Reducible systems and embedding procedures in the canonical formalism

We propose a systematic method of dealing with the canonical constrained structure of reducible systems in the Dirac and symplectic approaches which involves an enlargement of phase and configuration spaces, respectively. It is not necessary, as in the Dirac approach, to isolate the independent subset of constraints or to introduce, as in the symplectic analysis, a series of lagrange multipliers-for-lagrange multipiers. This analysis illuminates the close connection between the Dirac and symplectic approaches of treating reducible theories, which is otherwise lacking. The example of p-form gauge fields (p=2,3) is analyzed in details.Comment: Latex 23 pages, some corrections and improvements in the text. To appear in Annals of Physic

Evaluating the epidemiology and needs of oral cancer patients from Aurangabad district, Maharashtra, India

Background: India is facing burden of non-communicable diseases and oral cancer is one of the leading public health issue. This is a descriptive study from Aurangabad district, Maharashtra, India to evaluate epidemiologic profile of oral cancer patients who underwent treatment during 2012 to 2016.Methods: Demographic and clinical profile of 500 patients was recorded with validated questionnaire.Results: With male: female ratio was 2.90:1; the mean age of the patients of oral cancer was 47.73 years. Tobacco consumption was the leading cause associated with statistically significant association (p value < 0.000) among the gender and tobacco use suggesting men are more prone to use tobacco than women. 74% patients received satisfactory treatment and all the patients strongly reported need of doctor’s advice, family support, discontinuation of substance abuse habits and financial help. Patients reported the need of acceptance by society and good diet and nutrition. However, many denied the need of psychological counseling and regular check-up. There was statistically significant association (p value < 0.001) found among the gender and needs for good diet and nutrition, psychological counseling, regular check-up, discontinuation of tobacco habits. Statistically significant association (p value < 0.001) found among the occupation and needs for good diet and nutrition, psychological counseling and acceptance by society.Conclusions: The study projects the epidemiology and focuses on the needs of the patients which require the specific attention and efforts through patient’s education and awareness

The Symmetries of Nature

The study of the symmetries of nature has fascinated scientists for eons. The application of the formal mathematical description of symmetries during the last century has produced many breakthroughs in our understanding of the substructure of matter. In this talk, a number of these advances are discussed, and the important role that George Sudarshan played in their development is emphasize

The spin-statistics connection in classical field theory

The spin-statistics connection is obtained for a simple formulation of a classical field theory containing even and odd Grassmann variables. To that end, the construction of irreducible canonical realizations of the rotation group corresponding to general causal fields is reviewed. The connection is obtained by imposing local commutativity on the fields and exploiting the parity operation to exchange spatial coordinates in the scalar product of classical field evaluated at one spatial location with the same field evaluated at a distinct location. The spin-statistics connection for irreducible canonical realizations of the Poincar\'{e} group of spin $j$ is obtained in the form: Classical fields and their conjugate momenta satisfy fundamental field-theoretic Poisson bracket relations for 2$j$ even, and fundamental Poisson antibracket relations for 2$j$ oddComment: 27 pages. Typos and sign error corrected; minor revisions to tex

Gauge invariances vis-{\'a}-vis Diffeomorphisms in second order metric gravity: A new Hamiltonian approach

A new analysis of the gauge invariances and their unity with diffeomorphism invariances in second order metric gravity is presented which strictly follows Dirac's constrained Hamiltonian approach.Comment: 6 Pages, revTex, paper modified substantiall

Quantum theory of magnetic electron lenses based on the Dirac equation

A quantum theory of magnetic electron lenses based on a convenient formulation of the Dirac theory is outlined. It is shown that the passage from the conventional scalar theory to the spinor theory can be accomplished through a simple algebraic rule in analogy with the passage from scalar to vector light optics

Hamilton's theory of turns generalized to Sp(2,R)

We present a generalization of Hamilton's geometric theory of turns, originally invented for SU(2), to the noncompact group Sp(2,R) relevant in a variety of physical applications