15,888 research outputs found
Poisson Algebra of Wilson Loops and Derivations of Free Algebras
We describe a finite analogue of the Poisson algebra of Wilson loops in
Yang-Mills theory. It is shown that this algebra arises in an apparently
completely different context; as a Lie algebra of vector fields on a
non-commutative space. This suggests that non-commutative geometry plays a
fundamental role in the manifestly gauge invariant formulation of Yang-Mills
theory. We also construct the deformation of the loop algebra induced by
quantization, in the large N_c limit.Comment: 20 pages, no special macros necessar
Parton Model from Bi-local Solitonic Picture of the Baryon in two-dimensions
We study a previously introduced bi-local gauge invariant reformulation of
two dimensional QCD, called 2d HadronDynamics. The baryon arises as a
topological soliton in HadronDynamics. We derive an interacting parton model
from the soliton model, thus reconciling these two seemingly different points
of view. The valence quark model is obtained as a variational approximation to
HadronDynamics. A succession of better approximations to the soliton picture
are obtained. The next simplest case corresponds to a system of interacting
valence, `sea' and anti-quarks. We also obtain this `embellished' parton model
directly from the valence quark system through a unitary transformation. Using
the solitonic point of view, we estimate the quark and anti-quark distributions
of 2d QCD. Possible applications to Deep Inelastic Structure Functions are
pointed out.Comment: 12 page
System Comparisons between Organic, Biodynamic, Conventional and GMO’s in cotton production & Organic, Biodynamic, Conventional systems in Soya and Wheat in Central India
Over the past 05 years the organic cotton production in India has grown many folds. In the conventional cotton arena the genetically modified cotton is growing at an unprecedented rate. Considering the above factors it was considered necessary to carry out a `System’ comparisons in which the four systems can be compared. Further the research hopes to answer the larger questions
o Put the discussion regarding the benefits and drawbacks of organic agriculture on a rational footing;
o Help to identify challenges for organic agriculture that can then be addressed systematically;
o Provide physical reference points for stakeholders in agricultural research and development and thus support decision-making and agricultural policy dialogue at different levels.
At the farmers level the following outcomes are expected:
What happens to yields of the crops when you stop using fertilizers and pesticides ?
What happens to the pests when you don’t usefertilizers and pesticides?
How do the crops grow when only farmyard manure or compost is used?
Can we effectively control pests in the organic and biodynamic systems using a range of botnaical sprays ?
Are the biodynamic preparations effective?
What are the costs of cultivation of the different systems that we are comparing?
What are impacts on the qulaity of the produce in the different systems ?
What are impacts on t soils of the different systems
The Carath\'eodory-Fej\'er Interpolation Problems and the von-Neumann Inequality
The validity of the von-Neumann inequality for commuting - tuples of
matrices remains open for . We give a partial answer to
this question, which is used to obtain a necessary condition for the
Carath\'{e}odory-Fej\'{e}r interpolation problem on the polydisc
In the special case of (which follows from Ando's theorem as well), this
necessary condition is made explicit. An alternative approach to the
Carath\'{e}odory-Fej\'{e}r interpolation problem, in the special case of
adapting a theorem of Kor\'{a}nyi and Puk\'{a}nzsky is given. As a consequence,
a class of polynomials are isolated for which a complete solution to the
Carath\'{e}odory-Fej\'{e}r interpolation problem is easily obtained. A natural
generalization of the Hankel operators on the Hardy space of
then becomes apparent. Many of our results remain valid for any however, the computations are somewhat cumbersome for and are
omitted. The inequality , where
is the complex Grothendieck constant and
is due to Varopoulos. Here the
supremum is taken over all complex polynomials in variables of degree
at most and commuting - tuples of
contractions. We show that obtaining a slight improvement in the inequality of Varopoulos.
We show that the normed linear space has no isometric
embedding into complex matrices for any and
discuss several infinite dimensional operator space structures on it.Comment: This is my thesis submitted to Indian Institute of Science, Bangalore
on 20th July, 201
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