Gauge Field Theory Research Articles

Affine Connection Representation of Gauge Fields

There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincaré gauge theory and metric-affine gauge theory adopt the first approach. This paper adopts the second. In this approach, (i) gauge field and gravitational field can both be represented by affine connection; they can be described by a unified spatial frame. (ii) Time can be regarded as the total metric with respect to all dimensions of internal coordinate space and external coordinate space. On-shell can be regarded as gradient direction. Quantum theory can be regarded as a geometric theory of distribution of gradient directions. Hence, gauge theory, gravitational theory, and quantum theory all reflect intrinsic geometric properties of manifold. (iii) Coupling constants, chiral asymmetry, PMNS mixing, and CKM mixing arise spontaneously as geometric properties in affine connection representation, so they are not necessary to be regarded as direct postulates in the Lagrangian anymore. (iv) The unification theory of gauge fields that are represented by affine connection can avoid the problem that a proton decays into a lepton in theories such as S U 5 . (v) There exists a geometric interpretation to the color confinement of quarks. In the affine connection representation, we can get better interpretations to the above physical properties; therefore, to represent gauge fields by affine connection is probably a necessary step towards the ultimate theory of physics.

Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions

Combining experimental and algorithmic advances in quantum simulation improves the investigation of gauge field theories: pair creation is simulated for longer times using less computational resources.

Generalized Yang-Mills theory under rotor mechanism

This paper follows the previous work on generalized abelian gauge field theory of higher-order derivatives under rotor model and extends the study to the most generalized non-abelian case. We find that the rotor mechanism from the abelian case applies nicely to the non-abelian case under the Lorentz gauge condition. Under the rotor mechanism, the gauge field transforms as Tμa→□nTμa. When the order of field derivative is n=0, this restores back to the original Yang-Mills action. Our work gives an extensive generalization of the Yang-Mills theory with higher-order field derivatives. We also compute the equation of motion and Noether's current of the generalized non-abelian gauge field theory. Finally, we study the dynamic instability issue of the theory by the Ostrogradsky construction and the analysis of the 00-component of the energy-momentum tensor.

Quantization of Generalized Abelian Gauge Field Theory under Rotor Model

This paper is a follow-up work of the previous study of the generalized abelian gauge field theory under rotor model of order $n$ of higher order derivatives. We will study the quantization of this theory using path integral approach and find out the Feynman propagator (2-point correlation function) of this generalized theory. We also investigate the generalized Proca action under rotor model and derive the Feynman propagator for the massive case.

Complex topological soliton with real energy in particle physics

We summarise the procedure used to find the classical masses of Higgs particle, massive gauge boson and t’Hooft-Polyakov monopole in non-Hermitian gauge field theory. Their physical regions are explored, and the mechanism of the real value of the monopole solution is analysed in different physical regions.

Quantum phases of two-dimensional Z2 gauge theory coupled to single-component fermion matter

We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with $U(1)$ symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model reduces to (i) pure $\mathbb{Z}_2$ even and odd gauge theories, (ii) free fermions in a static background of deconfined $\mathbb{Z}_2$ gauge fields, (iii) the kinetic Rokhsar-Kivelson quantum dimer model at a generic dimer filling. We develop a local transformation that maps the lattice gauge theory onto a model of $\mathbb{Z}_2$ gauge-invariant spin $1/2$ degrees of freedom. Using the mapping, we perform numerical density matrix renormalization group calculations that corroborate our understanding of the limits identified above. Moreover, in the absence of the magnetic plaquette term, we reveal signatures of topologically ordered Dirac semimetal and staggered Mott insulator phases at half-filling. At strong coupling, the lattice gauge theory displays fracton phenomenology with isolated fermions being completely frozen and dimers exhibiting restricted mobility. In that limit, we predict that in the ground state dimers form compact clusters, whose hopping is suppressed exponentially in their size. We determine the band structure of the smallest clusters numerically using exact diagonalization. The rich phenomenology discussed in this paper can be probed in analog and digital quantum simulators of discrete gauge theories and in Kitaev spin-orbital liquids.

Critical behaviors of lattice U(1) gauge models and three-dimensional Abelian-Higgs gauge field theory

We investigate under which conditions the three-dimensional (3D) multicomponent Abelian-Higgs (AH) field theory (scalar electrodynamics) is the continuum limit of statistical lattice gauge models, i.e., when it characterizes the universal behavior at critical transitions occurring in these models. We perform Monte Carlo simulations of the lattice AH model with compact gauge fields and $N$-component scalar fields with charge $q\ge 2$ for $N=15$ and 25. Finite-size scaling analyses of the Monte Carlo data show that the transitions along the line separating the confined and deconfined phases are continuous and that they belong to the same universality class for any $q\ge 2$. Moreover, they are in the same universality class as the transitions in the lattice AH model with noncompact gauge fields along the Coulomb-to-Higgs transition line. We finally argue that these critical behaviors are described by the stable charged fixed point of the renormalization-group flow of the 3D AH field theory.

