Gauge Field Theory Research Articles

Geometric Relational Framework for General‐Relativistic Gauge Field Theories

AbstractIt is recalled how relationality arises as the core insight of general‐relativistic gauge field theories from the articulation of the generalized hole and point‐coincidence arguments. Hence, a compelling case for a manifestly relational framework ensues naturally. A formulation for such a framework is proposed, based on a significant development of the dressing field method of symmetry reduction. A version for the group of automorphisms of a principal bundle over a manifold is first developed, as it is the most natural and elegant, and as hosts all the mathematical structures relevant to general‐relativistic gauge field theory. However, as the standard formulation is local, on , the relational framework for local field theory is then developed. The generalized point‐coincidence argument is manifestly implemented, whereby the physical field‐theoretical degrees of freedoms co‐define each other and define, coordinatize, the physical spacetime itself. Applying the framework to General Relativity, relational Einstein equations are obtained, encompassing various notions of “scalar coordinatization” à la Kretschmann–Komar and Brown–Kuchař.

Pseudo-Quantum Electrodynamics: 30 Years of Reduced QED

Charged quasiparticles, which are constrained to move on a plane, interact by means of electromagnetic (EM) fields which are not subject to this constraint, living, thus, in three-dimensional space. We have, consequently, a hybrid situation where the particles of a given system and the EM fields (through which they interact) live in different dimensions. Pseudo-Quantum Electrodynamics (PQED) is a U(1) gauge field theory that, despite being strictly formulated in two-dimensional space, precisely describes the real EM interaction of charged particles confined to a plane. PQED is completely different from QED(2 + 1), namely, Quantum Electrodynamics of a planar gauge field. It produces, for instance, the correct 1/r Coulomb potential between static charges, whereas QED(2 + 1) produces lnr potential. In spite of possessing a nonlocal Lagrangian, it has been shown that PQED preserves both causality and unitarity, as well as the Huygens principle. PQED has been applied successfully to describe the EM interaction of numerous systems containing charged particles constrained to move on a plane. Among these are p-electrons in graphene, silicene, and transition-metal dichalcogenides; systems exhibiting the Valley Quantum Hall Effect; systems inside cavities; and bosonization in (2 + 1)D. Here, we present a review article on PQED (also known as Reduced Quantum Electrodynamics).

Magnetic monopole phenomenology at future hadron colliders

Abstract In the grand tapestry of Physics, the magnetic monopole is a holy grail. Therefore, numerous efforts
are underway in search of this hypothetical particle at CMS, ATLAS and MoEDAL experiments of LHC
by employing different production mechanisms. The cornerstone of our comprehension of monopoles lies
in Dirac’s theory which outlines their characteristics and dynamics. Within this theoretical framework, an
effective U (1) gauge field theory, derived from conventional models, delineates the interaction between spin
magnetically-charged fields and ordinary photons under electric-magnetic dualization.
The focus of this paper is the production of magnetic monopoles through Drell-Yan and the Photon-Fusion
mechanisms to generate velocity-dependent scalar, fermionic, and vector monopoles of spin angular mo-
mentum 0, 1
2 , 1 respectively at LHC. A computational study compares the monopole pair-production cross-
sections for both methods at various center-of-mass energies (√s) with different magnetic dipole moments.
The comparison of kinematic distributions of monopoles at Parton and reconstructed level are demonstrated
for both DY and PF mechanisms.
Extracted results showcase how modern machine-learning techniques can be used to study the production
of magnetic monopoles at the Future proton-proton Particle Colliders at 100 TeV. We demonstrate the ob-
servability of magnetic monopoles against the most relevant Standard Model background using multivariate
methods such as Boosted Decision Trees (BDT), Likelihood, and Multilayer Perceptron (MLP). This study
compares the performance of these classifiers with traditional cut-based and counting approaches, proving
the superiority of our methods

From the Cosserats mechanics backgrounds to modern field theory

In the paper, yet weekly known, Cosserats’ original four concepts as follow: the four-time unification of rigid body dynamics, statics of flexible rods, statics of elastic surfaces and 3D deformable body dynamics; the intrinsic formulation based on the local, von Helmholtz symmetry group of monodromy; the invariance under the Euclidean group. The concept of a set of low-dimensional branes immersed into Euclidean space are revalorized and explained in terms of the modern gauge field theory and the extended strings theory. Additionally, some useful mathematical tools that connect the continuum mechanics and the classical field theory (for instance, the convective coordinates, von Mises’ “Motorrechnung”, the Grassmann extensions, Euclidean invariance, etc.) are involved in the historical explanation that how the ideas were developing themself.

