Bogomol'nyi bounds for cosmic strings

We establish Bogomol'nyi inequalities for the deficit angle of some cylindrically symmetric asymptotically local flat (CALF) spacetimes containing cosmic strings. These results prove the stability against arbitrary cylindrical deformations of those configurations which saturate the bound. Such configuration satisfy first order equations which can, in some cases, be solved exactly.     

Notes on superconducting cosmic strings

Several problems in string electrodynamics are discussed. Electric currents induced in strings oscillating in stationary electric and magnetic fields are calculated. In some cases the currents grow linearly with time. The rate of pair production in the electromagnetic field of strings is estimated.     

On Bianchi-I cosmic strings coupled with Maxwell fields in bimetric relativity

Axially symmetric Bianchi-I model is studied with source cosmic cloud strings coupled with electromagnetic field in Rosen’s bimetric theory of relativity and observed that there is no contribution from cosmic strings and Maxwell fields in this theory.     

Current discontinuities on superconducting cosmic strings

The propagation of current perturbations on superconducting cosmic strings is considered. The conditions for the existence of discontinuities similar to shock waves have been found. The formulas relating the string parameters and the discontinuity propagation speed are derived. The current growth law in a shock wave is deduced. The propagation speeds of shock waves with arbitrary amplitudes are calculated. The reason why there are no shock waves in the case of time-like currents (in the “electric” regime) is explained; this is attributable to the shock wave instability with respect to perturbations of the string world sheet.     

Classical and quantum mechanics of non-abelian gauge fields

Classical and quantum mechanics of non-abelian gauge fields are investigated both with and without spontaneous symmetry breaking. The fundamental subsystem (FS) of Yang-Mills classical mechanics (YMCM) is considered. It is shown to be a Kolmogorov K-system, and hence to have strong statistical properties. Integrable systems are also found, to which in terms of KAM theory Yang-Mills-Higgs classical mechanics (YMHCM) is close. Quantum-mechanical properties of the YM system and their relation to the problem of confinement are discussed.     

Quantum mechanics of Klein-Gordon-type fields and quantum cosmology

With a view to address some of the basic problems of quantum cosmology, we formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (∂_t²+D)ψ(t)=0, where and D is a positive-definite operator acting in a Hilbert space . In particular, we determine all the positive-definite inner products on the space of the solutions of such an equation and establish their physical equivalence. This specifies the Hilbert space structure of uniquely. We use a simple realization of the latter to construct the observables of the theory explicitly. The field equation does not fix the choice of a Hamiltonian operator unless it is supplemented by an underlying classical system and a quantization scheme supported by a correspondence principle. In general, there are infinitely many choices for the Hamiltonian each leading to a different notion of time-evolution in . Among these is a particular choice that generates t-translations in and identifies t with time whenever D is t-independent. For a t-dependent D, we show that regardless of the choice of the inner product the t-translations do not correspond to unitary evolutions in , and t cannot be identified with time. We apply these ideas to develop a formulation of quantum cosmology based on the Wheeler-DeWitt equation for a Friedman-Robertson-Walker model coupled to a real scalar field with an arbitrary positive confining potential. In particular, we offer a complete solution of the Hilbert space problem, construct the observables, use a position-like observable to introduce the wave functions of the universe (which differ from the Wheeler-DeWitt fields), reformulate the corresponding quantum theory in terms of the latter, reduce the problem of the identification of time to the determination of a Hamiltonian operator acting in , show that the factor-ordering problem is irrelevant for the kinematics of the quantum theory, and propose a formulation of the dynamics. Our method is based on the central postulates of nonrelativistic quantum mechanics, especially the quest for a genuine probabilistic interpretation and a unitary Schrödinger time-evolution. It generalizes to arbitrary minisuperspace (spatially homogeneous) models and provides a way of unifying the two main approaches to the canonical quantum cosmology based on these models, namely quantization before and after imposing the Hamiltonian constraint.     

De Sitter cosmic strings and supersymmetry

We study massive spinor fields in the geometry of a straight cosmic string in a de Sitter background. We find a hidden N = 2 supersymmetry in the fermionic solutions of the equations of motion. We connect the zero mode solutions to the heat-kernel regularized Witten index of the supersymmetric algebra.