Higher Spin Conserved Currents in Sp(2M) Symmetric Spacetime

An infinite set of higher spin conserved charges is found for the sp(2M) symmetric dynamical systems in M(M+ 1)/2-dimensional generalized spacetime _M. Since the dynamics in _M is equivalent to the conformal dynamics of infinite towers of fields in d-dimensional Minkowski spacetime with d = 3, 4, 6, 10, ... for M = 2, 4, 8, 16, ..., respectively, the constructed currents in _M generate infinite towers of (mostly new) higher spin conformal currents in Minkowski spacetime. The charges have a form of integrals of M-forms which are bilinear in the field variables and are closed as a consequence of the field equations. Conservation implies independence of a value of charge of a local variation of a M-dimensional integration surface _M analogous to Cauchy surface in the usual spacetime. The scalar conserved charge provides an invariant bilinear form on the space of solutions of the field equations that gives rise to a positive-definite norm on the space of quantum states.     

Stability of Schwarzschild-AdS for the Spherically Symmetric Einstein-Klein-Gordon System

In this paper, we study the global behavior of solutions to the spherically symmetric coupled Einstein-Klein-Gordon (EKG) system in the presence of a negative cosmological constant. For the Klein-Gordon mass-squared satisfying a ≥ ?1 (the Breitenlohner-Freedman bound being a > ?9/8), we prove that the Schwarzschild-AdS spacetimes are asymptotically stable: Small perturbations of Schwarzschild-AdS initial data again lead to regular black holes, with the metric on the black hole exterior approaching, at an exponential rate, a Schwarzschild-AdS spacetime. The main difficulties in the proof arise from the lack of monotonicity for the Hawking mass and the asymptotically AdS boundary conditions, which render even (part of) the orbital stability intricate. These issues are resolved in a bootstrap argument on the black hole exterior, with the redshift effect and weighted Hardy inequalities playing the fundamental role in the analysis. Both integrated decay and pointwise decay estimates are obtained. As a corollary of our estimates on the Klein-Gordon field, one obtains in particular exponential decay in time of spherically-symmetric solutions to the linear Klein-Gordon equation on Schwarzschild-AdS.     

The LSW Model for Domain Coarsening: Asymptotic Behavior for Conserved Total Mass

In the classical theory of domain coarsening the particles of the coarsening phase evolve by diffusional mass transfer with a mean field. We study the long-time behavior of measure-valued solutions with compact support to this model coupled with the constraint of conserved total mass, including mean-field mass. Unlike the case of conserved volume fraction, this system has no precisely self-similar solutions, and sufficiently low supersaturation can lead to the finite-time extinction of all particles. We find a new explicit family of asymptotically self-similar solutions, and in case that the largest particle size is unbounded we establish results similar to the volume-conserved case. These include necessary criteria for asymptotic self-similarity, and sensitive dependence of long-time behavior on the distribution of largest particles in the system.     

Spacetime Embedding Diagrams for Black Holes

We show that the 1 + 1 dimensional reduction(i.e., the radial plane) of the Kruskal black hole canbe embedded in 2 + 1 Minkowski spacetime and discuss howfeatures of this spacetime can be seen from theembedding diagram. The purpose of this work iseducational: The associated embedding diagrams may beuseful for explaining aspects of black holes to studentswho are familiar with special relativity, but notgeneral relativity.     

Contracted Representation of Yang's Spacetime Algebra and Buniy-Hsu-Zee's Discrete Spacetime

Motivated by the recent proposition by Buniy, Hsu, and Zee with respect to discrete spacetime and finite spatial degrees of freedom of our physical world with short- and long-distance scales, l _P and L, we reconsider the Lorentz-covariant Yang's quantized spacetime algebra (YSTA), which is intrinsically equipped with two such kinds of scale parameters, λ and R. In accordance with their proposition, we find the so-called contracted representation of YSTA with finite spatial degrees of freedom associated with the ratio R/λ, which gives a possibility of the divergence-free noncommutative field theory on YSTA. The canonical commutation relations familiar in the ordinary quantum mechanics appear as the cooperative Inonu-Wigner's contraction limit of YSTA, λ → 0 and R → ∓.     