Floquet engineering of a dynamical Z2 lattice gauge field with ultracold atoms

Abstract Gauge field theory is a fundamental concept in modern physics, attracting many theoretical and experimental efforts towards its simulation. In this paper we propose that a simple model, in which fermions coupled to a dynamical lattice gauge field, can be engineered via the Floquet approach. The model possesses both an independent Maxwell term and local Z 2 gauge symmetry. Our proposal relies on a species-dependent optical lattice, and can be achieved in one, two or three dimensions. By a unitary transformation, this model can be mapped into a non-interacting composite fermion system with fluctuating background charge. With the help of this composite fermion picture, two characteristic observations are predicted. One is radio-frequency spectroscopy, which exhibits no dispersion in all parameter regimes. The second is dynamical localization, which depends on the structure of the initial states.

An effective gauge field theory of the nucleon interactions

We discuss the possibility of constructing an effective gauge field theory of the nucleon interactions based on the ideas of isotopic invariance as well as hypercharge invariance as a local gauge symmetry and spontaneous breaking of this symmetry. The constructed effective field theory predicts the structure of interactions of protons and neutrons with ρ- and σ-mesons, and with pi-mesons and photons, as well as interactions of these particles with each other. The Lagrangian of the theory consists of several parts involving dimension 4 and 5 gauge invariant operators. Feynman rules for physical degrees of freedom that follow on from the Lagrangian define the structure of diagrams for one-boson exchanges between nucleons, predicting the internucleon one-boson-exchange potential as well as nucleon scattering amplitudes. The range of applicability of the effective theory is discussed and estimates are made of the resulting coupling constants. The theory predicts the mass of the neutral ρ 0-meson to be about 1 MeV larger than the mass of the charged mesons ρ ±. The vector ω-meson, which is a sterile particle with respect to the considered gauge group SU I (2) × U Y (1), can be added to the scheme via a gauge-invariant operator of dimension 5, as shown in the appendix.

Effective Abelian lattice gauge field theories for scalar-matter-monopole interactions

Effective Abelian lattice gauge field theories for scalar-matter-monopole interactions

Study of polarization for even-denominator fractional quantum Hall states in SU(4) Graphene

Abstract We have focused on studying the even-denominator fractional quantum Hall (EDFQH) states observed in monolayer graphene. In this article, we have studied polarization mainly for the two EDFQH states at filling fractions ν = 1/2, 1/4, which are observed in an experimental study [Nat. Phys. 14, 930 (2018)] a few years ago. We have applied Chern-Simon’s gauge field theory to explain the possible variational wave functions for different polarized states and calculated their ground state energies using the Coulomb potential. We have chosen the lowest energy states using suitable combinations of attached flux quanta to the electrons for different polarized states of those EDFQH states.

On Covariant and Canonical Hamiltonian Formalisms for Gauge Theories

The Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms, have received a lot of attention in the literature. However, a full understanding of the relation between them is not available, especially when the gauge theories are defined over regions with boundaries. Here, we consider this issue, by first making it precise what we mean by equivalence between the two formalisms. Then, we explore several first-order gauge theories and assess whether their corresponding descriptions satisfy the notion of equivalence. We shall show that, even when in several cases the two formalisms are indeed equivalent, there are counterexamples that signal that this is not always the case. Thus, non-equivalence is a generic feature of gauge field theories. These results call for a deeper understanding of the subject.

Covariant canonical formulations of classical field theories

We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) and we discuss the relationships between these approaches as well as the relation with the standard (non-covariant) Hamiltonian formulation. Particular attention is paid to conservation laws (notably related to geometric symmetries) within the different approaches. Moreover, for each of these approaches, the impact of space-time boundaries is also addressed. To make the text accessible to a wider audience, we have included an outline of Poisson and symplectic geometry for both classical mechanics and field theory.

