Gauge Principle Research Articles

Consistent actions for massive particles interacting with electromagnetism and gravity

Consistent interactions with electromagnetism and gravity for mass m particles of any spin are obtained. This is done by finding interactions which preserve the covariantized massive gauge symmetry present in recently constructed massive particle actions. This gauge principle is sufficient for finding consistent completions of minimal as well as non-minimal couplings of any type. For spins s ≥ 3/2, consistency requires infinitely many interaction terms in the action, including arbitrarily high order derivatives of electromagnetic and gravitational curvatures, with correspondingly high powers of 1/m. These interactions may be formally resummed and expressed in terms of non-local operators. Finally, although the interactions appear non-local, evidence is presented for the existence of a field redefinition which makes the interacting action local. This work provides the first explicit realization of an exactly gauge invariant formulation of massive particles interacting with electromagnetism and gravity.

Note on the group of vertical diffeomorphisms of a principal bundle & its relation to the Frölicher-Nijenhuis bracket

The group of vertical diffeomorphisms of a principal bundle forms the action Lie groupoid associated to the bundle. The former is generated by the group of maps with value in the structure group, which is also the group of bisections of the groupoid. The corresponding Lie algebra of general vertical vector fields is generated by maps with value in the Lie algebra of the structure group. The bracket on these maps, induced by the bracket of vertical vector fields, is an “extended” bracket on gauge parameters: it has been introduced heuristically in physics, notably in the study of asymptotic symmetries of gravity. Seeing the set of Lie algebra-valued maps as sections of the action Lie algebroid associated to the bundle, the extended bracket is understood to be a Lie algebroid bracket on those sections.Here, we highlight that this bracket can also be seen to arise from the Frölicher-Nijenhuis bracket of vector-valued differential forms. The benefit of this viewpoint is to insert this extended bracket within the general framework of derivations of forms on a bundle. Identities relating it to the usual operations of Cartan calculus — inner product, exterior and (Nijenhuis-) Lie derivative — are immediately read as special cases of general results. We also consider the generalised gauge transformations induced by vertical diffeomorphisms, and discuss their peculiar features. In particular, locally, and contrary to standard gauge transformations arising from vertical bundle automorphisms, they are distinguishable from local gluings when iterated. Yet, the gauge principle still holds.

Spin Currents via the Gauge Principle for Meta-Generalized Gradient Exchange-Correlation Functionals.

The prominence of density functional theory in the field of electronic structure computation stems from its ability to usefully balance accuracy and computational effort. At the base of this ability is a functional of the electron density: the exchange-correlation energy. This functional satisfies known exact conditions that guide the derivation of approximations. The strongly constrained and appropriately normed (SCAN) approximation stands out as a successful, modern, example. In this Letter, we demonstrate how the SU(2) gauge invariance of the exchange-correlation functional in spin current density functional theory allows us to add an explicit dependence on spin currents in the SCAN functional (here called JSCAN)-and similar meta-generalized-gradient functional approximations-solely invoking first principles. In passing, a spin-current dependent generalization of the electron localization function (here called JELF) is also derived. The extended forms are implemented in a developer's version of the crystal23 program. Applications on molecules and materials confirm the practical relevance of the extensions.

Non-gravitational signals of dark energy under a gauge symmetry

We investigate non-gravitational signals of dark energy within the framework of gauge symmetry in the dark energy sector. Traditionally, dark energy has been primarily studied through gravitational effects within general relativity or its extensions. On the other hand, the gauge principles have played a central role in the standard model sector and dark matter sector. If the dark energy field operates under a gauge symmetry, it introduces the possibility of studying all major components of the present universe under the same gauge principle. This approach marks a significant shift from conventional methodologies, offering a new avenue to explore dark energy.

Baby Weight and Length Measurement System with Data Storage Using MySQL Database

Baby weight and length measurement system has been designed based on ultrasonic and load cell sensors with data storage using MySQL database and website interface. This research aims to produce a baby weight and length measurement system with microcontroller NodeMCU ESP32. The system is designed with an ultrasonic sensor HC-SR04 and four half-bridge load cells of 50 kg. The ultrasonic sensor works on the piezoelectric and inverse piezoelectric principles, while load cell sensors work on strain gauge principles. An ultrasonic sensor measures body length, while a load cell sensor measures body weight. According to the Ministry of Health of the Republic of Indonesia’s regulations, this system also has an LCD 20×4 to display measurement and nutritional status assessment results. The experiment used four doll objects with different lengths and weights. This research shows that the ultrasonic sensor HC-SR04 used in this research has an average error of 0.494% in length measurement. The load cell sensor and HX711 ADC used in this research has an average error of 0.949% in weight measurement. The designed system automatically assesses the nutritional status and stores the measurement result and nutritional status in the database to be displayed on the website.

