Quantum field theory, solitons and other quantum dynamical systems

晶格(规范)理论和任意子的数值模拟：我们希望研究规范场理论，将U(1)规范理论的分析推广到三维欧氏四面体晶格上。现在我们想把我们的结果推广到Z3格点规范理论，这是一个非阿贝尔SU(3)规范理论的中心截断。四面体晶格提供了一种新颖性，它允许测量磁通量为三分之一的磁通量管。我们希望在这一理论中看到限制。我们还希望继续研究这个模型中的任意子。计算更高的维里系数和任意子气体的其他热力学参数是一个有趣的问题。 共形引力：我们希望继续我们对共形引力的研究，这是一种替代的引力理论，可以解释缺失的物质，而不需要暗物质。我们证明了对应于自发共形对称破缺的孤子的存在。我们还证明了理论中的引力波不携带任何能量到二阶，相应的一阶波是纯规范伪影。这一事实支持了该理论可以始终如一地量子化的观点。 弦激发的宇宙学中的真空不稳定性和孤子：在宇宙学中，弦理论的大胆新提议对应于作为弦理论的结果而获得膨胀的宇宙学场景。印度理工学院孟买分校和乌得梅大学的研究人员正在进行合作，探索一些关于稳定性的现有弦理论建议的稳健性，以期在高能物理以及凝聚态物理中出现的不寻常状态的物质的现象学应用中。弦宇宙学模型的不稳定性将对弦理论在宇宙学中的可行性产生深远的影响。

NUMERCIAL SIMULATIONS IN LATTICE (GAUGE) THEORY AND ANYONS: We wish to study of gauge field theory extending the analysis of U(1) gauge theory on a tetrahedral lattice in 3 Euclidean dimensions. Now we wish to extend our results to a Z3 lattice gauge theory a truncation of a non-abelian SU(3) gauge theory to its centre. The tetrahedral lattice affords the novelty that it allows for gauge flux tubes of magnetic flux one third. We hope to see confinement in this theory. Also we wish to continue our study of anyons in this model. It is an interesting question to compute higher virial coefficients and other thermodynamic quantities of an anyon gas. CONFORMAL GRAVITY: We wish to continue our study of conformal gravity, which is an alternative theory of gravity that can explain missing matter without the need for dark matter. We have proven the existence of solitons which correspond to spontaneous conformal symmetry breaking. We have also shown that gravitational waves in the theory do not carry any energy to second order, and the corresponding first order waves are pure gauge artefacts. This fact lends credence to the idea that the theory can be consistently quantized. VACUUM INSTABILITY AND SOLITONS IN STRING INSPIRED COSMOLOGY: Bold new proposals of string theory in cosmology correspond to obtaining the inflationary cosmological scenario as a consequence of string theory. There exists an ongoing collaboration between researchers at the IIT Bombay and UdeM exploring the robustness of some of the existing string theory proposals regarding stability with a view to phenomenological applications in high-energy physics as well as to unusual states of matter occurring in condensed matter physics. Instability of string cosmology models would have far reaching consequences on the viability of string theory in cosmology.