On the Gauge-invariant Functional Measure for Gauge Fields on CP^2

We introduce a general parametrization for nonabelian gauge fields on the four-dimensional space ${\mathbb{CP}}^2$. The volume element for the gauge-orbit space or the space of physical configurations is then investigated. The leading divergence in this volume element is obtained in terms of a higher dimensional Wess-Zumino-Witten action, which has previously been studied in the context of K\"ahler-Chern-Simons theories. This term, it is argued, implies that one needs to introduce a dimensional parameter to specify the integration measure, a step which is a nonperturbative version of the well-known dimensional transmutation in four-dimensional gauge theories.Comment: 16 pages, affiliation added, typos correcte

The Quantum Effective Action, Wave Functions and Yang-Mills (2+1)

We explore the relationship between the quantum effective action and the ground state (and excited state) wave functions of a field theory. Applied to the Yang-Mills theory in 2+1 dimensions, we find the leading terms of the effective action from the ground state wave function previously obtained in the Hamiltonian formalism by solving the Schrodinger equation.Comment: 16 pages, expanded discussion section, added references, version accepted for Phys. Rev.

Quantum mechanics on the noncommutative plane and sphere

We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point, where the density of states becomes infinite, for the value of the magnetic field equal to the inverse of the noncommutativity parameter. The Landau problem on the noncommutative two-sphere is also solved and compared to the plane problem.Comment: 12 pages, no figures; references adde