Modern Physics Letters A

We present some methods which aim to express multi-leg and multi-loop Feynman diagrams in a form suited for a fast and reliable numerical evaluation, without any restriction on masses and phase-space region of the process.

We calculate the quantum statistical force acting on a partition wall that divides a one-dimensional box into two halves. The two half boxes containing the same (fixed) number of noninteracting bosons are kept at the same temperature, and admit the same boundary conditions at the outer walls; the only difference is the distinct boundary conditions imposed at the two sides of the partition wall. The net force acting on the partition wall is nonzero at zero temperature and remains almost constant for low temperatures. As the temperature increases, the force starts to decrease considerably, but after reaching a minimum it starts to increase, and tends to infinity with a square-root-of-temperature asympotics. This example demonstrates clearly that distinct boundary conditions cause remarkable physical effects for quantum systems.

The well-known topological monopoles originally investigated by 't Hooft and Polyakov are known to arise in classical Yang–Mills–Higgs theory. With a pure gauge theory, it is known that the classical Yang–Mills field equation do not have such finite energy configurations. Here we argue that such configurations may arise in a semi-quantized Yang–Mills theory, where the original gauge group, SU(3), is reduced to a smaller gauge group, SU(2), and with some combination of the coset fields of the SU(3) to SU(2) reduction acting as effective scalar fields. The procedure is called semi-quantized since some of the original gauge fields are treated as quantum degrees of freedom, while others are postulated to be effectively described as classical degrees of freedom. Some speculation is offer on a possible connection between these monopole configurations and the confinement problem, and the nucleon spin puzzle.

We show that the large, direct CP-violation parameter A_ππ=-C_ππ, reported by the BELLE collaboration in the decays , implies an unusual situation in which the presence of a very large difference between two strong-interaction phases (~ -110°) plays an essential role. We make the demonstration within a model of strong, two-body quasi-elastic interactions between physical hadrons. The model can accommodate a large difference between two strong-interaction phases, for which it provides a natural enhancement.

In the framework of a relativistic constituent quark model we propose some confining potentials behaving like r and r² at large distances which allow for analytical solutions of the Dirac equation. The solutions are given in explicit form.

A class of metrics g_ab(xⁱ) describing spacetimes with horizons (and associated thermodynamics) can be thought of as a limiting case of a family of metrics g_ab(xⁱ;λ)without horizons when λ→0. We construct specific examples in which the curvature corresponding g_ab(xⁱ;λ) becomes a Dirac delta function and gets concentrated on the horizon when the limit λ→0 is taken, but the action remains finite. When the horizon is interpreted in this manner, one needs to remove the corresponding surface from the Euclidean sector, leading to winding numbers and thermal behavior. In particular, the Rindler spacetime can be thought of as the limiting case of (horizon-free) metrics of the form [g₀₀=ε²+a²x²; g_μν=-δ_μν] or [g₀₀=-g^xx=(ε²+4a²x²)^1/2, g_yy=g_zz=-1] when ε→0. In the Euclidean sector, the curvature gets concentrated on the origin of t_E-x plane in a manner analogous to Aharanov–Bohm effect (in which the vector potential is a pure gauge everywhere except at the origin) and the curvature at the origin leads to nontrivial topological features and winding number.

In this paper, we present a general modified dispersion relation derived from q-deformed noncommutative theory and apply it to the ultrahigh energy cosmic ray and the TeV-photon paradoxes — threshold anomalies. Our purpose is not only trying to solve these puzzles by noncommutative theory but also to support noncommutative theory through the coincidence of the region in the parameter space for resolving the threshold anomalies with the one from the q-deformed noncommutative theory.