Yang-Mills Gauge Field Theory Research Articles

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.

Quantum Chromodynamics — The perfect Yang–Mills gauge field theory

Quantum Chromodynamics — The perfect Yang–Mills gauge field theory

Yang–Mills theory and fermionic path integrals

The Yang–Mills gauge field theory, which was proposed 60 years ago, is extremely successful in describing the basic interactions of fundamental particles. The Yang–Mills theory in the course of its developments also stimulated many important field theoretical machinery. In this brief review I discuss the path integral techniques, in particular, the fermionic path integrals which were developed together with the successful applications of quantized Yang–Mills field theory. I start with the Faddeev–Popov path integral formula with emphasis on the treatment of fermionic ghosts as an application of Grassmann numbers. I then discuss the ordinary fermionic path integrals and the general treatment of quantum anomalies. The contents of this review are mostly pedagogical except for a recent analysis of path integral bosonization.

"Conference on 60 Years of Yang-Mills Gauge Field Theories"

In 1954 Prof. Chen Ning Yang spent some time at Brookhaven National Laboratories where he met Robert Mills. They decided to study an extension of Quantum Electro Dynamics, where the local symmetry, the gauge symmetry, was a non-abelian symmetry algebra, SU(2), with three vector bosons mediating the forces between a doublet of matter particles. The symmetry that the authors had in mind was the isotopic symmetry and hence this was a prototype model for the strong interactions between protons and neutrons. The mass of the vector bosons was zero classically and the authors speculated that that they might obtain masses during quantization. On 1 October 1954 the Yang-Mills paper was published in the Physical Review. It was criticized directly by Wolfgang Pauli and others who argued that the vector particles would be massless leading to long-range interactions that was in contradiction to the experimental facts about the strong interactions. The interest in the paper was not so strong in the beginning.

量子真空能及其对引力规范理论的启示

电磁规范理论及其推广(Yang-Mills理论)在量子场论和粒子物理领域取得了成功要求引力理论也应当是某种局域规范对称下的规范场论；对于量子真空能巨大引力效应与宇宙学观察事实之间的矛盾等问题的探究表明传统引力理论可能是一个低能唯象理论，可能还存在新的高能引力相互作用基本理论。本文介绍了一个新的自旋联络引力规范理论，它以局域Lorentz群为规范对称群、以自旋仿射联络作为非Abel规范场。在低能条件下，我们可以获得一个度规的三阶微分方程作为引力场方程，而爱因斯坦引力场方程作为其一个首次积分解呈现。在该理论中，量子真空能巨大引力效应不再存在，并产生了一个等效宇宙学常数(作为首次积分解的积分常数)，这可能为解决宇宙学常数之谜提供了一条思路。对引力规范理论本身及其在宇宙学中的运用作了一些讨论, 如该引力规范理论会呈现一种准流体(它在四维宇宙中类似暗辐射；在五维宇宙中，则呈现更为丰富的物态)，因此基于该引力规范理论的五维宇宙学在不需要引入真实暗物质和暗能量的条件下也能产生等效的暗物质和暗能量效应。Since electromagnetic gauge theory and its generalization (Yang-Mills gauge field theory) have succeeded in quantum field theory and particle physics, it requires that the theory of gravitation also be a gauge field theory under certain local gauge symmetries, e.g., local Lorentz or Poincare invariance. The discrepancy between unusually large quantum vacuum energy density and ob-servational cosmology may indicate that the generic gravity theory of Einstein is a low-energy phenomenological theory, and a more fundamental theory of gravity might be hidden behind it. A new spin-connection gauge theory for gravitational interaction at high energies (close to the Planck energy scale) is introduced. In such a gravitational gauge field theory, the local Lorentz group is the gauge symmetry group, and the spin-affine connection serves as a non-Abel gauge field (fundamental dynamical variable). A third-order differential equation of metric can be obtained as the gravitational gauge field equation, where the Einstein field equation of gravitation is a first-integral solution. As the vacuum energy density is a constant, the covariant derivative of its energy-momentum tensor unavoidably vanishes. Therefore, the quantum vacuum energy term disappears in the gravitational gauge field equation, and the anomalously large vacuum energy density does not make a practical contribution to gravity. This would enable us to seek for a new route to the longstanding vacuum-energy cosmological constant problem. Some topics relevant to gravitational gauge theory and its applications in cosmology are also addressed. For example, the five-dimensional cosmology within the framework of the present gravitational gauge theory, in which a quasi fluid is emergent, can exhibit the effects of equivalent dark matter and dark energy.

