General heat kernel coefficients for massless free spin-3/2 Rarita-Schwinger field

We review the general heat kernel method for the Dirac spinor field as an elementary example in any arbitrary background. We, then compute the first three Seeley-DeWitt coefficients for the massless free spin-3/2 Rarita-Schwinger field without imposing any limitations on the background geometry.Comment: 13 page

An approach to dynkin diagrams associated with KAC-moody superalgebra

In the present project report, a sincere report has been made to construct and study the basic portions related to Simple Lie Algebras, Lie superalgebras and Kac-Moody (super-) algebras and their corresponding Dynkin Diagrams. In chapter-1, I have given the precise definitions of Lie Algebra and some of the terms related to Lie algebra, i.e. subalgebras, ideals, commutativity, solvability, nilpotency etc. Also, I have done the classifications of Classical Lie algebras. In chapter-2, I made a review over the basics of Representation Theory, i.e. structure constants, modules, reflections in a Euclidean space, root systems (simple roots) and their corresponding root diagrams. Then I have discussed the formation of Dynkin Diagrams associated with the roots of the simple lie algebras. After that, in chapter-3, the introductory parts of Lie superalgebras, i.e. Z2 graded algebra, definition of lie superalgebra, modules, the killing form, root systems and simple root systems (distinguished root systems) are addressed. In this section, also the classifications of simple lie superalgebras are plotted and the Dynkin Diagrams related to the Basic Lie superalgebras are presented. In chapter-4, I gave the necessary theory based on Kac-Moody Lie superalgebras and their classifications. Then the definition of the extended Dynkin diagrams for Affinization of Kac-Moody superalgebras and the Dynkin Diagrams associated with the affine Kac-Moody superalgebras are provided

Using time-dependent indirect CPCP asymmetries to measure TT and CPTCPT violation in B0B^0-Bˉ0{\bar B}^0 mixing

Quantum field theory, which is the basis for all of particle physics, requires that all processes respect $CPT$ invariance. It is therefore of paramount importance to test the validity of $CPT$ conservation. In this Letter, we show that the time-dependent, indirect $CP$ asymmetries involving $B$ decays to a $CP$ eigenstate contain enough information to measure $T$ and $CPT$ violation in $B^0$-${\bar B}^0$ mixing, in addition to the standard $CP$-violating weak phases. Entangled $B^0{\bar B}^0$ states are not required (so that this analysis can be carried out at LHCb, as well as at the $B$ factories), penguin pollution need not be neglected, and the measurements can be made even if the $B^0$-${\bar B}^0$ width difference vanishes.Comment: 10 pages, no figures, changes: removed almost all discussion of what can and cannot be done with the method of entangled states; explained that CPT- and T-violating parameters also contribute to CP-violating effects; reorganized the presentation of the paper; added footnotes and reference

The study of multifragmentation around transition energy in intermediate energy heavy-ion collisions

Fragmentation of light charged particles is studied for various systems at different incident energies between 50 and 1000 MeV/nucleon. We analyze fragment production at incident energies above, below and at transition energies using the isospin dependent quantum molecular dynamics(IQMD) model. The trends observed for the fragment production and rapidity distributions depend upon the incident energy, size of the fragments, composite mass of the reacting system as well as on the impact parameter of the reaction. The free nucleons and light charged particles show continous homogeneous changes irrespective of the transition energies indicating that there is no relation between the transition energy and production of the free as well as light charged particles