Space Of Gauge Potentials Research Articles

Topology and Elastic Theory of DNA Molecule

We have determined at this point that the DNA molecule may be considered as a long chain of an antiferromagnetic spin adjustment when the spin is accurate to be situated on the axis of the supercoil. Furthermore, we examine that as two polynucleotide chains are coiled regarding the same axis with an exact helical sense in a DNA molecule, this can be considered as if a spin with a specific point of reference is confined on the axis of the coil such that two contiguous coils have reverse direction of the spin. Actually, with each turn two strands move in the opposite side of the axis and so the spin direction accredited for the two adjacent coils should be opposite to each other. As soon as spins are defined in the Lie algebra of SU (2) the linking number can be established from the Chern-Simon’s topology linked with the spin system. We shall study the topological property of a DNA supercoil from the angle of such a spin chain. Also, we shall put together the elastic properties of a DNA molecule from on analysis of the spin degrees of freedom. As spins are considered at this time as gauge currents formulated from SU (2) gauge fields we map the elastic properties onto the space of gauge potentials. In quantum field theory the divergence of this current is non-zero which gives increase to chiral anomaly caused by chiral balance contravention.

Gravitationally induced zero modes of the Faddeev-Popov operator in the Coulomb gauge for Abelian gauge theories

It is shown that on curved backgrounds, the Coulomb gauge Faddeev-Popov operator can have zero modes even in the abelian case. These zero modes cannot be eliminated by restricting the path integral over a certain region in the space of gauge potentials. The conditions for the existence of these zero modes are studied for static spherically symmetric spacetimes in arbitrary dimensions. For this class of metrics, the general analytic expression of the metric components in terms of the zero modes is constructed. Such expression allows to find the asymptotic behavior of background metrics, which induce zero modes in the Coulomb gauge, an interesting example being the three dimensional Anti de-Sitter spacetime. Some of the implications for quantum field theory on curved spacetimes are discussed.

Cohomology and topological anomalies

The chiral anomaly can be considered as an object defined either on the space of gauge potentials or on the orbit space. We will discuss the relation between the two descriptions. We will also relate to the cohomology of the group of gauge transformations.

Quantizing Yang-Mills theory: From Parisi-Wu stochastic quantization to a global path integral

Based on a generalization of the stochastic quantization scheme we recently proposed a generalized, globally defined Faddeev-Popov path integral density for the quantization of Yang-Mills theory. In this talk first our approach on the whole space of gauge potentials is shortly reviewed; in the following we discuss the corresponding global path integral on the gauge orbit space relating it to the original Parisi-Wu stochastic quantization scheme.

Global path integral quantization of Yang–Mills theory

Based on a generalization of the stochastic quantization scheme recently a modified Faddeev–Popov path integral density for the quantization of Yang–Mills theory was derived, the modification consisting in the presence of specific finite contributions of the pure gauge degrees of freedom. Due to the Gribov problem the gauge fixing can be defined only locally and the whole space of gauge potentials has to be partitioned into patches. We propose a global path integral density for the Yang–Mills theory by summing over all patches, which can be proven to be manifestly independent of the specific local choices of patches and gauge fixing conditions, respectively. In addition to the formulation on the whole space of gauge potentials we discuss the corresponding global path integral on the gauge orbit space relating it to the original Parisi–Wu stochastic quantization scheme and to a proposal of Stora, respectively.

Kähler-Chern-Simons theory and symmetries of anti-self-dual gauge fields

Kähler-Chern-Simons theory, which was proposed as a generalization of ordinary Chern-Simons theory, is explored in more detail. The theory describes anti-self-dual instantons on a four-dimensional Kähler manifold. The phase space is the space of gauge potentials, whose symplectic reduction by the constraints of anti-self-duality leads to the moduli space of instantons. We show that infinitesimal Bäcklund transformations, previously related to “hidden symmetries” of instantons, are canonical transformations generated by the anti-self-duality constraints. The quantum wave functions naturally lead to a generalized Wess-Zumino-Witten action, which in turn has associated chiral current algebras. The dimensional reduction of the anti-self-duality equations leading to integrable two-dimensional theories is briefly discussed in this framework.

Structure of the space of reducible connections for Yang-Mills theories

The geometrical structure of the gauge equivalence classes of reducible connections are investigated. The general procedure to determine the set of orbit types (strata) generated by the action of the gauge group on the space of gauge potentials is given. In the so obtained classification, a stratum, containing generically certain reducible connections, corresponds to a class of isomorphic subbundles given by an orbit of the structure and gauge group. The structure of every stratum is completely clarified. A nonmain stratum can be understood in terms of the main stratum corresponding to a stratification at the level of a subbundle.

Wilson-loop instantons.

Wilson-loop symmetry breaking is considered on a space-time of the form M4 x K, where M4 is a four-dimensional space-time and K is an internal space with nontrivial and finite fundamental group. It is shown in a simple model that the different vacua obtained by breaking a non-Abelian gauge group by Wilson loops are separated in the space of gauge potentials by a finite energy barrier. An interpolating gauge configuration is then constructed between these vacua and shown to have minimum energy. Finally some implications of this construction are discussed.

Screening of classical color

Color screening of static, spherically symmetric sources by classical SU(2) Yang-Mills fields is studied. Owing to the presence of a source, the global color symmetry SO(3) is broken to U(1), and the function space of gauge potentials is partitioned into topologically inequivalent sectors. The extent and nature of screening of the external source is shown to be dependent upon the associated topological charge $M$ of the source-field system. This is illustrated in the case of a $\ensuremath{\delta}$-shell distribution of external color. For systems of unit topological charge, static, spherically symmetric, total screening solutions of the field equations are constructed, extending the work of Jackiw, Jacobs, and Rebbi. However, in the $M=0$ sector, self-consistent arguments are presented which suggest that the external charge is never totally screened and, when the external charge exceeds a certain critical value, the minimum of the energy functional breaks the rotational symmetry of the Lagrangian.