scholarly journals Fundamental Forces of Nature: The Story of Gauge Fields Fundamental Forces of Nature: The Story of Gauge Fields , Kerson Huang , World Scientific, Hackensack, NJ, 2007. $54.00, $30.00 paper (270 pp.). ISBN 978-981-270-644-7, ISBN 978-981-270-645-4 paper

Physics Today ◽  
2008 ◽  
Vol 61 (4) ◽  
pp. 70-72
Author(s):  
Hans C. von Baeyer
Keyword(s):  
Gauge Fields ◽  
World Scientific ◽  
Fundamental Forces

scholarly journals A pedagogical discussion of N = 1 four-dimensional supergravity in superspace

2021 ◽  
pp. 2130015
Author(s):  
Robin Ducrocq ◽  
Michel Rausch de Traubenberg ◽  
Mauricio Valenzuela
Keyword(s):  
Gauge Fields ◽  
Short Introduction ◽  
World Scientific ◽  
Four Dimensions ◽  
Action Coupling ◽  
Pedagogical Discussion

A short introduction to N = 1 supergravity in four dimensions in the superspace approach is given emphasizing on all steps to obtain the final Lagrangian. In particular, starting from geometrical principles and the introduction of superfields in curved superspace, the action coupling matter and gauge fields to supergravity is derived. This paper is based on the book [M. Rausch de Traubenberg and M. Valenzuela, A Supergravity Primer: From Geometrical Principles to the Final Lagrangian (World Scientific, 2020)] and on several lectures given at the doctoral school of Strasbourg.

The Yukawa Potential Function and Reciprocal Univalent Function

2013 ◽  
Vol 3 (2) ◽  
pp. 197-202
Author(s):  
Amir Pishkoo ◽  
Maslina Darus
Keyword(s):  
Mathematical Model ◽  
Unit Disk ◽  
Potential Function ◽  
Univalent Function ◽  
Open Problem ◽  
Yukawa Potential ◽  
Reciprocal Theorem ◽  
Problem Statement ◽  
Fundamental Forces

This paper presents a mathematical model that provides analytic connection between four fundamental forces (interactions), by using modified reciprocal theorem,derived in the paper, as a convenient template. The essential premise of this work is to demonstrate that if we obtain with a form of the Yukawa potential function [as a meromorphic univalent function], we may eventually obtain the Coloumb Potential as a univalent function outside of the unit disk. Finally, we introduce the new problem statement about assigning Meijer's G-functions to Yukawa and Coloumb potentials as an open problem.

Q & A. Lisa Randall. [interview]

2019 ◽  
Author(s):  
Adib Rifqi Setiawan
Keyword(s):  
New York ◽  
New York City ◽  
Particle Physics ◽  
Harvard University ◽  
The Past ◽  
Talent Search ◽  
Cosmological Inflation ◽  
On Line ◽  
Theoretical Physicist ◽  
Fundamental Forces

Lisa Randall is a theoretical physicist working in particle physics and cosmology. She was born in Queens, New York City, on June 18, 1962. Lisa Randall is an alumna of Hampshire College Summer Studies in Mathematics; and she graduated from Stuyvesant High School in 1980. She won first place in the 1980 Westinghouse Science Talent Search at the age of 18; and at Harvard University, Lisa Randall earned both a BA in physics (1983) and a PhD in theoretical particle physics (1987) under advisor Howard Mason Georgi III, a theoretical physicist. She is currently Frank B. Baird, Jr. Professor of Science on the physics faculty of Harvard University, where he has been for the past a decade. Her works concerns elementary particles and fundamental forces, and has involved the study of a wide variety of models, the most recent involving dimensions. She has also worked on supersymmetry, Standard Model observables, cosmological inflation, baryogenesis, grand unified theories, and general relativity. Consequently, her studies have made her among the most cited and influential theoretical physicists and she has received numerous awards and honors for her scientific endeavors. Since December 27, 2010 at 00:42 (GMT+7), Lisa Randall is Twitter’s user with account @lirarandall. “Thanks to new followers. Interesting how different it feels broadcasting on line vs.via book or article. Explanations? Pithiness? Rapidity?” is her first tweet.

Unification of Gauge Forces and Gravity using Tangled Vortex Knots and Entanglement Dynamics

2020 ◽  
Author(s):  
Mrittunjoy Guha Majumdar
Keyword(s):  
Field Theory ◽  
Short Range ◽  
Gauge Fields ◽  
Entanglement Dynamics ◽  
Unified Field Theory ◽  
Linear Dynamics ◽  
Unified Field ◽  
The Standard Model ◽  
Theory Of Everything ◽  
The Continuum

In this paper, the statistics of excitation-tangles in a postulated background ideal-superfluid field is studied. The structure of the Standard Model is derived in terms of tangle vortex-knots and soliton. Gravity is observed in terms of torsion and curvature in the continuum. In this way, non-linear dynamics and excitations give rise to a unified field theory as well as a Theory of Everything. As a result of this unification, spacetime and matter are shown to be fundamentally equivalent, while gauge fields arise from reorientation and excitations of the the fundamental underlying field. Finally, the equivalence of topological and quantum entanglement is explored to posit a theory of everything in terms of long- and short-range entanglement between fundamental quantum units (bits) of information.

scholarly journals Non-Abelian generalizations of the Hofstadter model: spin–orbit-coupled butterfly pairs

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Yi Yang ◽  
Bo Zhen ◽  
John D. Joannopoulos ◽  
Marin Soljačić
Keyword(s):  
Quantum Hall ◽  
Building Blocks ◽  
Real Space ◽  
Gauge Fields ◽  
Spin Orbit ◽  
Abelian Gauge ◽  
Experimental Realization ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum ◽  
Necessary And Sufficient

Abstract The Hofstadter model, well known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum Hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment, we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin–orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to topological insulators. We conclude by discussing possible schemes for experimental realization of the models on photonic platforms.

ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Scalar Field ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Linear Equations ◽  
Dual Solutions ◽  
Gauge Fields ◽  
System Of Equations ◽  
Semisimple Lie Algebra ◽  
Yang Mills ◽  
Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

scholarly journals Nilpotent symmetries as a mechanism for Grand Unification

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lars Andersson ◽  
András László ◽  
Błażej Ruba
Keyword(s):  
Gauge Field ◽  
Scalar Product ◽  
Local Symmetry ◽  
Matter Field ◽  
Gauge Fields ◽  
Spacetime Symmetries ◽  
Invariant Scalar ◽  
Spacetime Manifold ◽  
Local Symmetries ◽  
Dilatation Group

Abstract In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

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