Charge Conjugation and the B(3) Field: A Reply to Comay

The argument for non-existence of the B(3) field proposed by E. Comay is based on adding π radians to the phase of a plane wave. This is trivially incorrect because B(3) is a vacuum component of a C conserving Yang-Mills gauge field theory.

Boundary terms and their hamiltonian dynamics

It is described how the standard Poisson bracket formulas should be modified in order to incorporate integrals of divergences into the Hamiltonian formalism and why this is necessary. Examples from Einstein gravity and Yang-Mills gauge field theory are given.

Bifurcating and screening solutions of the topologically massive Yang-Mills gauge field theories with external matter sources.

Using a suitable ansatz for the gauge potentials and the external source currents, we demonstrate that solutions for the topologically massive gauge field theories can be constructed to exhibit branching in the total energy versus total external charge plot. As the gauge field is massive, charge screening of the external matter source also occurs.

Notes on solutions to the (2+1)-dimensional topologically massive Yang-Mills gauge field theories.

We demonstrate that the Bessel function solutions obtained previously are related to the (2 + 1)-dimensional vortex solutions when the Higgs fields are absent. Time-dependent solutions are also exhibited.

COMPACTIFICATION OF SPACE-TIME DIMENSIONS IN LATTICE GAUGE THEORY

The pure SU(2) Yang-Mills gauge field theory is studied in D=5 Euclidean dimensions in which case the continuum theory is nonrenormalizable. By a compactification of one dimension the effective theory, on the tree level, is equivalent to a D=4 SU(2) gauge theory with adjoint scalar fields. In a Monte Carlo (MC) simulation of the lattice regularized theory we confirm the existence of a first order phase transition; on asymmetric lattices we also find a higher order phase “finite temperature” transition. It is argued that the low energy continuum limit of the compactified theory nonperturbatively agrees with the renormalizable adjoint Higgs model in D=4 in the unbroken, confining phase.

Perturbative Ward identities for Yang-Mills field theory stochastically quantized.

We compute the divergent part of the three-point vertex function of the non-Abelian Yang-Mills gauge field theory within the stochastic quantization approach to the one-loop order. This calculation allows us to find four renormalization constants which, together with the four previously obtained, verify, to the calculated order, some Ward identities.

Renormalization group analysis of Yang-Mills field theory stochastically quantized

The renormalization group equations are solved to one-loop order, for non-abelian Yang-Mills gauge field theory in stochastic quantization. It is shown that the universal functions that appear in the renormalization group equations associated with the coupling constant and diffusion parameter, respectively, are gauge invariant. Finally, expressions for the effective coupling constant and diffusion parameter, which are renormalization group invariant, are given.

Concluding Talk

The Symposium on Yang-Mills Gauge Field Theories is now approaching a successful end. The invited review talks on the various aspects of Yang-Mills theories and talks on special topics offer a general survey of the panorama of the consequences and successes of Yang-Mills theories.

Gravity as an internal Yang-Mills gauge field theory of the Poincar� group

In the framework of affine bundles we present gravity as an “internal” gauge field theory of the Poincare group. The resulting geometry is a Riemann-Cartan space-time carrying torsion and curvature. In order to admit a nontrivial action of the translation group we formally extend the matter Lagrangian to affine field variables. Finally, we establish the relation of our approach with the formalism of Hehl et al.