Edge modes as reference frames and boundary actions from post-selection

We introduce a general framework realizing edge modes in (classical) gauge field theory as dynamical reference frames, an often suggested interpretation that we make entirely explicit. We focus on a bounded region M with a co-dimension one time-like boundary Γ, which we embed in a global spacetime. Taking as input a variational principle at the global level, we develop a systematic formalism inducing consistent variational principles (and in particular, boundary actions) for the subregion M. This relies on a post-selection procedure on Γ, which isolates the subsector of the global theory compatible with a general choice of gauge-invariant boundary conditions for the dynamics in M. Crucially, the latter relate the configuration fields on Γ to a dynamical frame field carrying information about the spacetime complement of M; as such, they may be equivalently interpreted as frame-dressed or relational observables. Generically, the external frame field keeps an imprint on the ensuing dynamics for subregion M, where it materializes itself as a local field on the time-like boundary Γ; in other words, an edge mode. We identify boundary symmetries as frame reorientations and show that they divide into three types, depending on the boundary conditions, that affect the physical status of the edge modes. Our construction relies on the covariant phase space formalism, and is in principle applicable to any gauge (field) theory. We illustrate it on three standard examples: Maxwell, Abelian Chern-Simons and non-Abelian Yang-Mills theories. In complement, we also analyze a mechanical toy-model to connect our work with recent efforts on (quantum) reference frames.

A Life in Mathematical Physics: Conference in Honour of Tekin Dereli

1. IntroductionThe friends and colleagues of Prof. Dr. Tekin Dereli came together to celebrate his 72nd birthday and the 50th year of his mathematical physics career. The three-days event took place online over the Zoom on 26-28 November 2021. His scientific and scholarly achievements, his kindness as a colleague, his thoughtful guidance of students and his service to the physics community in Turkey as a whole and last but not the least his open and easy accessibility to anyone needing his expert counseling have been appreciated by all.¨ We are grateful to the Turkish Academy of Sciences (TUBA) for sponsoring the online, open-access publication of the proceedings as a special issue in The Journal of Physics: Conference Series.2. Biography of Tekin DereliTekin Dereli was born in Ankara in 1949 where he completed his early education at Ankara Science High School in 1967. He earned his Bachelor’s degree in physics with high honors in 1971 at the Middle East Technical University (METU), where he also completed his PhD in 1976, with a thesis entitled “Fermions in Yang-Mills Potentials”. He gave his habilitation in 1981 with a thesis on “Dynamics of Neutrinos in Gravitational Fields” (in Turkish). His academic career began at METU as an instructor in 1973, where he later became an associate professor. He was promoted to professorship in 1987 at Ankara University and then returned to METU in 1993. He was invited to Ko¸c University as Professor of Physics in 2001 where he worked till 2021.Tekin Dereli held various research positions abroad, being always on-leave from METU. These include a visiting scientist position at Yale University during 1974-1975 under the hosting of Feza Gürsey and a research associate position at Brandeis University during 1976-1977 under the hosting of Stanley Deser. He collaborated with Peter C. Aichelburg as Einstein-Memorial Foundation Fellow at the Institute for Theoretical Physics, University of Vienna during 1977-1978. He was SRC Research Associate at Lancaster University between 1979-1981 where a long and fruitful collaboration with Robin W. Tucker has begun. He had been an Associate Member of ICTP between 1986-1991 and Alexander von Humboldt Foundation Fellow at Karlsruhe University during 1988-1989 under the hosting of Julius Wess.Tekin Dereli’s research interests cover a broad range of subjects. He published papers on magnetic monopoles in Yang-Mills gauge field theories, supersymmetry and supergravity, the role of quaternions and octonions in physics. He studied Clifford algebras and spin structures associated with the space-time. He worked on generalised theories of gravity, both in higher and lower dimensions than four, emphasizing their differential geometric gauge structure. In particular he investigated various aspects of black hole and gravitational wave solutions.Furthermore he constructed higher dimensional cosmological models. Tekin Dereli also worked on dualities in physics and mathematics in general and deformation quantisation in the context of the Landau problem.List of Scientific Bibliography of Tekin Dereli (1975-2021), Theses Supervised by Tekin Dereli, Alphabetical List of Contributors, Organising Committee are available in this pdf.

