Zero-dimensional field theory

A study of zero-dimensional theories, based on exact results, is presented. First, relying on a simple diagrammatic representation of the theory, equations involving the generating function of all connected Green's functions are constructed. Second, exact solutions of these equations are obtained for several theories. Finally, renormalization is carried out. Based on the anticipated knowledge of the exact solutionsthe full dependence on the renormalized coupling constant is studied.Comment: 38 pages, LaTe

Zero-dimensional analogue of the global gauge anomaly

A zero-dimensional analogue of Witten's global gauge anomaly is considered. For example, a zero-dimensional reduction of the two-dimensional \SO(2N) Yang-Mills theory with a single Majorana-Weyl fermion in the fundamental representation suffers from this anomaly. Another example is a zero-dimensional reduction of two- and three-dimensional \SU(2N_c) Yang-Mills theories which couple to a single Majorana fermion in the adjoint representation. In this case, any expectation value is either indeterminate or infinite.Comment: 6 pages, uses PTPTeX.cls, the final version to appear in Prog. Theor. Phy

Products and h-homogeneity

Building on work of Terada, we prove that h-homogeneity is productive in the class of zero-dimensional spaces. Then, by generalizing a result of Motorov, we show that for every non-empty zero-dimensional space $X$ there exists a non-empty zero-dimensional space $Y$ such that $X\times Y$ is h-homogeneous. Also, we simultaneously generalize results of Motorov and Terada by showing that if $X$ is a space such that the isolated points are dense then $X^\kappa$ is h-homogeneous for every infinite cardinal $\kappa$. Finally, we show that a question of Terada (whether $X^\omega$ is h-homogeneous for every zero-dimensional first-countable $X$) is equivalent to a question of Motorov (whether such an infinite power is always divisible by 2) and give some partial answers.Comment: 10 page