Composite Operators and Topological Contributions in Gauge Theory

In $D$-dimensional gauge theory with a kinetic term based on the p-form tensor gauge field, we introduce a gauge invariant operator associated with the composite formed from a electric $(p-1)$-brane and a magnetic $(q-1)$-brane in $D=p+q+1$ spacetime dimensions. By evaluating the partition function for this operator, we show that the expectation value of this operator gives rise to the topological contributions identical to those in gauge theory with a topological Chern-Simons BF term.Comment: 8 pages, Latex fil

Lorentz-Covariant Spin Operator for Spin 1/2 Massive Fields As a Physical Observable

We derive a relativistic-covariant spin operator for massive case directly from space-time symmetry in Minkowski space-time and investigate the physical properties of a derived spin operator. In the derivation we require only two conditions: First, a spin operator should be the generator of the SU(2) little group of the Poincare group. Second, a spin operator should covariantly transform under the Lorentz transformation. A space inversion transformation is shown to play a role to derive a unique relativistic-covariant spin operator, we call the field spin operator, whose eigenvalue labels the spin of a massive (classical) field that provides the irreducible representation space of the Poincare group. The field spin becomes the covariant spin in the covariant Dirac representation, which is shown to be the only spin that describes the Wigner rotation properly in the covariant Dirac representation. Surprisingly, the field spin also gives the non-covariant spin, which is the FW spin for the positive energy state. We also show that the field spin operator is the unique spin operator that generate the (internal) SU(2) little group transformation of the Poincare group properly.Comment: Published version is found in the Journal referenc

Stochastic Processes and the Dirac Equation with External Fields

The equation describing the stochastic motion of a classical particle in 1+1-dimensional space-time is connected to the Dirac equation with external gauge fields. The effects of assigning different turning probabilities to the forward and the backward moving particles in time are discussed.Comment: 9 pages, 1 figure, scalar parts eliminate

Optimal Quantum State Estimation with Use of the No-Signaling Principle

A simple derivation of the optimal state estimation of a quantum bit was obtained by using the no-signaling principle. In particular, the no-signaling principle determines a unique form of the guessing probability independently of figures of merit, such as the fidelity or information gain. This proves that the optimal estimation for a quantum bit can be achieved by the same measurement for almost all figures of merit.Comment: 3 pages, 1 figur

Quantum State Discrimination with General Figures of Merit

We solve the problem of quantum state discrimination with "general (symmetric) figures of merit" for an even number of symmetric quantum bits with use of the no-signaling principle. It turns out that conditional probability has the same form for any figure of merit. Optimal measurement and corresponding conditional probability are the same for any monotonous figure of merit.Comment: 5 pages, 2 figure