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Some features of the high temperature gluonic matter, such as the breakdown of the fundamental group symmetry by the kinetic energy, the screening of test quarks by some unusual gluon states and the explanation of the absence of isolated…
The connection between two nonperturbative approaches in quantum chromodynamics is considered. The first one is based on a collective coordinate method, the second one on a spin-charge separation. It is shown that both approaches have some…
Quantum chromodynamics predicts that the interaction between its fundamental constituents, quarks and gluons, can lead to different states of strongly interacting matter, dependent on its temperature and baryon density. We first survey the…
We study quantum chromodynamics from the viewpoint of untruncated Dyson-Schwinger equations turned to an ordinary differential equation for the gluon anomalous dimension. This nonlinear equation is parameterized by a function P(x) which is…
In the preceeding works, we have given a non-Abelian dual superconductivity picture for quark confinement, and demonstrated the numerical evidences on the lattice. In this talk, we discuss the confinement and deconfinement phase transition…
The classical Lagrangian of chromodynamics, its quantization in the perturbation theory framework, and renormalization form the subject of these lectures. Symmetries of the theory are discussed. The dependence of the coupling constant…
Color confinement is a consequence of an unbroken non-Abelian gauge symmetry and the resulting asymptotic freedom inherent in quantum chromodynamics. A qualitative sketch of its proof is presented.
These lectures give an introduction to duality in Quantum Field Theory. We discuss the phases of gauge theories and the implications of the electric-magnetic duality transformation to describe the mechanism of confinement. We review the…
Gaining insight about ensembles of magnetic configurations, that could originate the confining string tension between quarks, constitutes a major concern in current lattice investigations. This interest also applies to a different approach,…
A general discussion is presented of the possible symmetries responsible for confinement of color and of their evidence in lattice simulations. The consequences on the phase diagram of $QCD$ are also analyzed.
We propose an orbifold lattice formulation of QCD suitable for quantum simulations. We show explicitly how to encode gauge degrees of freedom into qubits using noncompact variables, and how to write down a simple truncated Hamiltonian in…
We sketch the basic ideas of the lattice regularization in Quantum Field Theory, the corresponding Monte Carlo simulations, and applications to Quantum Chromodynamics (QCD). This approach enables the numerical measurement of observables at…
The real-world properties of quantum chromodynamics (QCD) - the strongly-interacting piece of the Standard Model - are dominated by two emergent phenomena: confinement; namely, the theory's elementary degrees-of-freedom - quarks and gluons…
The systematic approach to study bound states in quantum chromodynamics is presented. The method utilizes nonperturbative flow equations in the confining background, that makes possible to perform perturbative renormalization and to bring…
Surface critical phenomena and the related onset of Goldstone modes probe the fundamental properties of the confining flux in Quantum Chromodynamics. New ideas on surface roughening and their implications for lattice studies of quark…
Based on the dual superconductor picture, we study the confinement phenomena systematically, using the lattice QCD, the monopole-current dynamics and the dual Ginzburg-Landau (DGL) theory. (1) We study the origin of abelian dominance for…
Systematic description of a spin one-half system endowed with magnetic moment or any other two-level system (qubit) interacting with the quantized electromagnetic field is developed. This description exploits a close analogy between a…
A synthesis of Polyakov loop models of the deconfinement transition and quasiparticle models of gluon plasma thermodynamics leads to a class of models in which gluons move in a non-trivial Polyakov loop background. These models are…
QCD possesses a compact gauge group, and this implies a non-trivial topological structure of the vacuum. In this contribution to the Gribov-85 Memorial volume, we first discuss the origin of Gribov copies and their interpretation in terms…
Quantum chromodynamics (QCD) at non-zero isospin chemical potential is studied in a canonical approach by analyzing systems of fixed isospin number density. To construct these systems, we develop a range of new algorithms for performing the…