Regularizacija u teorijama kvantnog polja

Introduction/purpose: The principal techniques of regularization schemes and their validity for gauge field theories are discussed. Methods: Schemes of dimensional regularization, Pauli-Villars and lattice regularization are discussed. Results: The Coleman-Mandula theorem shows which gauge theories are renormalizable. Conclusion: Some gauge field theories are renormalizable, the Standard Model in particular.

PHENOMEN OF THE SCIENTIFIC REVOLUTIONS MISSED OPPORTUNITIES IN THE FUNDAMENTAL PHYSICS OF THE XXth CENTURY

The phenomenon of missed opportunities in the course of two scientific revolutions in fundamental physics is investigated: in the quantum relativistic revolution of the first third of the 20th century and in the gauge revolution that led to the creation of a standard model in elementary particle physics (1954-1974). Two cases of missed opportunities related to H. Poincare and his role in the history of the creation of the special theory of relativity are examined on the material of the first revolution. Two other cases of missed opportunities concerning A. Einstein in connection with the theory of the expanding Universe and with failed attempts to build a unified field theory based on a geometric field program are also considered. It is shown that in these cases epistemological and metaphysical outlooks of scientists were in many respects the causes of the «omissions». We mean the conventionalism of Poincare, as well as Einstein’s belief in the stationarity of the Universe and in the incredible power of mathematics as the only creative beginning in the construction of the physical theories. Two similar plots are explored on the material of the second revolution. The first story refers to the Young-Mills’ concept of the gauge fields, which played a key role in the creation of standard model. Several theorists came very close to this concept and, above all, V. Pauli, who for various reasons did not make a decisive step and missed opportunities to associate their names with the theory of gauge fields. Pauli believed that, despite its theoretical attraction, it could not overcome experimentally - empirical difficulties. The second story is related to the quantum field program being rejected in 1950-1960s by most theorists in favor of the phenomenological S-matrix program. As a result, many theorists have missed their opportunities to contribute to the creation of a standard model. And this “omission” was partly motivated by the positivist thesis that in theory only fundamentally observable values should appear. It is emphasized also that the phenomenon of missed opportunities opens the way for the study of the problem of alternative history of science.

Nonlinearity of the non-Abelian lattice gauge field theory according to the spectrum of Kolmogorov-Sinai entropy and complexity

Abstract The quark-gluon plasma is written by the non-Abelian gauge theory. The dynamics of the gauge SU(2) are given by the Hamiltonian function, which contains the quadratic part of the field strength tensor F μ v a {\rm{F}}_{\mu v}^{\rm{a}} expressed in Minkowski space. The homogeneous Yang-Mills equations are solved on lattice Nd considering classical approximation, which exhibits chaotic dynamics. We research the time-dependent entropy-energy relation, which can be shown by the energy spectrum of Kolmogorov-Sinai entropy and the spectra of the statistical complexity.

Two-Dimensional Electron-Hole System under the Influence of the Chern–Simons Gauge Field Created by the Quantum Point Vortices

In the present work the Chern-Simons(C-S) gauge field theory developed by Jackiw and Pi [1] and widely used to explain the fractional quantum Hall effects, was applied to describe the two-dimensional (2D) electron-hole (e-h) system in a strong perpendicular magnetic field under the influence of the quantum point vortices creating the Chern-Simons(C-S) gauge field. The composite particles formed by electrons and by holes with equal integer positive numbers of the attached quantum point vortices are described by the dressed field operators, which obey to the Fermi or to the Bose statistics depending on the even or odd numbers . It is shown that the phase operators as well as the vector and the scalar potentials of the C-S gauge field depend on the difference of the electron and of the hole density operators. They vanish in the mean field approximation, when the average values of the electron and of the whole densities coincide. Nevertheless, even in this case, the quantum fluctuations of the C-S gauge field lead to new physics of the 2D e-h system.

Gauge field theory vacuum and cosmological inflation without scalar field

We derive the quantum energy–momentum tensor and the corresponding quantum equation of state for gauge field theory using the effective Lagrangian approach. The energy–momentum tensor has a term proportional to the space–time metric and provides a finite non-diverging contribution to the effective cosmological term. This allows to investigate the influence of the gauge field theory vacuum polarisation on the evolution of Friedmann cosmology, inflation and primordial gravitational waves. The Type I–IV solutions of the Friedmann equations induced by the gauge field theory vacuum polarisation provide an alternative inflationary mechanism and a possibility for late-time acceleration. The Type II solution of the Friedmann equations generates the initial exponential expansion of the universe of finite duration and the Type IV solution demonstrates late-time acceleration. The solutions fulfil the necessary conditions for the amplification of primordial gravitational waves.

