International Journal of Modern Physics A

An effective string theory in physically relevant cosmological and black hole space–times is reviewed. Explicit computations of the quantum string entropy, partition function and quantum string emission by black holes (Schwarzschild, rotating, charged, asymptotically flat, de Sitter dS and anti-de Sitter AdS space–times) in the framework of effective string theory in curved backgrounds provide an amount of new quantum gravity results as: (i) gravitational phase transitions appear with a distinctive universal feature: a square-root branch point singularity in any space–time dimensions. This is of the type of the de Vega–Sánchez transition for the thermal self-gravitating gas of point particles. (ii) There are no phase transitions in AdS alone. (iii) For dS background, upper bounds of the Hubble constant H are found, dictated by the quantum string phase transition. (iv) The Hawking temperature and the Hagedorn temperature are the same concept but in different (semiclassical and quantum) gravity regimes respectively. (v) The last stage of black hole evaporation is a microscopic string state with a finite string critical temperature which decays as usual quantum strings do in nonthermal pure quantum radiation (no information loss). (vi) New lower string bounds are given for the Kerr–Newman black hole angular momentum and charge, which are entirely different from the upper classical bounds. (vii) Semiclassical gravity states undergo a phase transition into quantum string states of the same system, these states are duals of each other in the precise sense of the usual classical–quantum (wave–particle) duality, which is universal irrespective of any symmetry or isommetry of the space–time and of the number or the kind of space–time dimensions.

Yang's theorem forbids the process Z⁰ →2γ in any Poincaré invariant theory if photons are bosons and their two-particle states transform under the Poincaré group in the standard way (under the standard coproduct of the Poincaré group). This is an important result as it does not depend on the assumptions of quantum field theory. Recent work on noncommutative geometry requires deforming the above coproduct by the Drinfel'd twist. We prove that Z⁰ →2γ is forbidden for the twisted coproduct as well. This result is also independent of the assumptions of quantum field theory. As an illustration of the use of our general formulae, we further show that Z⁰ →ν+ ν is forbidden for the standard or twisted coproduct of the Poincaré group if the neutrino is massless, even if lepton number is violated. This is a special case of our general result that a massive particle of spin j cannot decay into two identical massless particles of the same helicity if j is odd, regardless of the coproduct used.

We build the complete supersymmetric version of a 3-4-1 gauge model using the superfield formalism. We point out that a discrete symmetry, similar to the R-symmetry in the minimal supersymmetric standard model, is possible to be defined in this model. Hence we have both R-conserving and R-violating possibilities. We also discuss some phenomenological results coming from this model.

We revisit the harmonic oscillator algebra in an indefinite metric by reinterpreting consistently the time-like components in a way compatible with a positive-definite metric. We show that, despite its unusual features, the relativistic oscillator algebra can be derived starting from the Euclidean q-oscillator algebra. The consistency of this isomorphism is examined at different levels including the possible implication on the dynamics of the two formalisms by means of their respective Hamiltonians.

Using the Stueckelberg formalism, we construct a gauge-invariant version of the vector Schwinger model (VSM) with a photon mass term studied by one of us recently. This model describes two-dimensional massive electrodynamics with massless fermions, where the left-handed and right-handed fermions are coupled to the electromagnetic field with equal couplings. This model describing the 2D massive electrodynamics becomes gauge-noninvariant (GNI). This is in contrast to the case of the massless VSM which is a gauge-invariant (GI) theory (as a consequence of demanding the regularization for the theory to be GI). In this work we first construct a GI theory corresponding to this model describing the 2D massive electrodynamics, using the Stueckelberg formalism and then we recover the physical contents of the original GNI theory studied earlier, under some special gauge choice. We then study the Hamiltonian, path integral and BRST formulations of this GI theory under appropriate gauge-fixing. The theory presents a new class of models in the 2D quantum electrodynamics with massless fermions but with a photon mass term.

We use a new approach to study string scale gauge coupling unification systematically, allowing both the possibility of noncanonical U(1)_Y normalization and the existence of vector-like particles whose quantum numbers are the same as those of the Standard Model (SM) fermions and their Hermitian conjugates and the SM adjoint particles. We first give all the independent sets (Yi) of particles that can be employed to achieve SU(3)_C and SU(2)_L string scale gauge coupling unification and calculate their masses. Second, for a noncanonical U(1)_Y normalization, we obtain string scale SU(3)_C ×SU(2)_L ×U(1)_Y gauge coupling unification by choosing suitable U(1)_Y normalizations for each of the Yi sets. Alternatively, for the canonical U(1)_Y normalization, we achieve string scale gauge coupling unification by considering suitable combinations of the Yi sets or by introducing additional independent sets (Zi), that do not affect the SU(3)_C ×SU(2)_L unification at tree level, and then choosing suitable combinations, one from the Yi sets and one from the Zi sets. We also briefly discuss string scale gauge coupling unification in models with higher Kac–Moody levels for SU(2)_L or SU(3)_C.

The production of the sigma (σ) meson is investigated in the quantum molecular dynamics model for the p+A reactions with the nuclei A being ¹²C, ⁴⁰Ca and ²⁰⁸Pb at the incident proton energies E_p = 1.50 GeV. The simulation results indicates a distinctive A dependence of the sigma production, that is, the increase of A is followed by an increase of the production cross-sections. The σ meson production in proton induced reactions is strongly medium-dependent, and the produced σ mesons decaying in a denser medium experience a stronger mass shift towards lower masses. This mass shift is an experimentally accessible observable in the final state pion pairs which did not suffer reabsorption by the surrounding nucleons. It is pointed out that the ratio of the simulation results of measurable σ mesons (in the form of two pions) cross-sections as a function of the sigma invariant-mass from various reactions opens the possibility to address experimentally the mass shift of the σ in a dense nuclear environment.

It is shown that if physical space–time were truly compact there would only be of the order-of-one solutions to the classical field equations with a weighting to be explained. But that would not allow any peculiar choice of initial conditions that could support a nontrivial second law of thermodynamics. We present a no-go theorem: irreversible processes would be extremely unlikely to occur for the almost unique solution for the intrinsically compact space–time world, although irreversible processes are well known to occur in general. What we assume here — the compact space–time — is that universe could not exist eternally. In other word if universe stays on forever (i.e. noncompact in time direction) our no-go theorem is not applicable.

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of space–time must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.

In the context of the minimal supersymmetric seesaw model, the CP-violating neutrino Yukawa couplings might induce an electron electric dipole moment (EDM). The same interactions may also be responsible for the generation of the observed baryon asymmetry of the universe via leptogenesis. In the framework of mSUGRA, we identify in a model-independent way those patterns within the seesaw models which predict, barring unnatural cancelations, an electron EDM at a level probed by planned laboratory experiments and show that negative searches on τ→eγ decay may provide the strongest upper bound on the electron EDM. We also conclude that a possible future detection of the electron EDM is incompatible with thermal leptogenesis, even when flavor effects are accounted for.

The Chamseddine–Fröhlich approach to noncommutative geometry is extended by the introduction of the strong interaction sector in the mathematical formalism, and generalization of the Dirac operator and scalar product. This new approach is applied to the reformulation of the two-doublets Higgs model where the fuzzy mass, coupling and unitarity relations as well as mixing angles are derived. These tree level relations are no more preserved under the renormalization group flow in the context of the standard quantization method.