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Register a new userVacuum and color confinement in quantum Yang-Mills theory
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A microscopic description of vacuum structure and color singlet quantum states in Yang-Mills theory is presented. Our approach is based on an idea that classical stationary solutions defining a Hilbert space of one particle quantum states possess quantum stability and symmetry under Weyl color group transformations. We demonstrate that Weyl symmetry and stability condition provide color singlet states and reveals the origin of color confinement in $SU(3)$ quantum Yang-Mills theory.
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We consider two fundamental long-standing problems in quantum chromodynamics (QCD): the origin of color confinement and structure of a true vacuum and color singlet quantum states. There is a common belief that resolution to these problems needs a knowledge of a strict non-perturbative quantum Yang-Mills theory and new ideas. Our principal idea in resolving these problems is that structure of color confinement and color singlet quantum states must be determined by a Weyl symmetry which is an intrinsic symmetry of the Yang-Mills gauge theory, and by properties of a selected class of solutions satisfying special requirements. Following this idea we construct for the first time a space of color singlet one particle quantum states for primary gluons and quarks and reveal the structure of color confinement in quantum Yang-Mills theory. As an application we demonstrate formation of physical observables in a pure QCD, pure glueballs.
Color confinement is the most puzzling phenomenon in the theory of strong interaction based on a quantum SU(3) Yang-Mills theory. The origin of color confinement supposed to be intimately related to non-perturbative features of the non-Abelian gauge theory, and touches very foundations of the theory. We revise basic concepts underlying QCD concentrating mainly on concepts of gluons and quarks and color structure of quantum states. Our main idea is that a Weyl symmetry is the only color symmetry which determines all color attributes of quantum states and physical observables. We construct an ansatz for classical Weyl symmetric dynamical solutions in SU(3) Yang-Mills theory which describe one particle color singlet quantum states for gluons and quarks. Abelian Weyl symmetric solutions provide microscopic structure of a color invariant vacuum and vacuum gluon condensates. This resolves a problem of existence of a gauge invariant and stable vacuum in QCD. Generalization of our consideration to SU(N) (N=4,5) Yang-Mills theory implies that the color confinement phase is possible only in SU(3) Yang-Mills theory.
We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a marginally confining theory. The potential we obtain agrees fairly well with preceding findings in literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali-Kim-Nair analysis. Classical solutions depend on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory and is now fully justified. The agreement obtained with the lattice results for the ground state of the theory is well below 1% at any value of the degree of the group.
In this work, we extend the construction of dual color decomposition in Yang-Mills theory to one-loop level, i.e., we show how to write one-loop integrands in Yang-Mills theory to the dual DDM-form and the dual trace-form. In dual forms, integrands are decomposed in terms of color-ordered one-loop integrands for color scalar theory with proper dual color coefficients.In dual DDM decomposition, The dual color coefficients can be obtained directly from BCJ-form by applying Jacobi-like identities for kinematic factors. In dual trace decomposition, the dual trace factors can be obtained by imposing one-loop KK relations, reflection relation and their relation with the kinematic factors in dual DDM-form.
This work presents concisely the results obtained from the analysis of the two-point function of the gauge field in the $SU(2)$ and $SU(2)times U(1)$ gauge theories, in the Landau gauge, coupled to a scalar Higgs field in the fundamental or adjoint representation. Non-perturbative effects are considered by taking into account the Gribov ambiguity. In general, in both Yang-Mills models the gluon propagator has non-trivial contributions of physical and non-physical modes, which clearly depends on the group representation of the Higgs field. These results were presented during the Fourth Winter Workshop on Non-perturbative Quantum Field Theory, which took place in Sophia-Antipolis - France.
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