BRST invariant formulation of the Bell-CHSH inequality in gauge field theories

A study of the Bell-CHSH inequality in gauge field theories is presented. By using the Kugo-Ojima analysis of the BRST charge cohomology in Fock space, the Bell-CHSH inequality is formulated in a manifestly BRST invariant way. The examples of the free four-dimensional Maxwell theory and the Abelian Higgs model are scrutinized. The inequality is probed by using BRST invariant squeezed states, allowing for large Bell-CHSH inequality violations, close to Tsirelson’s bound. An illustrative comparison with the entangled state of two 1/21/2 spin particles in Quantum Mechanics is provided.

Diagrammatic structures of the Nielsen identity

The Γ-function, or the effective potential of a gauge field theory should comply with the Nielsen identity, which implies how the effective potential evolves as we shift the gauge-fixing term. In this paper, relying on an abelian toy model, we aim at proving this identity in a diagrammatic form with the R‾ξ gauge. The basic idea is to find out the ghost chain after partially differentiating the diagram by the ξ parameter, and shrink the waists of the diagram into points to separate the bulk-part and C-part of the diagrams. The calculations can be generalized to the models implemented with non-abelian groups, multiple Higgs and fermion multiplets, and to the finite temperature cases.

Cosmological phase transitions in composite Higgs models

We investigate cosmological phase transitions in various composite Higgs models consisting of four-dimensional asymptotically-free gauge field theories. Each model may lead to a confinement-deconfinement transition and a phase transition associated with the spontaneous breaking of a global symmetry that realizes the Standard Model Higgs field as a pseudo-Nambu-Goldstone boson. Based on the argument of universality, we discuss the order of the phase transition associated with the global symmetry breaking by studying the renormalization group flow of the corresponding linear sigma model at finite temperature, which is calculated by utilizing the ϵ-expansion technique at the one-loop order. Our analysis indicates that some composite Higgs models accommodate phenomenologically interesting first-order phase transitions. We also explore the confinement-deconfinement transition in a UV-completed composite Higgs model based on a Sp(2Nc) gauge theory. It is found that the first-order phase transition is favored when the number of degrees of freedom for the Sp(2Nc) gauge field is much larger than that of matter fields in the fundamental representation of Sp(2Nc). We comment on the gravitational wave signal generated by the confinement-deconfinement transition and its detectability at future observations. Our discussions motivate further studies on phase transitions in composite Higgs models with the use of lattice simulations.

A gauge field theory of coherent matter waves

A gauge field treatment of a current oscillating at frequency ν of interacting neutral atoms leads to a set of matter-wave duals to Maxwell's equations for the electromagnetic field. In contrast to electromagnetics, the velocity of propagation has a lower limit rather than upper limit, and the wave impedance of otherwise free space is negative real-valued rather than 377 Ω. Quantization of the field leads to the matteron, the gauge boson dual to the photon. Unlike the photon, the matteron is bound to an atom and carries negative rather than positive energy, causing the source of the current to undergo cooling. Eigenstates of the combined matter and gauge field annihilation operator define the coherent state of the matter-wave field, which exhibits classical coherence in the limit of large excitation.

Non-Abelian Carroll–Field–Jackiw term in a Rarita-Schwinger model

In this paper, we demonstrate the possibility of generating a non-Abelian Carroll–Field–Jackiw (CFJ) term in the theory of a non-Abelian gauge field coupled to a spin-3/2 field in the presence of the constant axial vector field. Applying two regularization schemes, we prove that this term is finite and ambiguous, particularly vanishing within the 't Hooft-Veltman scheme.

Translation gauge field theory of gravity in Minkowski spacetime* *Supported by the National Nature Science Foundation of China (NSFC, 11975241)

The gravitational field with spin-2 is introduced naturally by the requirement that the Lagrangian is locally translation invariant in Minkowski spacetime. The interactions between the and spin-, 0, 1 matter fields are obtained along with the Lagrangian for the gravitational field including self-interactions. The deflection angle of light when it passes through the sun is calculated with different gauge conditions as an example. Our leading-order result is the same as that from general relativity, although the basic ideas are different. It is interesting that gravity can be described in a similar way to other fundamental interactions in Minkowski spacetime, and it may provide a new scenario for the Universe.