The P-v Criticality of a Noncommutative Geometry-Inspired Schwarzschild-AdS Black Hole

The P-v criticality and phase transition in the extended phase space of a noncommutative geometry-inspired Schwarzschild black hole in anti-de Sitter(AdS) spacetime are studied. The cosmological constant is treated as a dynamical pressure and its conjugate quantity is thermodynamic volume of the noncommutative geometryinspired Schwarzschild-AdS black hole. The noncommutative parameter is also treated as a variable, and as a consequence, a new thermodynamic quantity V_θ conjugate to P_θ=-(8πθ)~(-1) has to be defined further, which is required for consistency of both the first law of thermodynamics and the corresponding Smarr relation. We find that the P-v criticality and the small black hole/large black hole phase transition appear for the noncommutative Schwarzschild-AdS black hole. Numerical calculations indicate that the noncommutative parameter θ affects the phase transition as well as the critical temperature Te, horizon radius r_(+c), and pressure P_e.However, the critical ratio P_cr_(+c)/T_c is universal(independent of θ), which is very similar to the result in the van de Waals liquid-gas system, but different from that in the noncommutative geometry-inspired Reissner-Nordstrom-AdS black hole,where the critical ratio is no longer universal.     

Residual Representations of Spacetime

Spacetime is modelled by binary relations—by the classes of the automorphisms of a complex two-dimensional vector space with respect to the definite unitary subgroup U(2). In extension of Feynman propagators for particle quantum fields representing only the tangent spacetime structure, global spacetime representations are given, formulated as residues using energy–momentum distributions with the invariants as singularities. The associated quantum fields are characterized by two invariant masses—for time and position—supplementing the one mass for the definite unitary particle sector with another mass for the indefinite unitary interaction sector without asymptotic particle interpretation.     

Functional Methods for Arbitrary Densities in Curved Spacetime

This paper gives an introduction to the technique of functional differentiation and integration in curved spacetime, applied to examples from quantum field theory. Special attention is drawn on the choice of functional integral measure. Referring to a suggestion by Toms, fields are choosen as arbitrary scalar, spinorial or vectorial densities. The technique developed by Toms for a pure quadratic Lagrangian are extended to the calculation of the generating functional with external sources. Included are two examples of interacting theories, a self-interacting scalar field and a Yang-Mills theory. For these theories the complete set of Feynman graphs depending on the weight of variables is derived.     

Propagation of Photons in Spacetime

A quantum field theory QED formalism is systematically developed to describe photon propagation in spacetime as a time evolution process based on the actual physical process of propagation between emitters and detectors as applied to the reflection of photons. This development, as well as early studies by Feynman, clearly show that a practical, computational and predictive dynamical formalism in spacetime was lacking. The present one generalizes to different experimental situations and other interacting field theories as well emphasizing the practicality of the problem treated here.     

Spacetime path formalism for massive particles of any spin

Earlier work presented spacetime path formalism for relativistic quantum mechanics arising naturally from the fundamental principles of the Born probability rule, superposition, and spacetime translation invariance. The resulting formalism can be seen as a foundation for a number of previous parametrized approaches to relativistic quantum mechanics in the literature. Because time is treated similarly to the three-space coordinates, rather than as an evolution parameter, such approaches have proved particularly useful in the study of quantum gravity and cosmology. The present paper extends the foundational spacetime path formalism to include massive, non-scalar particles of any (integer or half-integer) spin. This is done by generalizing the principle of translational invariance used in the scalar case to the principle of full Poincaré invariance, leading to a formulation for the non-scalar propagator in terms of a path integral over the Poincaré group. Once the difficulty of the non-compactness of the component Lorentz group is dealt with, the subsequent development is remarkably parallel to the scalar case. This allows the formalism to retain a clear probabilistic interpretation throughout, with a natural reduction to non-relativistic quantum mechanics closely related to the well-known generalized Foldy-Wouthuysen transformation.     

