The detailed analysis is presented of an event which is interpreted as the mesonic cascade decay of a double hyperfragment produced by the capture of a E~ hyperon on a light emulsion nucleus. The most likely interprétations of the double hyperfragment are those in terms of either ^^Be'» or ^^Be".

Taking the simple examples of an Abelian 1-form gauge theory in two (1+1)-dimensions, a 2-form gauge theory in four (3+1)-dimensions and a 3-form gauge theory in six (5+1)-dimensions of space–time, we establish that such gauge theories respect, in addition to the gauge symmetry transformations that are generated by the first-class constraints of the theory, additional continuous symmetry transformations. We christen the latter symmetry transformations as the dual-gauge transformations. We generalize the above gauge and dual-gauge transformations to obtain the proper (anti-)BRST and (anti-)dual-BRST transformations for the Abelian 3-form gauge theory within the framework of BRST formalism. We concisely mention such symmetries for the 2D free Abelian 1-form and 4D free Abelian 2-form gauge theories and briefly discuss their topological aspects in our present endeavor. We conjecture that any arbitrary Abelian p-form gauge theory would respect the above cited additional symmetry in D = 2p(p = 1, 2, 3, …) dimensions of space–time. By exploiting the above inputs, we establish that the Abelian 3-form gauge theory, in six (5+1)-dimensions of space–time, is a perfect model for the Hodge theory whose discrete and continuous symmetry transformations provide the physical realizations of all aspects of the de Rham cohomological operators of differential geometry. As far as the physical utility of the above nilpotent symmetries is concerned, we demonstrate that the 2D Abelian 1-form gauge theory is a perfect model of a new class of topological theory and 4D Abelian 2-form as well as 6D Abelian 3-form gauge theories are the field theoretic models for the quasi-topological field theory.

In addition to the usual supersymmetric (SUSY) continuous symmetry transformations for the general N = 2 SUSY quantum mechanical model, we show the existence of a set of novel discrete symmetry transformations for the Lagrangian of the above SUSY quantum mechanical model. Out of all these discrete symmetry transformations, a unique discrete transformation corresponds to the Hodge duality operation of differential geometry and the above SUSY continuous symmetry transformations (and their anticommutator) provide the physical realizations of the de Rham cohomological operators of differential geometry. Thus, we provide a concrete proof of our earlier conjecture that any arbitrary N = 2 SUSY quantum mechanical model is an example of a Hodge theory where the cohomological operators find their physical realizations in the language of symmetry transformations of this theory. Possible physical implications of our present study are pointed out, too.Keywords N = 2 supersymmetric quantum mechanics · superspace approach · continuous and discrete symmetries · de Rham cohomological operators · Hodge duality operation · a physical model for the Hodge theory PACS 11.30.Pb · 03.65.-w · 02.40.-k

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Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we demonstrate the existence of the novel off-shell nilpotent (anti-)dual-BRST symmetries in the context of a six (5 + 1)-dimensional (6D) free Abelian 3-form gauge theory. Under these local and continuous symmetry transformations, the total gauge-fixing term of the Lagrangian density remains invariant. This observation should be contrasted with the offshell nilpotent (anti-)BRST symmetry transformations, under which, the total kinetic term of the theory remains invariant. The anticommutator of the above nilpotent (anti-)BRST and (anti-)dual-BRST transformations leads to the derivation of a bosonic symmetry in the theory. There exists a discrete symmetry transformation in the theory which provides a thread of connection between the nilpotent (anti-)BRST and (anti-)dual-BRST transformations. This theory is endowed with a ghost-scale symmetry, too. We discuss the algebra of these symmetry transformations and show that the structure of the algebra is reminiscent of the algebra of de Rham cohomological operators of differential geometry.