scholarly journals The Gribov legacy, gauge theories and the physical S-matrix

2016 ◽  
Vol 31 (28n29) ◽  
pp. 1645014
Author(s):  
Alan R. White
Keyword(s):  
Gauge Theory ◽  
Gauge Field ◽  
Crucial Role ◽  
Gauge Theories ◽  
Bound State ◽  
Abelian Gauge ◽  
Distant Future ◽  
S Matrix ◽  
Gribov Ambiguity

Reggeon unitarity and non-Abelian gauge field copies are focused on as two Gribov discoveries that, it is suggested, may ultimately be seen as the most significant and that could, in the far distant future, form the cornerstones of his legacy. The crucial role played by the Gribov ambiguity in the construction of gauge theory bound-state amplitudes via reggeon unitarity is described. It is suggested that the existence of a physical, unitary, S-Matrix in a gauge theory is a major requirement that could even determine the theory.

scholarly journals The Gribov problem in noncommutative gauge theory

2018 ◽  
Vol 15 (07) ◽  
pp. 1850119 ◽  
Author(s):  
Maxim Kurkov ◽  
Patrizia Vitale
Keyword(s):  
Gauge Theory ◽  
Noncommutative Geometry ◽  
Infinite Number ◽  
Gauge Theories ◽  
Number Of Solutions ◽  
Abelian Gauge ◽  
Noncommutative Gauge Theory ◽  
Gribov Ambiguity ◽  
Gribov Copies ◽  
Noncommutative Parameter

After reviewing Gribov ambiguity of non-Abelian gauge theories, a phenomenon related to the topology of the bundle of gauge connections, we show that there is a similar feature for noncommutative QED over Moyal space, despite the structure group being Abelian, and we exhibit an infinite number of solutions for the equation of Gribov copies. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.

scholarly journals GRIBOV PROBLEM FOR GAUGE THEORIES: A PEDAGOGICAL INTRODUCTION

2004 ◽  
Vol 01 (04) ◽  
pp. 423-441 ◽  
Author(s):  
GIAMPIERO ESPOSITO ◽  
DIEGO N. PELLICCIA ◽  
FRANCESCO ZACCARIA
Keyword(s):  
Cross Sections ◽  
Gauge Theories ◽  
Functional Integral ◽  
Point Of View ◽  
Spherically Symmetric ◽  
Abelian Gauge ◽  
Gauge Transformations ◽  
Recent Developments ◽  
Gribov Ambiguity ◽  
Gribov Copies

The functional-integral quantization of non-Abelian gauge theories is affected by the Gribov problem at non-perturbative level: the requirement of preserving the supplementary conditions under gauge transformations leads to a nonlinear differential equation, and the various solutions of such a nonlinear equation represent different gauge configurations known as Gribov copies. Their occurrence (lack of global cross-sections from the point of view of differential geometry) is called Gribov ambiguity, and is here presented within the framework of a global approach to quantum field theory. We first give a simple (standard) example for the SU(2) group and spherically symmetric potentials, then we discuss this phenomenon in general relativity, and recent developments, including lattice calculations.

SUPERSYMMETRIC TENSOR GAUGE THEORIES

1989 ◽  
Vol 04 (14) ◽  
pp. 1343-1353 ◽  
Author(s):  
T.E. CLARK ◽  
C.-H. LEE ◽  
S.T. LOVE
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Sigma Models ◽  
Gauge Field ◽  
Gauge Theories ◽  
Symmetric Tensor ◽  
Global Symmetry ◽  
Invariant Action ◽  
Symmetry Transformations ◽  
Linear Sigma Models

The supersymmetric extensions of anti-symmetric tensor gauge theories and their associated tensor gauge symmetry transformations are constructed. The classical equivalence between such supersymmetric tensor gauge theories and supersymmetric non-linear sigma models is established. The global symmetry of the supersymmetric tensor gauge theory is gauged and the locally invariant action is obtained. The supercurrent on the Kähler manifold is found in terms of the supersymmetric tensor gauge field.

scholarly journals Review of strongly-coupled composite dark matter models and lattice simulations

2016 ◽  
Vol 31 (22) ◽  
pp. 1643004 ◽  
Author(s):  
Graham D. Kribs ◽  
Ethan T. Neil
Keyword(s):  
Dark Matter ◽  
Gauge Theory ◽  
Direct Detection ◽  
Bound State ◽  
New Physics ◽  
Abelian Gauge ◽  
Strongly Coupled ◽  
Abelian Gauge Theory ◽  
Lattice Calculations ◽  
Composite Description

We review models of new physics in which dark matter arises as a composite bound state from a confining strongly-coupled non-Abelian gauge theory. We discuss several qualitatively distinct classes of composite candidates, including dark mesons, dark baryons, and dark glueballs. We highlight some of the promising strategies for direct detection, especially through dark moments, using the symmetries and properties of the composite description to identify the operators that dominate the interactions of dark matter with matter, as well as dark matter self-interactions. We briefly discuss the implications of these theories at colliders, especially the (potentially novel) phenomenology of dark mesons in various regimes of the models. Throughout the review, we highlight the use of lattice calculations in the study of these strongly-coupled theories, to obtain precise quantitative predictions and new insights into the dynamics.

