Related papers: Comment on confinement and unitarity interrelation
In these lectures we review the motivation, principles of and (circumstantial) evidence for the program of unification of the fundamental forces. In an appendix, we review the group theory pertinent to the program.
The mechanism of dual superconductivity for confinement is reviewed.
It has been noticed that confinement effects can be described by the addition of a $ \sqrt {- F_{\mu \nu}^a F^{a\mu \nu}} $ term in the Lagrangian density. We now study the combined effect of such "confinement term" and that of a mass term.…
We present a close relationship between matching number, covering numbers and their fractional versions in combinatorial optimization and ordinary powers, integral closures of powers, and symbolic powers of monomial ideals. This…
The status of our understanding of confinement is reviewed. The evidence from lattice is that monopole condensation, or dual superconductivity, is at work. Confinement is an order-disorder transition. Different monopole species look…
We develop a unitary dependence theory to characterize the behaviors of quantum circuits and states in terms of how quantum gates manipulate qubits and determine their measurement probabilities. A qubit has dependence on a 1-qubit unitary…
In this short note we will explore some recent connections between positivity, singularities, and boundedness in various contexts focusing on birational geometry.
The concept of distance rationalizability of social choice rules has been explored in recent years by several authors. We deal here with several foundational questions, and unify, correct, and generalize previous work. For example, we study…
We prove the irrationality of some factorial series. To do so we combine methods from elementary and analytic number theory with methods from the theory of uniform distribution.
I reexamine the Nayak's criticism [Phys. Rev. Lett. 85, 178 (2000); 86, 943 (2001).] on the U(1) gauge theory approach to the strongly correlated systems. Contrary to his conclusion, the arbitrariness of the charge assignment observed by…
We illustrate why color deconfines when chiral symmetry is restored in gauge theories with quarks in the fundamental representation, and while these transitions do not need to coincide when quarks are in the adjoint representation,…
From the Dirac sea concept and the Quark Model, we infer a phenomenological accompanying excitation concept. This concept will give an explanation for the confinement of quarks.
Confinement can have a dramatic effect on the behavior of all sorts of particulate systems and it therefore is an important phenomenon in many different areas of physics and technology. Here, we investigate the role played by the softness…
In this paper we present a rigorous method for deciding whether a birational three point mapping that has the singularity confinement property is integrable or not, based only on the structure of its (confined) singularity patterns. We also…
We explore the consequences of requiring that quantum theories of gravity be unitary, mostly focusing on simple cosmological models to illustrate the main points. We show that unitarity for a clock that encounters a classical singularity at…
This is the second of the two last papers by V. N. Gribov concluding his 20 year long study of the problem of quark confinement in QCD. In this paper the analytic structure of quark and gluon Green's functions is investigated in the…
A new renormalization scheme for theories with nontrivial internal symmetry is proposed. The scheme is regularization independent and respects the symmetry requirements.
We document a connection between constraint reasoning and probabilistic reasoning. We present an algorithm, called {em probabilistic arc consistency}, which is both a generalization of a well known algorithm for arc consistency used in…
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.
An updated review is presented of lattice investigations of colour confinement.