Title: Symmetries of a 3D Field-Theoretic Model Show Chinese title

Title: 三维场论模型的对称性

Abstract: We discuss the discrete as well as the continuous symmetry transformations for a three $(2+1)$-dimensional $(3D)$ combined system of the free Abelian 1-form and 2-form gauge theories within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism and establish their relevance in the context of the algebraic structures that are obeyed by the de Rham cohomological operators of differential geometry. In fact, our present field-theoretic system respects six continuous symmetry transformations and a couple of very useful discrete duality symmetry transformations. Out of the above six continuous symmetry transformations four are off-shell nilpotent (i.e. fermionic) in nature and two are bosonic. The algebraic structures, obeyed by the symmetry operators, are reminiscent of the algebra satisfied by the de Rham cohomological operators. Hence, our present $3D$ field-theoretic system provides a perfect example for Hodge theory where there is convergence of ideas from the physical aspects of the BRST formalism and mathematical ingredients that are connected with the cohomological operators of differential geometry at the algebraic level. One of the highlights of our present investigation is the appearance of a pseudo-scalar field in our theory (on the symmetry ground alone) which carries the negative kinetic term. Thus, it is one of the possible candidates for the ``phantom" fields of the cyclic, bouncing and self-accelerated cosmological models of the Universe. Show Chinese abstract

Abstract: 我们讨论在Becchi-Rouet-Stora-Tyutin (BRST)形式框架下，自由阿贝尔1-形式和2-形式规范理论的三维$(2+1)$-维$(3D)$组合系统的离散和连续对称变换，并确立它们在微分几何的de Rham上同调算子所服从的代数结构中的相关性。 事实上，我们目前的场论系统尊重六种连续对称变换和一对非常有用的离散对偶对称变换。 在上述六种连续对称变换中，四种是具有非壳态幂零性质（即费米子性质）的，两种是玻色子性质的。 对称算子所服从的代数结构类似于de Rham上同调算子所满足的代数。 因此，我们目前的$3D$场论系统为Hodge理论提供了一个完美的例子，其中物理方面的BRST形式的观念与微分几何的上同调算子相关的数学要素在代数层面上有所交汇。 我们目前研究的一个亮点是，在对称性的基础上，我们的理论中出现了伪标量场，它携带负的动能项。 因此，它是宇宙循环、反弹和自加速宇宙模型中“幽灵”场的可能候选之一。