Spacetime Embedding Diagrams for Spherically Symmetric Black Holes

We show that it is possible to embed the 1 + 1 dimensional reduction of certain spherically symmetric black hole spacetimes into 2 + 1 Minkowski space. The spacetimes of interest (Schwarzschild de-Sitter, Schwarzschild anti de-Sitter, and Reissner-Nordström near the outer horizon) represent a class of metrics whose geometries allow for such embeddings. The embedding diagrams have a dynamic character which allows one to represent the motion of test particles. We also analyze various features of the embedding construction, deriving the general conditions under which our procedure provides a smooth embedding. These conditions also yield an embedding constant related to the surface gravity of the relevant horizon.     

Area Spectrum of D-Dimensional Large Schwarzschild-AdS Black Hole from Asymptotic Quasinormal Modes

We investigate the area and entropy spectra of D-dimensional large Schwarzschild black holes. By utilizing the new physical interpretation of quasinormal mode frequency we find that a large Schwarzschild-AdS black hole has an equally spaced area spectrum and an equidistant entropy spectrum; both are dependent on the spacetime dimension.     

Relocalization of Ce 5d electrons from host conduction band

Single crystal fibers of Ce³⁺ doped SrAl₂O₄ and CaAl₄O₇ were prepared through the laser heated pedestal growth method. Sites dependent Ce³⁺ emissions were found at 385 nm (427 nm) and 420 nm (325 nm) in SrAl₂O₄ and CaAl₄O₇ hosts, respectively. The Ce³⁺ emissions at 385 nm and 420 nm in the two hosts exhibited strong afterglows. They could persist for more than 10 h. The long persistence and sites dependence of Ce³⁺ emissions were originated from charge compensation of doping Ce³⁺ into divalent cation sites. The lifetimes of Ce³⁺ emissions in both hosts were found to depend on the laser excitation wavelengths. With 266 nm laser excitation, Ce³⁺ 5d electrons were delocalized into the host's conduction band, resulting in a prolonged decay time. The 355 nm laser excitation did not delocalize the 5d electrons and hence the measured lifetimes were the intrinsic Ce³⁺ emission lifetimes that were 17 and 35.5 ns in SrAl₂O₄ and CaAl₄O₇ hosts, respectively. The prolonged Ce³⁺ emission lifetime on 266 nm laser excitation was because of the relocalization of the 5d electrons from the host conduction band. The lifetimes of Ce³⁺ 5d electrons within the conduction band were found to be 34 and 44 ns in SrAl₂O₄ and CaAl₄O₇ hosts, respectively.     

Spacetime locality of the BRST formalism

The spacetime locality of the BRST formalism is investigated. The analysis covers gauge theories with either closed or open algebras and is undertaken in the explicit context of the antifield formulation of the BRST theory. Under appropriate conditions, the homology of the Koszul-Tate differential modulo the spacetime exterior derivative is shown to be trivial in the space of non-integrated densities with positive antighost and pure ghost numbers. As a result: (i) the solution of the master equation can be taken to be a local functional; (ii) the gauge fixed action is also a local functional provided one takes the gauge fixing fermion to be a local functional as well; and (iii) the BRST transformation is local.     

Common Space of Spin and Spacetime

Given Lorentz invariance in Minkowski spacetime, we investigate a common space of spin and spacetime. To obtain a finite spinor representation of the non-compact homogeneous Lorentz group including Lorentz boosts, we introduce an indefinite inner product space (IIPS) with a normalized positive probability. In this IIPS, the common momentum and common variable of a massive fermion turn out to be “doubly strict plus-operators”. Due to this nice property, it is straightforward to show an uncertainty relation between fermion mass and proper time. Also in IIPS, the newly-defined Lagrangian operators are self-adjoint, and the fermion field equations are derivable from the Lagrangians. Finally, the nonlinear QED equations and Lagrangians are presented as an example.