On the theory of point-particles

It is deduced from the conservation of the energy-momentum tensor that if the flow of energy and momentum into a tube surrounding a time-like world-line, on which the field is singular, become singular as the size of the tube is contracted to zero, then the singular terms are necessarily perfect differentials of quantities on the world-line with respect to the proper time along the world-line. The same can be proved of any other tensor, as, for example, the angular-momentum tensor, which is conserved. It is proved from this that for any point-particle whatever having charge, spin or other properties, which need not be specified, it is always possible to deduce exact equations of motion which are finite. It is proved further that if the energy-momentum tensor is altered by the addition of partial Kμ ν σ/partial xσ, where Kμ ν σ is any tensor antisymmetric in ν and σ , then the equations of motion are unaltered, but it is possible to choose Kμ ν σ in such a way as to make the flow of energy and momentum into a given tube non-singular

Phylogenetic Study of Indian Collembolan: an Evaluation in Uttar Pradesh

Springtails (Collembola) from the largest of the three lineages of modern hexapods that are no longer considered insects (the other two are the Protura and Diplura). Although the three orders are sometimes grouped together in a class called Entognatha because they have internal mouthparts, they do not appear to be any more closely related to one another than they all are to insects, which have external mouthparts. Collembolans are omnivorous, free-living organisms that prefer moist conditions. They do not directly engage in the decomposition of organic matter but contribute to it indirectly through the fragmentation of organic matter and the control of soil microbial communities. The word "Collembola" is from the ancient Greek "Glue" and "Peg"; this name was given due to the existence of the collophore, which was previously thought to stick to surfaces in order to stabilize the insect. It is necessary to study the phylogeny of collembolans to explore evolutionary status

Phylogenetic study of Indian Collembolan: an evaluation in Uttar Pradesh

Springtails (Collembola) from the largest of the three lineages of modern hexapods that are no longer considered insects (the other two are the Protura and Diplura). Although the three orders are sometimes grouped together in a class called Entognatha because they have internal mouthparts, they do not appear to be any more closely related to one another than they all are to insects, which have external mouthparts. Collembolans are omnivorous, free-living organisms that prefer moist conditions. They do not directly engage in the decomposition of organic matter but contribute to it indirectly through the fragmentation of organic matter and the control of soil microbial communities. The word "Collembola" is from the ancient Greek "Glue" and "Peg"; this name was given due to the existence of the collophore, which was previously thought to stick to surfaces in order to stabilize the insect. It is necessary to study the phylogeny of collembolans to explore evolutionary status

Coherent state triplets and their inner products

It is shown that if H is a Hilbert space for a representation of a group G, then there are triplets of spaces F_H, H, F^H, in which F^H is a space of coherent state or vector coherent state wave functions and F_H is its dual relative to a conveniently defined measure. It is shown also that there is a sequence of maps F_H -> H -> F^H which facilitates the construction of the corresponding inner products. After completion if necessary, the F_H, H, and F^H, become isomorphic Hilbert spaces. It is shown that the inner product for H is often easier to evaluate in F_H than F^H. Thus, we obtain integral expressions for the inner products of coherent state and vector coherent state representations. These expressions are equivalent to the algebraic expressions of K-matrix theory, but they are frequently more efficient to apply. The construction is illustrated by many examples.Comment: 33 pages, RevTex (Latex2.09) This paper is withdrawn because it contained errors that are being correcte

On Batalin-Vilkovisky Formalism of Non-Commutative Field Theories

We apply the BV formalism to non-commutative field theories, introduce BRST symmetry, and gauge-fix the models. Interestingly, we find that treating the full gauge symmetry in non-commutative models can lead to reducible gauge algebras. As one example we apply the formalism to the Connes-Lott two-point model. Finally, we offer a derivation of a superversion of the Harish-Chandra-Itzykson-Zuber integral.Comment: 20 pages, LaTeX. v2: minor corrections. v3: Added an Appendix about Harish-Chandra-Itzykson-Zuber integrals. v4: Added Reference

Level Repulsion in Constrained Gaussian Random-Matrix Ensembles

Introducing sets of constraints, we define new classes of random-matrix ensembles, the constrained Gaussian unitary (CGUE) and the deformed Gaussian unitary (DGUE) ensembles. The latter interpolate between the GUE and the CGUE. We derive a sufficient condition for GUE-type level repulsion to persist in the presence of constraints. For special classes of constraints, we extend this approach to the orthogonal and to the symplectic ensembles. A generalized Fourier theorem relates the spectral properties of the constraining ensembles with those of the constrained ones. We find that in the DGUEs, level repulsion always prevails at a sufficiently short distance and may be lifted only in the limit of strictly enforced constraints.Comment: 20 pages, no figures. New section adde

Supersymmetric Extensions of Calogero--Moser--Sutherland like Models: Construction and Some Solutions

We introduce a new class of models for interacting particles. Our construction is based on Jacobians for the radial coordinates on certain superspaces. The resulting models contain two parameters determining the strengths of the interactions. This extends and generalizes the models of the Calogero--Moser--Sutherland type for interacting particles in ordinary spaces. The latter ones are included in our models as special cases. Using results which we obtained previously for spherical functions in superspaces, we obtain various properties and some explicit forms for the solutions. We present physical interpretations. Our models involve two kinds of interacting particles. One of the models can be viewed as describing interacting electrons in a lower and upper band of a one--dimensional semiconductor. Another model is quasi--two--dimensional. Two kinds of particles are confined to two different spatial directions, the interaction contains dipole--dipole or tensor forces.Comment: 21 pages, 4 figure

Explicit solution of the quantum three-body Calogero-Sutherland model

Quantum integrable systems generalizing Calogero-Sutherland systems were introduced by Olshanetsky and Perelomov (1977). Recently, it was proved that for systems with trigonometric potential, the series in the product of two wave functions is a deformation of the Clebsch-Gordan series. This yields recursion relations for the wave functions of those systems. In this note, this approach is used to compute the explicit expressions for the three-body Calogero-Sutherland wave functions, which are the Jack polynomials. We conjecture that similar results are also valid for the more general two-parameters deformation introduced by Macdonald.Comment: 10 page

Description of Digestive Tract of Notonecta glauca Linn., the Indian Backswimmer

The backswimmer, Notonecta glauca Linnaeus for the morphological and bioecological investigations were collected during, the months of July to November from various ponds, ditches, and canals of Mathura and its nearby areas. These bugs were easily recognised due to their oblong, convex body; large eye; short four jointed antennae; four joined rostrum; large triangular scutellum; anterior legs inserted at the posterior margin of the pronotum; moderate long pronotum; last joint of antennae being must shorter than the penultimate one and posterior tarsi being without unguiculi. These insects are commonly known as water boatman and backswimmer as they swim on their backs with the help of their long oar-like hind legs. They are extremely predaceous and are very common around the edges of freshwater reservoirs such as ponds, lakes, and streams throughout India and the way be easily taken with a net. In the present study, a detailed description of the digestive tract of the aforesaid insect has been noted