The hidden quantum origin of gauge connections

A fibre bundle viewpoint of gauge field theories is reviewed with focus on a possible quantum interpretation. The fundamental quantum properties of non-separability of state spaces is considered in the context of defining the connection on the fibre bundle, leading to an application of the quantum principles to the geometrical and topological definition of gauge theories. As a result, one could justifiably ask oneself if all interactions of the standard model, and perhaps even classical gravity have some quantum component after all. I employ a standard fibre bundle approach to introduce gauge theories, albeit it is known that a quantum bundle exists, simply because the main scope is to show that in the usual way in which we formulate classical gauge theories one can find quantum aspects that have been unknown until now. In a sense, I will try to justify the assessment that if we are to allow for gauge fields and parallel transport, we may have to allow at least some level of quantumness even in our classical gauge theories. The main statement is that propagation of interactions in spacetime is a quantum phenomenon. After writing the first draft of this article I noticed Y Shen C. Rosales-Guzman 2022 Laser & Photonics Reviews, 16,2100533 where the authors device entanglement of what they call ‘classical light’. This experiment supports my theoretical developments with the distinction that I interpret such phenomena also as fundamentally quantum. The distinction comes from the fact that the quantum nature of the experiments is manifested in a different way. My view on this is that there is no purely classical reality, no matter what the scale is at which we consider the description. I also discuss the fact that observing a quantum nature of ‘classical’ light propagation would amount to the requirement of modifying the causal structure defined in terms of the speed of light in a vacuum, on stronger grounds, based on the quantum interpretation of gauge connections.

Conservation of all Lipkin’s zilches from symmetries of the standard electromagnetic action and a hidden algebra

In 1964, Lipkin discovered the zilches, a set of conserved quantities in free electromagnetism. Among the zilches, optical chirality was identified by Tang and Cohen in 2010, serving as a measure of the handedness of light and leading to investigations into light’s interactions with chiral matter. While the symmetries underlying the conservation of the zilches have been examined, the derivation of zilch conservation laws from symmetries of the standard free electromagnetic (EM) action using Noether’s theorem has only been addressed in the case of optical chirality. We provide the full answer by demonstrating that the zilch symmetry transformations of the four-potential, A_{mu }, preserve the standard free EM action. We also show that the zilch symmetries belong to the enveloping algebra of a “hidden” invariance algebra of free Maxwell’s equations. This “hidden” algebra is generated by familiar conformal transformations and certain “hidden” symmetry transformations of A_{mu }. Generalizations of the “hidden” symmetries are discussed in the presence of a material four-current, as well as in the theory of a complex Abelian gauge field. Additionally, we extend the zilch symmetries of the standard free EM action to the standard interacting action (with a non-dynamical four-current), allowing for a new derivation of the continuity equation for optical chirality in the presence of electric charges and currents. Furthermore, new continuity equations for the remaining zilches are derived.

Generalized standard model with higher-order derivatives under rotor mechanism and its quantization

The Standard Model is the paradigm of particle physics which gives an accurate theory for fundamental particle interactions. However, the extension of Standard Model with higher-order derivatives is not a well-studied subject. This paper is a follow-up work of the previous study of the generalized Abelian gauge field theory and Yang–Mills theory under rotor mechanism of order n of higher order derivatives, and we apply it to the Standard Model of particle physics. Rotor mechanism on scalar field and Dirac field is also studied. We will study the quantization of the rotored Standard Model using path integral approach. We also inherit the previous result from the path integral quantization of generalized Abelian gauge field and apply it to our non-Abelian case. Then we carry out the generalized BRST quantization and prove the existence of the Slavnov–Taylor Identities of the rotor model. Finally, we discuss the possibility of rotor model on taming the infinities arise from the self-energy correction of the Higgs boson in high spacetime dimension, thus this provides a partial solution and new insights to the Hierarchy problem.

BRST characterization of the broken phase observables of a confining complex theory

Some time ago we have introduced a route to provide confinement in the sense that particle excitations would appear from condensates of fields that do not have physical asymptotic states. We envisaged this mechanism in an asymmetric vacuum phase of a complex gauge field theory. More recently, we showed how to define a BRST operator to the broken phase of a generic spontaneous broken field theory. Our intention here is to apply these late concepts to the previous complex field theory in order to give a cohomological characterization of those condensed states as actual physical observables of this theory in its broken phase.