Frequency–Redshift Relation of the Cosmic Microwave Background

We point out that a modified temperature–redshift relation (T-z relation) of the cosmic microwave background (CMB) cannot be deduced by any observational method that appeals to an a priori thermalisation to the CMB temperature T of the excited states in a probe environment of independently determined redshift z. For example, this applies to quasar-light absorption by a damped Lyman-alpha system due to atomic as well as ionic fine-splitting transitions or molecular rotational bands. Similarly, the thermal Sunyaev-Zel’dovich (thSZ) effect cannot be used to extract the CMB’s T-z relation. This is because the relative line strengths between ground and excited states in the former and the CMB spectral distortion in the latter case both depend, apart from environment-specific normalisations, solely on the dimensionless spectral variable x=hνkBT. Since the literature on extractions of the CMB’s T-z relation always assumes (i) ν(z)=(1+z)ν(z=0), where ν(z=0) is the observed frequency in the heliocentric rest frame, the finding (ii) T(z)=(1+z)T(z=0) just confirms the expected blackbody nature of the interacting CMB at z>0. In contrast to the emission of isolated, directed radiation, whose frequency–redshift relation (ν-z relation) is subject to (i), a non-conventional ν-z relation ν(z)=f(z)ν(z=0) of pure, isotropic blackbody radiation, subject to adiabatically slow cosmic expansion, necessarily has to follow that of the T-z relation T(z)=f(z)T(z=0) and vice versa. In general, the function f(z) is determined by the energy conservation of the CMB fluid in a Friedmann–Lemaitre–Robertson–Walker universe. If the pure CMB is subject to an SU(2) rather than a U(1) gauge principle, then f(z)=1/41/3(1+z) for z≫1, and f(z) is non-linear for z∼1.

Momentum gauge fields from curved momentum space through Kaluza–Klein reduction

In this work we investigate the relation between curved momentum space and momentum-dependent gauge fields. While the former is a classic idea that has been shown to be tied to minimal-length models, the latter constitutes a relatively recent development in quantum gravity phenomenology. In particular, the gauge principle in momentum space amounts to a modification of the position operator of the form akin to a gauge-covariant derivative in momentum space according to the minimal coupling prescription. Here, we derive both effects from a Kaluza–Klein reduction of a higher-dimensional geometry exhibiting curvature in momentum space. The interplay of the emerging gauge fields as well as the remaining curved momentum space lead to modifications of the Heisenberg algebra. While the gauge fields imply Moyal-type noncommutativity dependent on the analogue field strength tensor, the dimensionally reduced curved momentum space geometry translates to a Snyder-type noncommutative geometry.

Cosmological Parameters from Planck Data in SU(2)CMB, Their Local ΛCDM Values, and the Modified Photon Boltzmann Equation

AbstractA review of the spatially flat cosmological model SU(2)CMB, minimally induced by the postulate that the cosmic microwave background (CMB) is subject to an SU(2) rather than a U(1) gauge principle, is given. Cosmological parameter values, which are determined from the Planck CMB power spectra at small angular scales, are compared to their values in spatially flat ΛCDM from both local and global extractions. As a global model SU(2)CMB leans toward local ΛCDM cosmology and is in tension with some global ΛCDM parameter values. Spectral antiscreening / screening effects in SU(2)CMB radiance are presented within the Rayleigh– Jeans regime in dependence on temperature and frequency. Such radiance anomalies can cause CMB large‐angle anomalies. Therefore, it is pointed out how SU(2)CMB modifies the Boltzmann equation for the perturbations of the photon phase space distribution at low redshift and why this requires to the solve the ℓ‐hierarchy on a comoving momentum grid (q‐grid) for all z.

Gauge-invariant theory of truncated quantum light-matter interactions in arbitrary media

The loss of gauge invariance in models of light-matter interaction which arises from material and photonic space truncation can pose significant challenges to conventional quantum optical models when matter and light strongly hybridize. In structured photonic environments, necessary in practice to achieve strong light-matter coupling, a rigorous model of field quantization within the medium is also needed. Here we use the framework of macroscopic QED by quantizing the fields in an arbitrary material system, with a spatially dependent dispersive and absorptive dielectric, starting from a fundamental light-matter action. We truncate the material and mode degrees of freedom while respecting the gauge principle by imposing a partial gauge-fixing constraint during canonical quantization, which admits a large number of gauges including the Coulomb and multipolar gauges commonly used in quantum optics. We also consider gauge conditions with explicit time dependence, enabling us to unambiguously introduce additional phenomenologically time-dependent light-matter interactions in any gauge. Our results allow one to derive rigorous nonrelativistic models of ultrastrong light-matter interactions in structured photonic environments with no gauge ambiguity. Results for two-level systems and the dipole approximation are discussed, as well as how to go beyond the dipole approximation for effective single-particle models. By comparing with the limiting case of an inhomogeneous dielectric, where dispersion and absorption can be neglected and the fields can be expanded in terms of the generalized transverse eigenfunctions of the dielectric, we show how lossy systems can introduce an additional gauge ambiguity, which we resolve and predict to have fundamental implications for open quantum system models. Finally, we show how observables in mode-truncated systems can be calculated without ambiguity by using a simple gauge-invariant model of photodetection.

