General solution of classical master equation for reducible gauge theories

We give the general solution to the classical master equation (S,S)=0 for reducible gauge theories. To this aim, we construct a new coordinate system in the extended configuration space and transform the equation by changing variables. Then it can be solved by an iterative method.Comment: 15 pages; v3: refs. added, section 4 substantially improved, a section added; v4: reference and example adde

A Path Integral Approach To Noncommutative Superspace

A path integral formula for the associative star-product of two superfields is proposed. It is a generalization of the Kontsevich-Cattaneo-Felder's formula for the star-product of functions of bosonic coordinates. The associativity of the star-product imposes certain conditions on the background of our sigma model. For generic background the action is not supersymmetric. The supersymmetry invariance of the action constrains the background and leads to a simple formula for the star-product.Comment: Latex 13 pages. v2: references and footnotes adde

Local well-posedness for membranes in the light cone gauge

In this paper we consider the classical initial value problem for the bosonic membrane in light cone gauge. A Hamiltonian reduction gives a system with one constraint, the area preserving constraint. The Hamiltonian evolution equations corresponding to this system, however, fail to be hyperbolic. Making use of the area preserving constraint, an equivalent system of evolution equations is found, which is hyperbolic and has a well-posed initial value problem. We are thus able to solve the initial value problem for the Hamiltonian evolution equations by means of this equivalent system. We furthermore obtain a blowup criterion for the membrane evolution equations, and show, making use of the constraint, that one may achieve improved regularity estimates.Comment: 29 page

Star products made (somewhat) easier

We develop an approach to the deformation quantization on the real plane with an arbitrary Poisson structure which based on Weyl symmetrically ordered operator products. By using a polydifferential representation for deformed coordinates $\hat x^j$ we are able to formulate a simple and effective iterative procedure which allowed us to calculate the fourth order star product (and may be extended to the fifth order at the expense of tedious but otherwise straightforward calculations). Modulo some cohomology issues which we do not consider here, the method gives an explicit and physics-friendly description of the star products.Comment: 20 pages, v2, v3: comments and references adde

EEG biomarkers of activation of the lymphatic drainage system of the brain during sleep and opening of the blood-brain barrier

The lymphatic drainage system of the brain (LDSB) is the removal of metabolites and wastes from its tissues. A dysfunction of LDSB is an important sign of aging, brain oncology, the Alzheimer's and Parkinson's diseases. The development of new strategies for diagnosis of LDSB injuries can improve prevention of age-related cerebral amyloid angiopathy, neurodegenerative and cerebrovascular diseases. There are two conditions, such as deep sleep and opening of the blood-brain-barrier (OBBB) associated with the LDSB activation. A promising candidate for measurement of LDSB could be electroencephalography (EEG). In this pilot study on rats, we tested the hypothesis, whether deep sleep and OBBB can be an informative platform for an effective extracting of information about the LDSB functions. Using the nonlinear analysis of EEG dynamics and machine learning technology, we discovered that the LDSB activation during OBBB and sleep is associated with similar changes in the EEG θ-activity. The OBBB causes the higher LDSB activation vs. sleep that is accompanied by specific changes in the low frequency EEG activity extracted by the power spectra analysis of the EEG dynamics combined with the coherence function. Thus, our findings demonstrate a link between neural activity associated with the LDSB activation during sleep and OBBB that is an important informative platform for extraction of the EEG-biomarkers of the LDSB activity. These results open new perspectives for the development of technology for the LDSB diagnostics that would open a novel era in the prognosis of brain diseases caused by the LDSB disorders, including OBBB