Exact factorization of the time-dependent electron-nuclear wavefunction

We present an exact decomposition of the complete wavefunction for a system of nuclei and electrons evolving in a time-dependent external potential. We derive formally exact equations for the nuclear and electronic wavefunctions that lead to rigorous definitions of a time-dependent potential energy surface (TDPES) and a time-dependent geometric phase. For the $H_2^+$ molecular ion exposed to a laser field, the TDPES proves to be a useful interpretive tool to identify different mechanisms of dissociation.Comment: 4 pages, 2 figure

Nonequilibrium Dynamics in Noncommutative Spacetime

We study the effects of spacetime noncommutativity on the nonequilibrium dynamics of particles in a thermal bath. We show that the noncommutative thermal bath does not suffer from any further IR/UV mixing problem in the sense that all the finite-temperature non-planar quantities are free from infrared singularities. We also point out that the combined effect of finite temperature and noncommutative geometry has a distinct effect on the nonequilibrium dynamics of particles propagating in a thermal bath: depending on the momentum of the mode of concern, noncommutative geometry may switch on or switch off their decay and thermalization. This momentum dependent alternation of the decay and thermalization rates could have significant impacts on the nonequilibrium phenomena in the early universe at which spacetime noncommutativity may be present. Our results suggest a re-examination of some of the important processes in the early universe such as reheating after inflation, baryogenesis and the freeze-out of superheavy dark matter candidates.Comment: 24 pages, 2 figure

The Effect of Gravitational Tidal Forces on Renormalized Quantum Fields

The effect of gravitational tidal forces on renormalized quantum fields propagating in curved spacetime is investigated and a generalisation of the optical theorem to curved spacetime is proved. In the case of QED, the interaction of tidal forces with the vacuum polarization cloud of virtual e^+ e^- pairs dressing the renormalized photon has been shown to produce several novel phenomena. In particular, the photon field amplitude can locally increase as well as decrease, corresponding to a negative imaginary part of the refractive index, in apparent violation of unitarity and the optical theorem. Below threshold decays into e^+ e^- pairs may also occur. In this paper, these issues are studied from the point of view of a non-equilibrium initial-value problem, with the field evolution from an initial null surface being calculated for physically distinct initial conditions and for both scalar field theories and QED. It is shown how a generalised version of the optical theorem, valid in curved spacetime, allows a local increase in amplitude while maintaining consistency with unitarity. The picture emerges of the field being dressed and undressed as it propagates through curved spacetime, with the local gravitational tidal forces determining the degree of dressing and hence the amplitude of the renormalized quantum field. These effects are illustrated with many examples, including a description of the undressing of a photon in the vicinity of a black hole singularity.Comment: 76 pages, jheppub.sty, 10 figures, small corrections. arXiv admin note: text overlap with arXiv:1006.014

New Constraints (and Motivations) for Abelian Gauge Bosons in the MeV-TeV Mass Range

We survey the phenomenological constraints on abelian gauge bosons having masses in the MeV to multi-GeV mass range (using precision electroweak measurements, neutrino-electron and neutrino-nucleon scattering, electron and muon anomalous magnetic moments, upsilon decay, beam dump experiments, atomic parity violation, low-energy neutron scattering and primordial nucleosynthesis). We compute their implications for the three parameters that in general describe the low-energy properties of such bosons: their mass and their two possible types of dimensionless couplings (direct couplings to ordinary fermions and kinetic mixing with Standard Model hypercharge). We argue that gauge bosons with very small couplings to ordinary fermions in this mass range are natural in string compactifications and are likely to be generic in theories for which the gravity scale is systematically smaller than the Planck mass - such as in extra-dimensional models - because of the necessity to suppress proton decay. Furthermore, because its couplings are weak, in the low-energy theory relevant to experiments at and below TeV scales the charge gauged by the new boson can appear to be broken, both by classical effects and by anomalies. In particular, if the new gauge charge appears to be anomalous, anomaly cancellation does not also require the introduction of new light fermions in the low-energy theory. Furthermore, the charge can appear to be conserved in the low-energy theory, despite the corresponding gauge boson having a mass. Our results reduce to those of other authors in the special cases where there is no kinetic mixing or there is no direct coupling to ordinary fermions, such as for recently proposed dark-matter scenarios.Comment: 49 pages + appendix, 21 figures. This is the final version which appears in JHE

Composite gauge fields in renormalizable models

A generalization of the non-Abelian version of the CP{sup {ital N}{minus}1} models (also known as Grassmannian models) is presented. The generalization helps accommodate a partial breaking of the non-Abelian gauge symmetry. Constituents of the composite gauge fields, in many cases, are naturally constrained to belong to an anomaly-free representation which in turn generates a composite scalar-simulating Higgs mechanism to break the gauge symmetry dynamically for large {ital N}. Two cases are studied in detail: one based on the SU(2) gauge group and the other on SO(10). Breakings such as SU(2){r_arrow}U(1) or SO(10){r_arrow}SU(5){times}U(1) are found feasible. The properties of the composites fields and gauge boson masses are computed by doing a derivative expansion of the large {ital N} effective action

CP violation from finite groups

We discuss the origin of CP violation in settings with a discrete (flavor) symmetry G. We show that physical CP transformations always have to be class-inverting automorphisms of G. This allows us to categorize finite groups into three types: (i) Groups that do not exhibit such an automorphism and, therefore, in generic settings, explicitly violate CP. In settings based on such groups, CP violation can have pure group-theoretic origin and can be related to the complexity of some Clebsch-Gordan coefficients. (ii) Groups for which one can find a CP basis in which all the Clebsch-Gordan coefficients are real. For such groups, imposing CP invariance restricts the phases of coupling coefficients. (iii) Groups that do not admit real Clebsch-Gordan coefficients but possess a class-inverting automorphism that can be used to define a proper (generalized) CP transformation. For such groups, imposing CP invariance can lead to an additional symmetry that forbids certain couplings. We make use of the so-called twisted Frobenius-Schur indicator to distinguish between the three types of discrete groups. With δ(27), T ', and σ(72) we present one explicit example for each type of group, thereby illustrating the CP properties of models based on them. We also show that certain operations that have been dubbed generalized CP transformations in the recent literature do not lead to physical CP conservation. © 2014 The Authors