Momentum Gauge Fields and Non-Commutative Space–Time

In this work, we present a gauge principle that starts with the momentum space representation of the position operator (x^i=iℏ∂∂pi), rather than starting with the position space representation of the momentum operator (p^i=−iℏ∂∂xi). This extension of the gauge principle can be seen as a dynamical version of Born’s reciprocity theory, which exchanges position and momentum. We discuss some simple examples with this new type of gauge theory: (i) analog solutions from ordinary gauge theory in this momentum gauge theory, (ii) Landau levels using momentum gauge fields, and (iii) the emergence of non-commutative space–times from the momentum gauge fields. We find that the non-commutative space–time parameter can be momentum dependent, and one can construct a model where space–time is commutative at low momentum, but becomes non-commutative at high momentum.

A non-perturbative no-go theorem for photon condensation in approximate models

Equilibrium phase transitions between a normal and a photon condensate state (also known as superradiant phase transitions) are a highly debated research topic, where proposals for their occurrence and no-go theorems have chased each other for the past four decades. Recent no-go theorems have demonstrated that gauge invariance forbids second-order phase transitions to a photon condensate state when the cavity-photon mode is assumed to be {\it spatially uniform}. However, it has been theoretically predicted that a collection of three-level systems coupled to light can display a first-order phase transition to a photon condensate state. %{It has also been recently shown that truncation of the Hilbert space of the matter system can affect the gauge invariance of the theory. However, it is always possible to obtain approximate Hamiltonians obeying the gauge principle in the truncated Hilbert space.} Here, we demonstrate a general no-go theorem valid also for truncated, gauge-invariant models which forbid first-order as well as second-order superradiant phase transitions in the absence of a coupling with a magnetic field. In particular, we explicitly consider the cases of interacting electrons in a lattice and $M$-level systems.

Stranger than metals.

In traditional metals, the temperature (T) dependence of electrical resistivity vanishes at low or high T, albeit for different reasons. Here, we review a class of materials, known as "strange" metals, that can violate both of these principles. In strange metals, the change in slope of the resistivity as the mean free path drops below the lattice constant, or as T → 0, can be imperceptible, suggesting continuity between the charge carriers at low and high T. We focus on transport and spectroscopic data on candidate strange metals in an effort to isolate and identify a unifying physical principle. Special attention is paid to quantum criticality, Planckian dissipation, Mottness, and whether a new gauge principle is needed to account for the nonlocal transport seen in these materials.

Dual description of gauge theories from an iterative Noether approach

An iterative Noether scheme, advocated by Deser, is used to introduce gauge invariant couplings to nonrelativistic matter with global symmetries related to usual charge conservation and dipole conservation recently discussed in fractonic theories. No reference to any gauge principle, fractonic or otherwise, is required. A dual description is found where the theory is defined either in terms of the usual vector gauge field or, alternatively, in terms of higher derivatives of a symmetric tensor field given in fractonic theories. A connection between these two descriptions is obtained by providing an explicit map between the vector and tensor fields. This method yields a novel ‘minimal’ prescription involving tensor fields which is identified with the usual minimal prescription that involves vector fields, by using the mapping. It also spells out the structure of the pure gauge field action in both formulations. Extension of the abelian U(1) invariance to the nonabelian SU(N) invariance is done for the standard formulation.

Gauge-independent emission spectra and quantum correlations in the ultrastrong coupling regime of open system cavity-QED

Abstract A quantum dipole interacting with an optical cavity is one of the key models in cavity quantum electrodynamics (cavity-QED). To treat this system theoretically, the typical approach is to truncate the dipole to two levels. However, it has been shown that in the ultrastrong-coupling regime, this truncation naively destroys gauge invariance. By truncating in a manner consistent with the gauge principle, we introduce master equations for open systems to compute gauge-invariant emission spectra, photon flux rates, and quantum correlation functions which show significant disagreement with previous results obtained using the standard quantum Rabi model. Explicit examples are shown using both the dipole gauge and the Coulomb gauge.

Classical Gauge Principle - From Field Theories to Classical Mechanics

In this paper we discuss how the gauge principle can be applied to classical-mechanics models with finite degrees of freedom. The local invariance of a model is understood as its invariance under the action of a matrix Lie group of transformations parametrized by arbitrary functions. It is formally presented how this property can be introduced in such systems, followed by modern applications. Furthermore, Lagrangians describing classical-mechanics systems with local invariance are separated in equivalence classes according to their local structures.

