIST. Three working pressure standards from the institutes, in the form of piston-cylinder assemblies, were used for the comparison. The comparison and calculation methods used are discussed in this report. From the cross-float measurements, the differences between the working pressure standards of each institute were examined through an evaluation of the effective area of each piston-cylinder assembly with its uncertainty. From the comparison results, it was revealed that the values claimed by the participating institutes, NMIJ, NIST, and NIS, agree within the expanded (k = 2) uncertainties. The hydraulic pressure standards in the range 40 MPa to 200 MPa for gauge mode of the three participating NMIs were found to be equivalent within their claimed uncertainties.Main textTo reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Final report on supplementary comparison APMP.M.P-S6 in gas gauge pressure from 10 MPa to 100 MPa

A supplementary comparison of gas high-pressure standards was conducted between the National Metrology Institute of Japan (NMIJ/AIST) and the National Institute of Standards and Technology (NIST), within the framework of the Asia-Pacific Metrology Programme (APMP), in order to determine their degrees of equivalence in the pressure range from 10 MPa to 100 MPa in gauge mode. The pilot institute was NMIJ/AIST. The measurements were carried out from July 2014 to October 2014. Both participating institutes used pressure balances as their pressure standards. Different gases were used for the pressure medium: NMIJ/AIST used Nitrogen, while NIST used Helium. A set of two pressure monitors was used as the transfer standard. The pressure monitors were found sufficiently stable during the measurements. Characteristics of the pressure monitors were evaluated at the pilot institute, and then used for data corrections and uncertainty estimations. In particular, the effect of the gas medium on the pressure monitors was found to be significant, and then all the measurement data were corrected to those with Nitrogen. The degrees of equivalence between the two institutes were evaluated by the relative differences of the participant's results and their associated expanded (k = 2) uncertainties. The gas pressure standards in the range 10 MPa to 100 MPa for gauge mode of the two participating institutes were found to be equivalent within their claimed uncertainties.Main textTo reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Comparison in gas media (absolute and gauge mode)in the range from 25 kPa TO 200 kPa (EURAMET.M.P-K8)

It was decided at the EURAMET TC-M meeting in Torino in 2006 to realize a comparison in gauge and absolute pressure up to 200 kPa as it would allow a link to the CCM.P-K6 and CCM.P-K2 comparisons to be established. This project interested a lot of laboratories from the beginning with 23 participants, 22 of which have submitted results. The circulation of the transfer standard began in July 2009 and lasted until January 2012. No major problems occurred during the transport.The measurand of the comparison is the effective area of a piston-cylinder determined in gauge and absolute pressure from 25 kPa to 200 kPa with pressure steps of 25 kPa. The transfer standard is a gas lubricated tungsten carbide piston-cylinder with an effective area of ~9.8 cm2, fabricated by DH Instruments and compatible with a PG-7601 pressure balance. Some participants used their own pressure balance while a pressure balance with a reference vacuum sensor has been circulated for the participants not equipped with this system.One participant (SMU, Slovakia) has never provided the measurement results and another participant (FORCE Technology, Denmark) submitted a revised set of measurement results after the pilot laboratory mentioned that the equivalence was not met.After the determination of the reference value, all the 22 participants who delivered the results in gauge pressure demonstrated equivalence respective to the reference value on most of the range. In absolute pressure the equivalence is demonstrated, for all nominal pressures, by all 17 participants who submitted results.The comparison is linked to the CCM.P-K6 for gauge pressure and to CCM.P-K2 for absolute pressure. The link does not strongly affect the equivalence of the results and an excellent degree of equivalence is achieved in gauge and absolute pressure.Main textTo reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Leggett Modes and the Anderson-Higgs Mechanism in Superconductors without Inversion Symmetry

We develop a microscopic and gauge-invariant theory for collective modes resulting from the phase of the superconducting order parameter in noncentrosymmetric superconductors. Considering various crystal symmetries, we derive the corresponding gauge mode ω_{G}(q) and find, in particular, new Leggett modes ω_{L}(q) with characteristic properties that are unique to noncentrosymmetric superconductors. We calculate their mass and dispersion that reflect the underlying spin-orbit coupling and thus the balance between triplet and singlet superconductivity occurring simultaneously. Finally, we demonstrate the role of the Anderson-Higgs mechanism: while the long-range Coulomb interaction shifts ω_{G}(q) to the condensate plasma mode ω_{P}(q), it leaves the mass Λ_{0} of the new Leggett mode unaffected and only slightly modifies its dispersion.