DISCRETE GAUGE THEORIES

1991 ◽  
Vol 05 (16n17) ◽  
pp. 2641-2673 ◽  
Author(s):  
MARK G. ALFORD ◽  
JOHN MARCH-RUSSELL
Keyword(s):  
Gauge Theory ◽  
Order Parameter ◽  
Gauge Theories ◽  
Lattice Gauge Theory ◽  
Abelian Gauge ◽  
Gauge Symmetries ◽  
Lattice Gauge ◽  
Super Conducting ◽  
The Relationship ◽  
Discrete Charge

In this review we discuss the formulation and distinguishing characteristics of discrete gauge theories, and describe several important applications of the concept. For the abelian (ℤN) discrete gauge theories, we consider the construction of the discrete charge operator F(Σ*) and the associated gauge-invariant order parameter that distinguishes different Higgs phases of a spontaneously broken U(1) gauge theory. We sketch some of the important thermodynamic consequences of the resultant discrete quantum hair on black holes. We further show that, as a consequence of unbroken discrete gauge symmetries, Grand Unified cosmic strings generically exhibit a Callan-Rubakov effect. For non-abelian discrete gauge theories we discuss in some detail the charge measurement process, and in the context of a lattice formulation we construct the non-abelian generalization of F(Σ*). This enables us to build the order parameter that distinguishes the different Higgs phases of a non-abelian discrete lattice gauge theory with matter. We also describe some of the fascinating phenomena associated with non-abelian gauge vortices. For example, we argue that a loop of Alice string, or any non-abelian string, is super-conducting by virtue of charged zero modes whose charge cannot be localized anywhere on or around the string (“Cheshire charge”). Finally, we discuss the relationship between discrete gauge theories and the existence of excitations possessing exotic spin and statistics (and more generally excitations whose interactions are purely “topological”).

scholarly journals NON-ABELIAN GAUGE THEORIES AS A CONSEQUENCE OF PERTURBATIVE QUANTUM GAUGE INVARIANCE

1999 ◽  
Vol 14 (21) ◽  
pp. 3421-3432 ◽  
Author(s):  
A. ASTE ◽  
G. SCHARF
Keyword(s):  
Gauge Theory ◽  
Gauge Invariance ◽  
Gauge Theories ◽  
Fundamental Concept ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Yang Mills ◽  
Vector Bosons ◽  
Perturbative Quantum

We show for the case of interacting massless vector bosons, how the structure of Yang–Mills theories emerges automatically from a more fundamental concept, namely perturbative quantum gauge invariance. It turns out that the coupling in a non-Abelian gauge theory is necessarily of Yang–Mills type plus divergence- and coboundary-couplings. The extension of the method to massive gauge theories is briefly discussed.

scholarly journals SU(2) hadrons on a quantum computer via a variational approach

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Yasar Y. Atas ◽  
Jinglei Zhang ◽  
Randy Lewis ◽  
Amin Jahanpour ◽  
Jan F. Haase ◽  
...  
Keyword(s):  
Gauge Theory ◽  
Nuclear Physics ◽  
Variational Approach ◽  
Gauge Theories ◽  
Quantum Computer ◽  
Quantum Computers ◽  
Abelian Gauge ◽  
Quantum Simulations ◽  
Sign Problem ◽  
Matter Fields

AbstractQuantum computers have the potential to create important new opportunities for ongoing essential research on gauge theories. They can provide simulations that are unattainable on classical computers such as sign-problem afflicted models or time evolutions. In this work, we variationally prepare the low-lying eigenstates of a non-Abelian gauge theory with dynamically coupled matter on a quantum computer. This enables the observation of hadrons and the calculation of their associated masses. The SU(2) gauge group considered here represents an important first step towards ultimately studying quantum chromodynamics, the theory that describes the properties of protons, neutrons and other hadrons. Our calculations on an IBM superconducting platform utilize a variational quantum eigensolver to study both meson and baryon states, hadrons which have never been seen in a non-Abelian simulation on a quantum computer. We develop a hybrid resource-efficient approach by combining classical and quantum computing, that not only allows the study of an SU(2) gauge theory with dynamical matter fields on present-day quantum hardware, but further lays out the premises for future quantum simulations that will address currently unanswered questions in particle and nuclear physics.

scholarly journals SOME PROPERTIES OF RENORMALONS IN GAUGE THEORIES

1995 ◽  
Vol 10 (10) ◽  
pp. 1449-1463 ◽  
Author(s):  
G. DI CECIO ◽  
G. PAFFUTI
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Perturbative Expansion ◽  
Abelian Gauge ◽  
Nonlocal Operators ◽  
Abelian Gauge Theory ◽  
Effective Lagrangian ◽  
Local Operators

We find the explicit operatorial form of renormalon type singularities in Abelian gauge theory. Local operators of dimension six take care of the first UV renormalon; nonlocal operators are needed for IR singularities. In the effective Lagrangian constructed with these operators nonlocal imaginary parts appearing in the usual perturbative expansion at large orders are canceled.

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