International Journal of Modern Physics A

Sector decomposition is a constructive method to isolate divergences from parameter integrals occurring in perturbative quantum field theory. We explain the general algorithm in detail and review its application to multiloop Feynman parameter integrals as well as infrared divergent phase-space integrals over real radiation matrix elements.

Born's reciprocal relativity in flat space–times is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved space–times and construct a reciprocal general relativity theory (in curved space–times) as a local gauge theory of the quaplectic group and given by the semidirect product , where the non-Abelian Weyl–Heisenberg group is H(1, 3). The gauge theory has the same structure as that of complex non-Abelian gravity. Actions are presented and it is argued why such actions based on Born's reciprocal relativity principle, involving a maximal speed limit and a maximal proper force, is a very promising avenue to quantize gravity that does not rely in breaking the Lorentz symmetry at the Planck scale, in contrast to other approaches based on deformations of the Poincaré algebra, quantum groups. It is discussed how one could embed the quaplectic gauge theory into one based on the U(1, 4), U(2, 3) groups where the observed cosmological constant emerges in a natural way. We conclude with a brief discussion of complex coordinates and Finsler spaces with symmetric and nonsymmetric metrics studied by Eisenhart as relevant closed-string target space backgrounds where Born's principle may be operating.

By differentiating the dressed quark propagator with respect to a variable background field, the linear response of the dressed quark propagator in the presence of the background field can be obtained. From this general method, using the vector background field as an illustration, we derive a general formula for the four-quark condensate . This formula contains the corresponding fully dressed vector vertex and it is shown that factorization for holds only when the dressed vertex is taken to be the bare one. This property also holds for all other types of four-quark condensate. By comparing this formula with the general expression for the corresponding vacuum susceptibility, it is found that there exists some intrinsic relation between these two quantities, which are usually treated as independent phenomenological inputs in the QCD sum rule external field approach. The above results are also generalized to the case of finite chemical potential and the factorization problem of the four-quark condensate at finite chemical potential is discussed.

We show that from the R² high order gravity theory it is possible to produce, in the linearized approach, particles which can be seen as massive modes of gravitational waves (GW's). The presence of the mass generates a longitudinal force in addition of the transverse one which is proper of the massless gravitational waves and the response an interferometer to the effect is computed. This could be, in principle, important to discriminate among the gravity theories. The presence of the mass could also have important applications in cosmology because the fact that gravitational waves can have mass could give a contribution to the dark matter of the Universe.

The bound state solutions of the Schrödinger equation for a second Pöschl–Teller-like potential with the centrifugal term are obtained approximately. It is found that the solutions can be expressed in terms of the hypergeometric functions ₂F₁(a, b; c; z). To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other method for short-range potential. Two special cases for l = 0 and V₁ = V₂ are also studied briefly.

Chiral antisymmetric tensor fields can have chiral couplings to quarks and leptons. Their kinetic terms do not mix different representations of the Lorentz symmetry and a local mass term can be forbidden by symmetry. The chiral couplings to the fermions are asymptotically free, opening interesting perspectives for a possible solution to the gauge hierarchy problem. We argue that the interacting theory for such fields can be consistently quantized, in contrast to the free theory which is plagued by unstable solutions. We suggest that at the scale where the chiral couplings grow large the electroweak symmetry is spontaneously broken and a mass term for the chiral tensors is generated nonperturbatively. Massive chiral tensors correspond to massive spin-one particles that do not have problems of stability. We also propose an equivalent formulation in terms of gauge fields.

In Modern Physics Letters A15, 2265 (2000), in the context of domain wall backgrounds, it was shown that spontaneous breaking of diffeomorphism invariance results in gravitational Higgs mechanism. Recently in arXiv:0708.3184 't Hooft discussed gravitational Higgs mechanism in the context of obtaining massive gravity directly in four dimensions, and pointed out some subtleties with unitarity. We attribute these subtleties to breaking timelike diffeomorphisms, and discuss gravitational Higgs mechanism with all but timelike diffeomorphisms spontaneously broken. The resulting background is no longer flat but exhibits expansion, which is linear in time. For space–time dimensions D ≤ 10 the background is stable and has no nonunitary propagating modes. The absence of nonunitary modes is due to the unbroken timelike diffeomorphism invariance. The physical states correspond to those of a massive graviton. The effective mass squared of the graviton is positive for D < 10, and vanishes for D = 10. For D > 10 the graviton modes become effectively tachyonic. The special value of D = 10, which coincides with the critical dimension of superstring theory, arises in our setup completely classically.

The symmetry structures of the dimensionally reduced Einstein–Kalb–Ramond (EKR) theory is further studied. By using a so-called extended double (ED)-complex method, the usual Riemann–Hilbert (RH) problem is extended to an ED-complex formulation. A pair of ED RH transformations are constructed and they are verified to give infinite-dimensional double symmetry groups of the EKR theory, each of these symmetry groups has the structure of semidirect product of Kac–Moody group and Virasoro group. Moreover, the infinitesimal forms of these RH transformations are calculated out and they are found to give exactly the same results as previous, these demonstrate that the pair of ED RH transformations in this paper provide exponentiations of all the infinitesimal symmetries in our previous paper. The finite forms of symmetry transformations given in the present paper are more important and useful for theoretic studies and new solution generation, etc.

The Klein–Gordon and Dirac equations are considered in a semiinfinite laboratory (x > 0) in the presence of background metrics ds² = u²(x)η_μν dx^μ dx^ν and ds² = -dt² + u²(x)η_ij dxⁱ dx^j with u(x) = e^±gx. These metrics have nonconstant scalar-curvatures. Various aspects of the solutions are studied. For the first metric with u(x) = e^gx, it is shown that the spectra are discrete, with the ground state energy for spin-0 particles. For u(x) = e^-gx, the spectrums are found to be continuous. For the second metric with u(x) = e^-gx, each particle, depends on its transverse-momentum, can have continuous or discrete spectrum. For Klein–Gordon particles, this threshold transverse-momentum is , while for Dirac particles it is g/2. There is no solution for u(x) = e^gx case. Some geometrical properties of these metrics are also discussed.