A Note on the Faddeev–Popov Determinant and Chern–Simmons Perturbation Theory

A refined expression for the Faddeev–Popov determinant is derived for gauge theories quantised around a reducible classical solution. We apply this result to Chern–Simons perturbation theory on compact spacetime 3-manifolds with quantisation around an arbitrary flat gauge field isolated up to gauge transformations, pointing out that previous results on the finiteness and formal metric-independence of perturbative expansions of the partition function continue to hold.     

Asymptotic expansion of the one-loop approximation of the Chern–Simons integral in an abstract Wiener space setting

In an abstract Wiener space setting, we construct a rigorous mathematical model of the one-loop approximation of the perturbative Chern–Simons integral, and derive its explicit asymptotic expansion for stochastic Wilson lines.     

Exotic Yang–Mills Dilaton Gauge Theories

An exotic class of nonlinear p-form non-Abelian gauge theories is studied, arising from the most general allowed covariant deformation of linear Abelian gauge theory for a set of massless 1-form fields and 2-form fields in four dimensions. These theories combine a Chapline–Manton type coupling of the 1-forms and 2-forms, along with a Yang–Mills coupling of the 1-forms, a Freedman–Townsend coupling of the 2-forms, and an extended Freedman–Townsend type coupling between the 1-forms and 2-forms. It is shown that the resulting theories have a geometrically interesting dual formulation that is equivalent to an exotic Yang–Mills dilaton theory involving a nonlinear sigma field. In particular, the nonlinear sigma field couples to the Yang–Mills 1-form field through a generalized Chern class 4-form term.     

Maxwell-Chern-Simons Casimir Force Between Perfectly Conducting Parallel Lines

Using Feynman path integral method we calculate the Casimir force of Maxwell Chern Simons Abelian gauge field between perfectly conducting parallel lines.``     

高阶微商规范不变系统的整体对称性和量子守恒律

分别从Faddeev–Popov(FP)和Faddeev–Senjanovic(FS)路径积分量子化方法对高阶微商规范不变系统导致的位形空间和相空间生成泛函出发,导出规范系统在量子水平下的守恒律,用于高阶Maxwell非AbelChern–Simons(CS)理论.得到了高阶Maxwell非AbelCS理论与标量场耦合系统的量子BRS守恒荷和量子守恒角动量,无论从位形空间或相空间的生成泛函出发,其结果是相同的.并对CS理论中的分数自旋性质给予了讨论.     

关于Khler流形中的闭极小子流形的pinching定理

N~(2m) 为2m维Khler流形,它的全纯截面曲率H_N 在_x∈N~(2m)满足a(x)≤H_N ≤b(x) .M~n为N~(2m)的定向闭极小子流形.通过对第二基本形式模长平方的估计,导出了M~n的J.Simons型积分不等式,推广了已有的结论     

The many vacua of gauged extended supergravities

A novel method is presented which employs advanced numerical techniques used in the engineering sciences to find and study the properties of nontrivial vacua of gauged extended supergravity models. While this method only produces approximate numerical data rather than analytic results, it overcomes the previous limitation of only being able to find vacua with large residual unbroken gauge symmetry groups. The effectiveness of this method is demonstrated by applying it to the technically most challenging D ≥ 3 scalar potential—that of SO(8) × SO(8) gauged Chern–Simons Supergravity in D = 3. Extensive data on the properties of 99 different vacua (92 of them new) of this model are given. Furthermore, techniques are briefly discussed which should allow using this numerical information as an input to the construction of semi-automatic stringent analytic proofs on the locations and properties of vacua. It hence is argued that these combined techniques presumably are powerful enough to systematically map all the nontrivial vacua of every supergravity model.     

The Chern‐Simons Current in Systems of DNA‐RNA Transcriptions

A Chern‐Simons current, coming from ghost and anti‐ghost fields of supersymmetry theory, can be used to define a spectrum of gene expression in new time series data where a spinor field, as alternative representation of a gene, is adopted instead of using the standard alphabet sequence of bases . After a general discussion on the use of supersymmetry in biological systems, we give examples of the use of supersymmetry for living organism, discuss the codon and anti‐codon ghost fields and develop an algebraic construction for the trash DNA, the DNA area which does not seem active in biological systems. As a general result, all hidden states of codon can be computed by Chern‐Simons 3 forms. Finally, we plot a time series of genetic variations of viral glycoprotein gene and host T‐cell receptor gene by using a gene tensor correlation network related to the Chern‐Simons current. An empirical analysis of genetic shift, in host cell receptor genes with separated cluster of gene and genetic drift in viral gene, is obtained by using a tensor correlation plot over time series data derived as the empirical mode decomposition of Chern‐Simons current.     

Multiple Existence of the Multivortex Solutions of the Self-Dual Chern–Simons CP(1) Model on a Doubly Periodic Domain

In this Letter, we investigate multiple existence of the multivortex solutions of the self-dual Chern–Simons CP(1) model on a flat torus for each range of the symmetry breaking parameter. We also study asymptotics of solutions as the Chern–Simons coupling constant goes to zero.