Modern Physics Letters A

We study small x divergences in boost invariant similarity renormalization group approach to light-front QCD in a heavy quark–antiquark state. With the boost invariance maintained, the infrared divergences do not cancel out in the physical states, contrary to previous studies where boost invariance was violated by a choice of a renormalization scale. This may be an indication that the zero mode, or nontrivial light-cone vacuum structure, might be important for recovering full Lorentz invariance.

We consider sectionally-elliptical conical space–times and compute the energy–momentum tensor of the source generating such configurations. It turns out that the problem can be reduced to the calculation of the Gaussian curvature of the bidimensional elliptical cone defined by the foliation t = const., z = const. We then employ the method of smoothing the conical singularity by taking a sequence of regular bidimensional manifolds in order to compute the curvature. Finally, we conclude that the gravitational effects produced by sectionally-elliptical and sectionally-circular conical space–times are completely equivalent.

In the framework of the intermediate vector boson theory, developed in the early 1960s, T*-product induces false nonconservation of angular momentum in the π→μ+ν decay. It points out that if correctly formulated, the pion cannot decay and clarifies how this problem can be resolved in the electroweak theory. In this consideration, some unexpected facts are found.

The (group and spin space) matrix Hamiltonian describing the dynamics of a non-relativistic spin-½ particle moving in a static, but spatially dependent, non-Abelian magnetic field in two spatial dimensions is shown to take the form of an anticommutator of a nilpotent operator and its Hermitian conjugate. Consequently, the (group space) matrix Hamiltonians for the two different spin projections form partners of a supersymmetric quantum mechanical system. The resulting supersymmetry algebra is exploited to explicitly construct the exact zero energy ground state wave function(s) for the system. The remaining eigenstates and eigenvalues of the two partner Hamiltonians form positive energy degenerate pairs.

We reconsider the CP¹ model with the Hopf term by using the Batalin–Fradkin–Tyutin (BFT) scheme, which is an improved version of the Dirac quantization method. We also perform a semiclassical quantization of the topological charge Q sector by exploiting the collective coordinates to explicitly show the fractional spin statistics.

We show that the system where CP¹ model coupled to Hopf term can reveal fractional spin in a collective coordinate quantization scheme, provided that one makes a transition to physically inequivalent sector within the same solitonic sector characterized by a nonvanishing topological number.

The necessary and sufficient conditions are established for the second-class constraint surface to be (an almost) Kähler manifold. The deformation quantization for such systems is mentioned resulting in the Wick-type symbols for the respective Dirac brackets.