Derivation-based noncommutative field theories on AF algebras

In this paper, we start the investigation of a new natural approach to “unifying” noncommutative gauge field theories (NCGFT) based on approximately finite-dimensional ([Formula: see text]) [Formula: see text]-algebras. The defining inductive sequence of an [Formula: see text] [Formula: see text]-algebra is lifted to enable the construction of a sequence of NCGFT of Yang–Mills–Higgs types. This paper focuses on derivation-based noncommutative field theories. A mathematical study of the ingredients involved in the construction of a NCGFT is given in the framework of [Formula: see text] [Formula: see text]-algebras: derivation-based differential calculus, modules, connections, metrics and Hodge *-operators, and Lagrangians. Some physical applications concerning mass spectra generated by Spontaneous Symmetry Breaking Mechanisms (SSBM) are proposed using numerical computations for specific situations.

Non-Hermitian gauge field theories and BPS limits

We present an overview of some key results obtained in a recent series devoted to non-Hermitian quantum field theories for which we systematically modify the underlying symmetries. Particular attention is placed on the interplay between the continuous symmetry group that we alter from global to local, from Abelian to non-Abelian, from rank one to generic rank N, and the discrete anti-linear modified CPT-symmetries. The presence of the latter guarantees the reality of the mass spectrum in a certain parameter regime. We investigate the extension of Goldstone’s theorem and the Higgs mechanism, which we demonstrate to work in the conventional fashion in the CPT-symmetric regime, but which needs to be modified technically at the standard exceptional points of the mass spectrum and entirely fails at what we refer to as zero exceptional points as well as in the broken CPT-symmetric regime. In the full non-Hermitian non-Abelian gauge theory we identify the t’Hooft-Polyakov monopoles by means of a fourfold Bogomol’nyi-Prasad-Sommerfield (BPS) limit. We investigate this limit further for other types of non-Hermitian field theories in 1+1 dimensions that possess complex super-exponential and inverse hyperbolic kink/anti-kink solutions and for 3+1 dimensional Skyrme models for which we find new types of complex solutions, that all have real energies due to the presence of different types of CPT-symmetries.

Scalable Cold-Atom Quantum Simulator for Two-Dimensional QED.

We propose a scalable analog quantum simulator for quantum electrodynamics in two spatial dimensions. The setup for the U(1) lattice gauge field theory employs interspecies spin-changing collisions in an ultracold atomic mixture trapped in an optical lattice. We engineer spatial plaquette terms for magnetic fields, thus solving a major obstacle toward experimental realizations of realistic gauge theories in higher dimensions. We apply our approach to the pure gauge theory of compact QED and discuss how the phenomenon of confinement of electric charges can be described by the quantum simulator.

Lie algebroids and the geometry of off-shell BRST

It is well-known that principal bundles and associated bundles underlie the geometric structure of classical gauge field theories. In this paper, we explore the reformulation of gauge theories in terms of Lie algebroids and their associated bundles. This turns out to be a simple but elegant change, mathematically involving a quotient that removes spurious structure. The payoff is that the entire geometric structure involves only vector bundles over space-time, and we emphasize that familiar concepts such as BRST are built into the geometry, rather than appearing as adjunct structure. Thus the formulation of gauge theories in terms of Lie algebroids provides a fully off-shell account of the BRST complex. We expect that this formulation will have appealing impacts on the geometric understanding of quantization and anomalies, as well as entanglement in gauge theories. The formalism covers all gauge theories, and we discuss Yang-Mills theories with matter as well as gravitational theories explicitly.

Generalized abelian gauge field theory under rotor model

Gauge field theory with rank-one field [Formula: see text] is a quantum field theory that describes the interaction of elementary spin-1 particles, of which being massless to preserve gauge symmetry. In this paper, we give a generalized, extended study of abelian gauge field theory under successive rotor model in general [Formula: see text]-dimensional flat spacetime for spin-1 particles in the context of higher-order derivatives. We establish a theorem that [Formula: see text] rotor contributes to the [Formula: see text] fields in the integration-by-parts formalism of the action. This corresponds to the transformation of gauge field [Formula: see text] and gauge field strength [Formula: see text] in the action. The [Formula: see text] case restores back to the standard abelian gauge field theory. The equation of motion and Noether’s conserved current of the theory are also studied.

Instanton worldlines in five-dimensional \u03a9-deformed gauge theory

We discuss the Bosonic sector of a class of supersymmetric non-Lorentzian five-dimensional gauge field theories with an SU(1, 3) conformal symmetry. These actions have a Lagrange multiplier which imposes a novel Ω-deformed anti-self-dual gauge field constraint. Using a generalised ’t Hooft ansatz we find the constraint equation linearizes allowing us to construct a wide class of explicit solutions. These include finite action configurations that describe worldlines of anti-instantons which can be created and annihilated. We also describe the dynamics on the constraint surface.