Ultrastrong coupling of a qubit with a nonlinear optical resonator

The authors study the quantum Rabi model in the ultrastrong regime in the presence of cavity nonlinearities and identify inconsistencies from various nonlinear Hamiltonians. To resolve the issues, the authors develop a microscopic theory and provide a consistent nonlinear-resonator quantum Rabi model satisfying the gauge principle.

Fluid Gauge Theory

According to the general gauge principle, Fluid Gauge Theory is presented to cover a wider class of flow fields of a perfect fluid without internal energy dissipation under anisotropic stress field. Thus, the theory of fluid mechanics is extended to cover time dependent rotational flows under anisotropic stress field of a compressible perfect fluid, including turbulent flows. Eulerian fluid mechanics is characterized with isotropic pressure stress fields. The study is motivated from three observations. First one is experimental observations reporting large-scale structures coexisting with turbulent flow fields. This encourages a study of how such structures observed experimentally are possible in turbulent shear flows, Second one is a theoretical and mathematical observation: the ”General solution to Euler’s equation of motion” (found by Kambe in 2013) predicts a new set of four background-fields, existing in the linked 4d-spacetime. Third one is a physical query, ”what symmetry implies the current conservation law ?”. The latter two observations encourage a gauge-theoretic formulation by defining a differential one-form representing the interaction between the fluid-current field jμand a background field aμ.

Gauge Symmetries in Physical Fields (Review)

Gauge invariance is one of the fundamental symmetries in theoretical physics. In this paper, the gauge symmetry is reviewed to see how it is working in fundamental physical fields: Electromagnetism, Quantum Electro Dynamics and Geometric Theory of Gravity. In the 19th century, the gauge invariance was recognized as a mathematical non-uniqueness of the electromagnetic potentials. Real recognition of the gauge symmetry and its physical significance required two new fields developed in the 20th century: the relativity theory for physics of the world structure of linked 4d-spacetime and the quantum mechanics for the new dimension of a phase factor in complex representation of wave function. Finally the gauge theory was formulated on the basis of the gauge principle which played a role of guiding principle in the study of physicalfields such as Quantum Electrodynamics, Particle Physics and Theory of Gravitation. Fluid mechanics of a perfect fluid can join in this circles, which is another motivation of the present review. There is a hint of fluid gauge theory in the general representation of rotational flows of an ideal compressible fluid satisfying the Euler’s equation, found in 2013 by the author. In fact, law of mass conservation can be deduced from the gauge symmetry equipped in the new system of fluid-flow field combined with a gauge field, rather than given a priori.

Revisiting the compatibility problem between the gauge principle and the observability of the canonical orbital angular momentum in the Landau problem

As is widely-known, the eigen-functions of the Landau problem in the symmetric gauge are specified by two quantum numbers. The first is the familiar Landau quantum number n, whereas the second is the magnetic quantum number m, which is the eigen-value of the canonical orbital angular momentum (OAM) operator of the electron. The eigen-energies of the system depend only on the first quantum number n, and the second quantum number m does not correspond to any direct observables. This seems natural since the canonical OAM is generally believed to be a gauge-variant quantity, and observation of a gauge-variant quantity would contradict a fundamental principle of physics called the gauge principle. In recent researches, however, Bliokh et al. analyzed the motion of helical electron beam along the direction of a uniform magnetic field, which was mostly neglected in past analyses of the Landau states. Their analyses revealed highly non-trivial m-dependent rotational dynamics of the Landau electron, but the problem is that their papers give an impression that the quantum number m in the Landau eigen-states corresponds to a genuine observable. This compatibility problem between the gauge principle and the observability of the quantum number m in the Landau eigen-states was attacked in our previous letter paper. In the present paper, we try to give more convincing answer to this delicate problem of physics, especially by paying attention not only to the particle-like aspect but also to the wave-like aspect of the Landau electron.

Gauge principle and gauge invariance in two-level systems

The quantum Rabi model is a widespread description of the coupling between a two-level system and a quantized single mode of an electromagnetic resonator. Issues about this model's gauge invariance have been raised. These issues become evident when the light-matter interaction reaches the so-called ultrastrong coupling regime. Recently, a modified quantum Rabi model able to provide gauge-invariant physical results (e.g., energy levels, expectation values of observables, quantum probabilities) in any interaction regime was introduced [Nature Physics 15, 803 (2019)]. Here we provide an alternative derivation of this result, based on the implementation in two-state systems of the gauge principle, which is the principle from which all the fundamental interactions in quantum field theory are derived. The adopted procedure can be regarded as the two-site version of the general method used to implement the gauge principle in lattice gauge theories. Applying this method, we also obtain the gauge-invariant quantum Rabi model for asymmetric two-state systems, and the multi-mode gauge-invariant quantum Rabi model beyond the dipole approximation.