We investigate the effective action of the Polyakov loop with spatial variations. We expand the effective action not in powers of derivatives or momenta, but in powers of variational amplitudes. At one-loop order the results suggest that the instability towards the confining vacuum may be caused by the variational terms. 11.10. Wx, 12.38.Aw

The Casimir force has its origin in finite modification of the infinite zero-point energy induced by a specific boundary condition for the spatial configuration. In terms of the imaginary-time formalism at finite temperature, the root of Planck's law of radiation can be traced back to finite modification of the infinite vacuum energy induced by the periodic boundary condition in the temporal direction. We give the explicit conversion from the Casimir force to Planck's law of radiation, which shows the apparent correspondence between the system bounded by parallel conducting plates and the thermodynamic system. The temperature inversion symmetry and the duality relation in the thermodynamics are also discussed. We conclude that the effective temperature characterized by the spatial extension should no longer be regarded as genuine temperature.

In soliton models expressed in terms of the nonlinear chiral field, the electric current has an anomalous gauge-field contribution as the baryon current does. We study the spin polarized Skyrmions coupled with the electromagnetic field via the gauged Wess-Zumino term and calculate configurations of the Skyrmion and the gauge field with boundary conditions to ensure the physical charge number for baryons. Although the electromagnetic field via the gauged Wess-Zumino term affects physical quantities in small amounts, we find that the magnetic field forms a dipole structure owing to a circular electric current around the spin-quantization axis of the soliton. This is understood on an analogy with the Meissner effect in the super conductor. The electric-charge distributions turn out to have characteristic structures depending on the total charge, which suggests the intrinsic deformation of baryons due to orbital motions of the constituents.