Higher gauge theory -- differential versus integral formulation

The term higher gauge theory refers to the generalization of gauge theory to a theory of connections at two levels, essentially given by 1- and 2-forms. So far, there have been two approaches to this subject. The differential picture uses non-Abelian 1- and 2-forms in order to generalize the connection 1-form of a conventional gauge theory to the next level. The integral picture makes use of curves and surfaces labeled with elements of non-Abelian groups and generalizes the formulation of gauge theory in terms of parallel transports. We recall how to circumvent the classic no-go theorems in order to define non-Abelian surface ordered products in the integral picture. We then derive the differential picture from the integral formulation under the assumption that the curve and surface labels depend smoothly on the position of the curves and surfaces. We show that some aspects of the no-go theorems are still present in the differential (but not in the integral) picture. This implies a substantial structural difference between non-perturbative and perturbative approaches to higher gauge theory. We finally demonstrate that higher gauge theory provides a geometrical explanation for the extended topological symmetry of BF-theory in both pictures.Comment: 26 pages, LaTeX with XYPic diagrams; v2: typos corrected and presentation improve

Topologically Massive Non-Abelian Gauge Theories: Constraints and Deformations

We study the relationship between three non-Abelian topologically massive gauge theories, viz. the naive non-Abelian generalization of the Abelian model, Freedman-Townsend model and the dynamical 2-form theory, in the canonical framework. Hamiltonian formulation of the naive non-Abelian theory is presented first. The other two non-Abelian models are obtained by deforming the constraints of this model. We study the role of the auxiliary vector field in the dynamical 2-form theory in the canonical framework and show that the dynamical 2-form theory cannot be considered as the embedded version of naive non-Abelian model. The reducibility aspect and gauge algebra of the latter models are also discussed.Comment: ReVTeX, 17 pp; one reference added, version published in Phys. Rev.

Parallel transport on non-Abelian flux tubes

I propose a way of unambiguously parallel transporting fields on non-Abelian flux tubes, or strings, by means of two gauge fields. One gauge field transports along the tube, while the other transports normal to the tube. Ambiguity is removed by imposing an integrability condition on the pair of fields. The construction leads to a gauge theory of mathematical objects known as Lie 2-groups, which are known to result also from the parallel transport of the flux tubes themselves. The integrability condition is also shown to be equivalent to the assumption that parallel transport along nearby string configurations are equal up to arbitrary gauge transformations. Attempts to implement this condition in a field theory leads to effective actions for two-form fields.Comment: significant portions of text rewritten, references adde

Temperature-time dependent transmittance, sheet resistance and bonding energy of reduced graphene oxide on soda lime glass.

Reduced graphene oxide coated soda lime glass can act as an alternative transparent/conducting electrode for many opto-electronic applications. However, bonding between the deposited reduced graphene oxide film and the glass substrate is important for achieving better stability of the coating and an extended device lifetime. In the present study, delamination energy of reduced graphene oxide on soda lime glass was quantified by using nanoscratch technique. Graphene oxide was deposited on soda lime glass by dip coating technique and was thermally reduced at different temperatures (100 °C, 200 °C, 300 °C, 400 °C and 500 °C) and treatment time (2 h, 3 h, 4 h, 5 h and 10 h) in Ar (95%) with H2 (5%) atmosphere. An inverse behavior of delamination energy with temperature and treatment time was observed, which could be correlated with the removal of oxygen functional groups. Sheet resistance of the film demonstrated a steady decay with increasing temperature and treatment time. Functional groups attached to the graphene planes have more influence on conductivity than groups attached to the edges. Removal of functional groups could also be related to optical transmittance of the samples. Knowledge generated in this study with respect to delamination energy, sheet resistance and optical transmittance could be extensively used for various opto-electronic applications

Lithium alters expression of RNAs in a type-specific manner in differentiated human neuroblastoma neuronal cultures, including specific genes involved in Alzheimer's disease.

Lithium (Li) is a medication long-used to treat bipolar disorder. It is currently under investigation for multiple nervous system disorders, including Alzheimer's disease (AD). While perturbation of RNA levels by Li has been previously reported, its effects on the whole transcriptome has been given little attention. We, therefore, sought to determine comprehensive effects of Li treatment on RNA levels. We cultured and differentiated human neuroblastoma (SK-N-SH) cells to neuronal cells with all-trans retinoic acid (ATRA). We exposed cultures for one week to lithium chloride or distilled water, extracted total RNA, depleted ribosomal RNA and performed whole-transcriptome RT-sequencing. We analyzed results by RNA length and type. We further analyzed expression and protein interaction networks between selected Li-altered protein-coding RNAs and common AD-associated gene products. Lithium changed expression of RNAs in both non-specific (inverse to sequence length) and specific (according to RNA type) fashions. The non-coding small nucleolar RNAs (snoRNAs) were subject to the greatest length-adjusted Li influence. When RNA length effects were taken into account, microRNAs as a group were significantly less likely to have had levels altered by Li treatment. Notably, several Li-influenced protein-coding RNAs were co-expressed or produced proteins that interacted with several common AD-associated genes and proteins. Lithium's modification of RNA levels depends on both RNA length and type. Li activity on snoRNA levels may pertain to bipolar disorders while Li modification of protein coding RNAs may be relevant to AD

A nilpotent symmetry of quantum gauge theories

For the Becchi-Rouet-Stora-Tyutin (BRST) invariant extended action for any gauge theory, there exists another off-shell nilpotent symmetry. For linear gauges, it can be elevated to a symmetry of the quantum theory and used in the construction of the quantum effective action. Generalizations for nonlinear gauges and actions with higher order ghost terms are also possible.Comment: RevTeX, 9 pages, several changes to include generalizations to quartic and higher ghost terms and non-linear gauges. Abstract changed. Final version to be publishe

Local symmetries of the non-Abelian two-form

It is proposed that a non-Abelian adjoint two-form in BF type theories transform inhomogeneously under the gauge group. The resulting restrictions on invariant actions are discussed. The auxiliary one-form which is required for maintaining vector gauge symmetry transforms like a second gauge field, and hence cannot be fully absorbed in the two-form. But it can be replaced, via a vector gauge transformation, by the usual gauge field, leading to gauge equivalences between different types of theories. A new type of symmetry also appears, one which depends on local functions but cannot be generated by constraints. It is connected to the identity in the limit of a vanishing global parameter, so it should be called a semiglobal symmetry. The corresponding conserved currents and BRST charges are parametrized by the space of flat connections.Comment: RevTeX4, 11 pages, minor correction

Pauli equation and the method of supersymmetric factorization

We consider different variants of factorization of a 2x2 matrix Schroedinger/Pauli operator in two spatial dimensions. They allow to relate its spectrum to the sum of spectra of two scalar Schroedinger operators, in a manner similar to one-dimensional Darboux transformations. We consider both the case when such factorization is reduced to the ordinary 2-dimensional SUSY QM quasifactorization and a more general case which involves covariant derivatives. The admissible classes of electromagnetic fields are described and some illustrative examples are given.Comment: 18 pages, Late