International Journal of Modern Physics A

The geometrical and quantum-mechanical basis for Davies’ and Unruh’s acceleration temperature is traced to a type of quantum-mechanical (“achronal”) spin. Its existence and definition are based on pairs of causally disjoint accelerated frames. For bosons the expected spin vector of monochromatic particles is given by the “Planckian power” and the “r.m.s. thermal fluctuation” spectra. Under space–time translation the spin direction precesses around that “Planckian” vector. By exhibiting the conserved achronal spin four-current, we extend the identification of achronal spin from single quanta to multiparticle systems. Total achronal spin conservation is also shown to hold, even in the presence of quadratic interactions.

In addition, the Lorentz invariance of the acceleration temperature is made explicit by the introduction of pairs of “spherical” Rindler frames.

In the framework of a specific scheme of the QCD sum rules for S wave levels of the heavy quarkonium, we derive expressions relating the leptonic constants, the energetic density of quarkonium states and universal characteristics in the heavy quarkonium physics, such as the difference between the masses of heavy quark Q and meson and the number of heavy quarkonium levels below the threshold of decay.

A bilinear combination of Dirac spinors is expressed in terms of Lorentz vectors. The result is represented in a convenient form, which can lead to using it for analytical calculations of multiparticle amplitudes. A geometrical interpretation of the introduced vectors is given and the correspondence between Dirac spinors and two-forms in complexified Minkowski space is clarified.

A general calculation of the corrections to the Casimir force for configurations used in experiments is presented. These corrections are considered up to the second order with respect to the relative amplitudes of the deviations. It is shown that in the case of long scale deviations the leading correction is the first order one and may be both positive and negative. The relative corrections have estimated values of several tens of percent, so they must be taken into account in precision experiments on Casimir force measurements.

We use experimental information on D⁻→K*⁰ρ⁻ and B→ψ+K*, coupled with flavor independence of QCD, and with vector meson dominance, to show that long distance (LD) contributions to B→ρ+γ, especially to B⁻→ρ⁻+γ, are potentially very serious. Estimates based on the annihilation graph are shown to lead to similar conclusions. We emphasize that LD contributions can be appreciably different in B⁻→ρ⁻+γ and B⁰→ρ⁰(ω)+γ. All radiative decays of B, B_s are shown to be governed essentially by two LD and two short distance (SD) hadronic entities. Despite the presence of considerable LD contributions, we show how separate measurements of B⁻→ρ⁻+γ, B⁰→ρ⁰(ω)+γ, along with B→K*+γ, can be used for a systematic extraction of V_td. Measurements of B_s→ɸ+γ and K*⁰+γ could also provide very useful consistency checks.

The collective field procedure is an interesting way of deriving the field-antifield formalism from a standard BRST approach. Trivial shift symmetries are introduced in the original gauge theory and then a judicious choice of gauge-fixing leads to the identification of the antighosts of these extra symmetries as the antifields. When explicit extended BRST invariance (BRST and anti-BRST invariance) is required, two collective fields are necessary, and the gauge-fixing structure is more complex. In this article, with the purpose of clarifying some aspects of this procedure, we consider in detail the example of the Yang–Mills theory.

Motivated by the work of Kawai and Nakayama¹ on R² gravity in two dimensions, we consider a simple massive stringlike model with one scalar bosonic field. We show that the conformal anomaly in terms of the Liouville action occurring in the usual Polyakov model does not appear in the presence of a finite massive term, because the conformal anomaly originating from the kinetic term of the model is canceled by a corresponding term originating from the massive part. Instead of this term, we obtain a power series in the inverse mass, where the coefficients are integrals over the manifold of scalar polynomials in the metric, the Gaussian curvature and its covariant derivatives. The lowest-order term is an R² term.

An inclusive determination of the (Γ/M) ratios of mesons and baryons is made from the ansatz that there exists a short breathing mode for the temporary dissociation of a hadron into a pair of “quasifree” quarks (q) and/or diquarks (D) with significantly lower masses than their constituent values which subsequently hadronize with certainty. The coupling scheme for mesons to these and DD* pairs (which yields Γ directly) is determined by Schwinger’s partial symmetry for quarks (which “subsumes” the Sakurai gauge principle for ρ, ω, ɸ couplings to pairs). A similar construction holds for baryon couplings to quark(q)-diquark(D) pairs, with the same overall coupling constant(g_s) for both systems. Its tentative identification with the QCD value yields a surprisingly good pattern of agreement with data for both hadron types, using just two inputs (m_ud and m_s). The Γ/M ratios (R) are expressible as αs(M²) f(J, M/m_q), and indicate discreteness in R iff the standard Regge slope patterns in M² are taken into account.

For zero energy, E=0, we derive exact, quantum solutions for all power-law potentials, V(r)=−γ/r^ν, with γ>0 and −∞<ν<∞. The solutions are, in general, Bessel functions of powers of r. For ν>2 and l≥1 the solutions are normalizable. Surprisingly, the solutions for ν<−2, which correspond to highly repulsive potentials, are also normalizable, for all l≥0. For these |ν|>2 the partial-wave Hamiltonians, H_l, have overcomplete sets of normalizable eigensolutions. We discuss how to obtain self-adjoint extensions of H_l such that the above E=0 solutions become included in their domains. When 2>ν≥−2 the E=0 solutions are not square-integrable. The ν=2 solutions are also unnormalizable, but are exceptional solutions. We also find that, by increasing the dimension of the Schrödinger equation beyond 4, an effective centrifugal barrier is created which is sufficient to cause binding when E=0 and ν>2, even for l=0. We discuss the physics of the above solutions and compare them to the corresponding classical solutions, which are derived elsewhere.