Electromagnetism and multiple-valued loop-dependent wave functionals

We quantize the Maxwell theory in the presence of a electric charge in a "dual" Loop Representation, i.e. a geometric representation of magnetic Faraday's lines. It is found that the theory can be seen as a theory without sources, except by the fact that the wave functional becomes multivalued. This can be seen as the dual counterpart of what occurs in Maxwell theory with a magnetic pole, when it is quantized in the ordinary Loop Representation. The multivaluedness can be seen as a result of the multiply-connectedness of the configuration space of the quantum theory.Comment: 5 page

P.A.M. Dirac and the Discovery of Quantum Mechanics

Dirac's contributions to the discovery of non-relativistic quantum mechanics and quantum electrodynamics, prior to his discovery of the relativistic wave equation, are described

Extreme Fire as a Management Tool to Combat Regime Shifts in the Range of the Endangered American Burying Beetle

This study is focused on the population of federally-endangered American burying beetles in south-central Nebraska. It is focused on changes in land cover over time and at several levels of spatial scale, and how management efforts are impacting both the beetle and a changing landscape. Our findings are applicable to a large portion of the Great Plains, which is undergoing the same shift from grassland to woodland, and to areas where the beetle is still found

Geometric phases, gauge symmetries and ray representation

The conventional formulation of the non-adiabatic (Aharonov-Anandan) phase is based on the equivalence class $\{e^{i\alpha(t)}\psi(t,\vec{x})\}$ which is not a symmetry of the Schr\"{o}dinger equation. This equivalence class when understood as defining generalized rays in the Hilbert space is not generally consistent with the superposition principle in interference and polarization phenomena. The hidden local gauge symmetry, which arises from the arbitrariness of the choice of coordinates in the functional space, is then proposed as a basic gauge symmetry in the non-adiabatic phase. This re-formulation reproduces all the successful aspects of the non-adiabatic phase in a manner manifestly consistent with the conventional notion of rays and the superposition principle. The hidden local symmetry is thus identified as the natural origin of the gauge symmetry in both of the adiabatic and non-adiabatic phases in the absence of gauge fields, and it allows a unified treatment of all the geometric phases. The non-adiabatic phase may well be regarded as a special case of the adiabatic phase in this re-formulation, contrary to the customary understanding of the adiabatic phase as a special case of the non-adiabatic phase. Some explicit examples of geometric phases are discussed to illustrate this re-formulation.Comment: 30 pages. Some clarifying sentences have been added in abstract and in the body of the paper. A new additional reference and some typos have been corrected. To appear in Int. J. Mod. Phys.

Application of the canonical quantization of systems with curved phase space to the EMDA theory

The canonical quantization of dynamical systems with curved phase space introduced by I.A. Batalin, E.S. Fradkin and T.E. Fradkina is applied to the four-dimensional Einstein-Maxwell Dilaton-Axion theory. The spherically symmetric case with radial fields is considered. The Lagrangian density of the theory in the Einstein frame is written as an expression with first order in time derivatives of the fields. The phase space is curved due to the nontrivial interaction of the dilaton with the axion and the electromagnetic fields.Comment: 23 pages in late

Non-Abelian Gauged Chiral Boson with a Generalized Faddevian Regularization

We consider non-Abelian gauged version of chiral boson with a generalized Faddeevian regularization. It is a second class constrained theory. We quantize the theory and analyze the phase space. It is shown that in spite of the lack of manifest Lorentz invariance in the action, it has a consistent and Poincare' invariant phase space structure.Comment: 10 pages latex fil

Effective Constraints for Relativistic Quantum Systems

Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which are extended here to relativistic systems as they arise for instance in quantum cosmology. By side-stepping explicit constructions of states, such tools allow one to arrive much more feasibly at results for physical observables at least in semiclassical regimes. Several questions discussed recently regarding effective equations and state properties in quantum cosmology, including the spreading of states and quantum back-reaction, are addressed by the examples studied here.Comment: 27 pages, 2 figures; v2: new appendix comparing effective constraints and physical coherent states by an exampl

The Static Quantum Multiverse

We consider the multiverse in the intrinsically quantum mechanical framework recently proposed in Refs. [1,2]. By requiring that the principles of quantum mechanics are universally valid and that physical predictions do not depend on the reference frame one chooses to describe the multiverse, we find that the multiverse state must be static---in particular, the multiverse does not have a beginning or end. We argue that, despite its naive appearance, this does not contradict observation, including the fact that we observe that time flows in a definite direction. Selecting the multiverse state is ultimately boiled down to finding normalizable solutions to certain zero-eigenvalue equations, analogous to the case of the hydrogen atom. Unambiguous physical predictions would then follow, according to the rules of quantum mechanics.Comment: 27 pages, 2 figures; a typo in the abstract correcte

Chiral QED in Terms of Chiral Boson with a Generalized Fadeevian Regularization

Chiral QED with a generalized Fadeevian regularization is considered. Imposing a chiral constraint a gauged version of Floranini-Jackiw lagrangian is constructed. The imposition of the chiral constarint has spoiled t he manifestly Lorentz covariance of the theory. The phase space structure for this theory has been det ermined. It is found that spectrum changes drastically but it is Lorentz invariant. Chiral fermion di sappears from the spectra and the photon anquire mass as well. Poincare algebra has been calculated to show physicial Lorentz invariance explicitely.Comment: 11 page

On the Implementation of Constraints through Projection Operators

Quantum constraints of the type Q \psi = 0 can be straightforwardly implemented in cases where Q is a self-adjoint operator for which zero is an eigenvalue. In that case, the physical Hilbert space is obtained by projecting onto the kernel of Q, i.e. H_phys = ker(Q) = ker(Q*). It is, however, nontrivial to identify and project onto H_phys when zero is not in the point spectrum but instead is in the continuous spectrum of Q, because in this case the kernel of Q is empty. Here, we observe that the topology of the underlying Hilbert space can be harmlessly modified in the direction perpendicular to the constraint surface in such a way that Q becomes non-self-adjoint. This procedure then allows us to conveniently obtain H_phys as the proper Hilbert subspace H_phys = ker(Q*), on which one can project as usual. In the simplest case, the necessary change of topology amounts to passing from an L^2 Hilbert space to a Sobolev space.Comment: 22 pages, LaTe