Final report on key comparison APMP.M.P-K13 in hydraulic gauge pressure from 50 MPa to 500 MPa

This report describes the results of a key comparison of hydraulic high-pressure standards at nine National Metrology Institutes (NMIs: NMIJ/AIST, NPLI, NMC/A*STAR, NIMT, NMIA, NIM, CMS/ITRI, KIM-LIPI, and KRISS) within the framework of the Asia-Pacific Metrology Programme (APMP) in order to determine their degrees of equivalence in the pressure range from 50 MPa to 500 MPa in gauge mode. The pilot institute was the National Metrology Institute of Japan (NMIJ/AIST). All participating institutes used hydraulic pressure balances as their pressure standards. A set of pressure balance with a free-deformational piston-cylinder assembly was used as the transfer standard. Three piston-cylinder assemblies, only one at a time, were used to complete the measurements in the period from November 2010 to January 2013. Ten participants completed their measurements and reported the pressure-dependent effective areas of the transfer standard at specified pressures with the associated uncertainties. Since one of the participants withdrew its results, the measurement results of the nine participants were finally compared. The results were linked to the CCM.P-K13 reference values through the results of two linking laboratories, NMIJ/AIST and NPLI. The degrees of equivalence were evaluated by the relative deviations of the participants' results from the CCM.P-K13 key comparison reference values, and their associated combined expanded (k=2) uncertainties. The results of all the nine participating NMIs agree with the CCM.P-K13 reference values within their expanded (k=2) uncertainties in the entire pressure range from 50 MPa to 500 MPa. Main text.To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Final report on EURAMET.M.P-K4.2010: Key and supplementary comparison of national pressure standards in the range 1 Pa to 15 kPa of absolute and gauge pressure

This report describes a EURAMET comparison of five European National Metrology Institutes in low gauge and absolute pressure in gas (nitrogen), denoted as EURAMET.M.P-K4.2010. Its main intention is to state equivalence of the pressure standards, in particular those based on the technology of force-balanced piston gauges such as e.g. FRS by Furness Controls, UK and FPG8601 by DHI-Fluke, USA. It covers the range from 1 Pa to 15 kPa, both gauge and absolute. The comparison in absolute mode serves as a EURAMET Key Comparison which can be linked to CCM.P-K4 and CCM.P-K2 via PTB. The comparison in gauge mode is a supplementary comparison.The comparison was carried out from September 2008 till October 2012. The participating laboratories were the following: CMI, INRIM, LNE, MIKES, PTB-Berlin (absolute pressure 1 kPa and below) and PTB-Braunschweig (absolute pressure 1 kPa and above and gauge pressure). CMI was the pilot laboratory and provided a transfer standard for the comparison. This transfer standard was also the laboratory standard of CMI at the same time, which resulted in a unique and logistically difficult star comparison.Both in gauge and absolute pressures all the participating institutes successfully proved their equivalence with respect to the reference value and all also proved mutual bilateral equivalences in all the points. All the participating laboratories are also equivalent with the reference values of CCM.P-K4 and CCM.P-K2 in the relevant points. The comparison also proved the ability of FPG8601 to serve as a transfer standard.Main text.To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Fully non-linear and exact perturbations of the Friedmann world model

In 1988 Bardeen has suggested a pragmatic formulation of cosmological perturbation theory which is powerful in practice to employ various fundamental gauge conditions easily depending on the character of the problem. The perturbation equations are presented without fixing the temporal gauge condition and are arranged so that one can easily impose fundamental gauge conditions by simply setting one of the perturbation variables in the equations equal to zero. In this way one can use the gauge degrees of freedom as an advantage in handling problems. Except for the synchronous gauge condition, all the other fundamental gauge conditions completely fix the gauge mode, and consequently, each variable in such a gauge has a unique gauge invariant counterpart, so that we can identify the variable as the gauge-invariant one. Here, we extend Bardeen's linear formulation to fully nonlinear order in perturbations, with the gauge advantage kept intact. Derived equations are exact, and from these we can easily expand to higher order perturbations in a gauge-ready form. We consider scalar- and vector-type perturbations of an ideal fluid in a flat background; we also present the multiple components of ideal fluid case. As applications we present fully nonlinear density and velocity perturbation equations in Einstein's gravity in the zero-pressure medium, vorticity generation from pure scalar-type perturbation, and fluid formulation of a minimally coupled scalar field, all in the comoving gauge. We also present the equation of gravitational waves generated from pure scalar- and vector-type perturbations.