TransPlanckian Particles and the Quantization of Time

Trans-Planckian particles are elementary particles accelerated such that their energies surpass the Planck value. There are several reasons to believe that trans-Planckian particles do not represent independent degrees of freedom in Hilbert space, but they are controlled by the cis-Planckian particles. A way to learn more about the mechanisms at work here, is to study black hole horizons, starting from the scattering matrix Ansatz. By compactifying one of the three physical spacial dimensions, the scattering matrix Ansatz can be exploited more efficiently than before. The algebra of operators on a black hole horizon allows for a few distinct representations. It is found that this horizon can be seen as being built up from string bits with unit lengths, each of which being described by a representation of the SO(2,1) Lorentz group. We then demonstrate how the holographic principle works for this case, by constructing the operators corresponding to a field in space-time. The parameter t turns out to be quantized in Planckian units, divided by the period R of the compactified dimension.Comment: 12 pages plain tex, 1 figur

Geometry of Scattering at Planckian Energies

We present an alternative derivation and geometrical formulation of Verlinde topological field theory, which may describe scattering at center of mass energies comparable or larger than the Planck energy. A consistent trunckation of 3+1 dimensional Einstein action is performed using the standard geometrical objects, like tetrads and spin connections. The resulting topological invariant is given in terms of differential forms.Comment: 8

Thermal photon dispersion law and modified black-body spectra

Based on the postulate that photon propagation is governed by an SU(2) gauge principle we numerically compute the one-loop dispersion for thermalized photon propagation on the radiatively induced mass shell. Formerly, the dispersion was addressed by assuming $p^2=0$. While this approximation turns out to be excellent for temperatures $\le 2 T_{\tiny{CMB}}$ the exact result exhibits a much faster (power-like) shrinking of the gap in the black-body spectral intensity with rising temperature. Our previous statements on anomalous large-angle CMB temperature-temperature correlations, obtained in the approximation $p^2=0$, remain valid.Comment: v2: 13 pages, 6 figures; sec. 2.1. added to explain effective theory; references added; matches journal published versio

Perturbative Confinement

A Procedure is outlined that may be used as a starting point for a perturbative treatment of theories with permanent confinement. By using a counter term in the Lagrangian that renormalizes the infrared divergence in the Coulomb potential, it is achieved that the perturbation expansion at a finite value of the strong coupling constant may yield reasonably accurate properties of hadrons, and an expression for the string constant as a function of the QCD Lambda parameter.Comment: Presented at QCD'02, Montpellier, July 2002. 12 pages LaTeX, 8 Figures PostScript, uses gthstyle.sty Reprt-no: ITF-2002/39; SPIN-2002/2

Heavy meson semileptonic decays in two dimensions in the large Nc

We study QCD in 1+1 dimensions in the large Nc limit using light-front Hamiltonian perturbation theory in the 1/Nc expansion. We use this formalism to exactly compute hadronic transition matrix elements for arbitrary currents at leading order in 1/Nc, which we use to write the semileptonic differential decay rate of a heavy meson and its moments. We then compare with the results obtained using an effective field theory approach based on perturbative factorization, with the intention of better understanding quark-hadron duality. A very good numerical agreement is obtained between the exact result and the result using effective theories.Comment: Talk given at the High-Energy Physics International Conference on Quantum Chromodynamics, 3-7 July (2006), Montpellier (France

Black hole unitarity and antipodal entanglement

Hawking particles emitted by a black hole are usually found to have thermal spectra, if not exactly, then by a very good approximation. Here, we argue differently. It was discovered that spherical partial waves of in-going and out-going matter can be described by unitary evolution operators independently, which allows for studies of space-time properties that were not possible before. Unitarity dictates space-time, as seen by a distant observer, to be topologically non-trivial. Consequently, Hawking particles are only locally thermal, but globally not: we explain why Hawking particles emerging from one hemisphere of a black hole must be 100 % entangled with the Hawking particles emerging from the other hemisphere. This produces exclusively pure quantum states evolving in a unitary manner, and removes the interior region for the outside observer, while it still completely agrees locally with the laws of general relativity. Unitarity is a starting point; no other assumptions are made. Region I and the diametrically opposite region II of the Penrose diagram represent antipodal points in a PT or CPT relation, as was suggested before. On the horizon itself, antipodal points are identified. A candidate instanton is proposed to describe the formation and evaporation of virtual black holes of the type described here. Some important explanations and discussion points are added. In the latest of the paper, again some minor inaccuracies are corrected.Comment: 15 pages, 1 figur

The Grand View of Physics

Abdus Salam was known for his `grand views', grand views of science as well as grand views of society. In this talk the grand view of theoretical physics is put in perspective.Comment: 5 pages, 1 figure. Presented at Salam +50, Imperial College, London, July 7, 200

The mathematical basis for deterministic quantum mechanics

If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes is further elucidated, as it follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.Comment: 17 pages, 3 figures. Minor corrections, comments and explanations adde

The Evolution of Quantum Field Theory, From QED to Grand Unification

In the early 1970s, after a slow start, and lots of hurdles, Quantum Field Theory emerged as the superior doctrine for understanding the interactions between relativistic sub-atomic particles. After the conditions for a relativistic field theoretical model to be renormalizable were established, there were two other developments that quickly accelerated acceptance of this approach: first the Brout-Englert-Higgs mechanism, and then asymptotic freedom. Together, these gave us a complete understanding of the perturbative sector of the theory, enough to give us a detailed picture of what is now usually called the Standard Model. Crucial for this understanding were the strong indications and encouragements provided by numerous experimental findings. Subsequently, non-perturbative features of the quantum field theories were addressed, and the first proposals for completely unified quantum field theories were launched. Since the use of continuous symmetries of all sorts, together with other topics of advanced mathematics, were recognised to be of crucial importance, many new predictions were pointed out, such as the Higgs particle, supersymmetry and baryon number violation. There are still many challenges ahead.Comment: 25 pages in total. A contribution to: The Standard Theory up to the Higgs discovery - 60 years of CERN - L. Maiani and G. Rolandi, ed