Class Constraints Research Articles

‘You have to be well spoken’: students’ views on employability within the graduate labour market

This study reports upon the perceptions of a sample of Education Studies undergraduates of their employability within three jobs: teaching, accountancy and marketing/sales management. The concept of employability is framed around two themes analysed through a Bernsteinian conceptual analysis: transferable utility of an Education Studies degree for employment in the jobs and importance of class and gender to employment in the jobs. The question of how undergraduates, who would traditionally anticipate working in teaching-related employment, perceive jobs within different occupational areas has acquired particular interest following ongoing public sector cuts in the UK with consequent implications for employment within teaching. In focus group interviews students identified class and gender barriers in relation to all three jobs, thus demonstrating a wider sensitivity to the classed and gendered nature of the graduate labour market. While the students did not, generally, see either of the two business/finance jobs as completely closed to them in terms of class and gender-related constraints, there was a clear perception that their degree did not provide them with the necessary skills for employment within these jobs. This represents a rejection of dominant discourses regarding transferable graduate skills and challenges assumptions of graduate occupational mobility.

Path integral quantization of the first order Einstein–Hilbert action from its canonical structure

We consider the form of the path integral that follows from canonical quantization and apply it to the first order form of the Einstein–Hilbert action in d > 2 dimensions. We show that this is inequivalent to what is obtained from applying the Faddeev–Popov (FP) procedure directly. Due to the presence of tertiary first class constraints, the measure of the path integral is found to have a substantially different structure from what arises in the FP approach. In addition, the presence of second class constraints leads to non-trivial ghosts, which cannot be absorbed into the normalization of the path integral. The measure of the path integral lacks manifest covariance.

Improved Canonical Quantization Method of Self Dual Field

In this paper, the improved canonical quantization method of the self dual field is given in order to overcome linear combination problem about the second class constraint and the first class constraint number maximization problem in the Dirac method. In the improved canonical quantization method, there are no artificial linear combination and the first class constraint number maximization problems, at the same time, the stability of the system is considered. Therefore, the improved canonical quantization method is more natural and easier accepted by people than the usual Dirac method. We use the improved canonical quantization method to realize the canonical quantization of the self dual field, which has relation with string theory successfully and the results are equal to the results by using the Dirac method.

Viper

The reliability of future processors is threatened by decreasing transistor robustness. Current architectures focus on delivering high performance at low cost; lifetime device reliability is a secondary concern. As the rate of permanent hardware faults increases, robustness will become a first class constraint for even low-cost systems. Current research into reliable architectures has focused on ad-hoc solutions to improve designs without altering their centralized control logic. Unfortunately, this centralized control presents a single point of failure, which limits long-term robustness. To address this issue, we introduce Viper, an architecture built from a redundant collection of fine-grained hardware components. Instructions are perceived as customers that require a sequence of services in order to properly execute. The hardware components vie to perform what services they can, dynamically forming virtual pipelines that avoid defective hardware. This is done using distributed control logic, which avoids a single point of failure by construction. Viper can tolerate a high number of permanent faults due to its inherent redundancy. As fault counts increase, its performance degrades more gracefully than traditional centralized-logic architectures. We estimate that fault rates higher than one permanent faults per 12 million transistors, on average, cause the throughput of a classic CMP design to fall below that of a Viper design of similar size.

Nonlinear massive gravity with additional primary constraint and absence of ghosts

We complete the Hamiltonian analysis of specific model of non-linear massive gravity that was started in arXiv:1112.5267. We identify the primary constraint and corresponding secondary constraint. We show that they are the second class constraints and hence they lead to the elimination of the additional scalar mode. We also find that the remaining constraints are the first class constraints with the structure that corresponds to the manifestly diffeomorphism invariant theory. Finally we determine the number of physical degrees of freedom and we show that it corresponds to the number of physical modes of massive gravity.

UNIQUENESS OF CANONICAL TENSOR MODEL WITH LOCAL TIME

Canonical formalism of the rank-three tensor model has recently been proposed, in which "local" time is consistently incorporated by a set of first class constraints. By brute-force analysis, this paper shows that there exist only two forms of a Hamiltonian constraint which satisfies the following assumptions: (i) A Hamiltonian constraint has one index. (ii) The kinematical symmetry is given by an orthogonal group. (iii) A consistent first class constraint algebra is formed by a Hamiltonian constraint and the generators of the kinematical symmetry. (iv) A Hamiltonian constraint is invariant under time reversal transformation. (v) A Hamiltonian constraint is an at most cubic polynomial function of canonical variables. (vi) There are no disconnected terms in a constraint algebra. The two forms are the same except for a slight difference in index contractions. The Hamiltonian constraint which was obtained in the previous paper and behaved oddly under time reversal symmetry can actually be transformed to one of them by a canonical change of variables.

Degenerate Plebanski sector and spin foam quantization

We show that the degenerate sector of Spin(4) Plebanski formulation of four-dimensional gravity is exactly solvable and describes covariantly embedded SU(2) BF theory. This fact ensures that its spin foam quantization is given by the SU(2) Crane–Yetter model and allows to test various approaches of imposing the simplicity constraints. Our analysis strongly suggests that restricting representations and intertwiners in the state sum for Spin(4) BF theory is not sufficient to get the correct vertex amplitude. Instead, for a general theory of Plebanski type, we propose a quantization procedure which is by construction equivalent to the canonical path integral quantization and, being applied to our model, reproduces the SU(2) Crane–Yetter state sum. A characteristic feature of this procedure is the use of secondary second class constraints on an equal footing with the primary simplicity constraints, which leads to a new formula for the vertex amplitude.

Testing the imposition of the spin foam simplicity constraints

We introduce a three-dimensional Plebanski action for the gauge group SO(4). In this model, the B field satisfies quadratic simplicity constraints similar to that of the four-dimensional Plebanski theory, but with the difference that the B field is now a 1-form. We exhibit a natural notion of ‘simple 1-form’, and identify a gravitational sector, a topological sector and a degenerate sector in the space of solutions to the simplicity constraints. Classically, in the gravitational sector, the action is shown to be equivalent to that of three-dimensional first-order Riemannian gravity. This enables us to perform the complete spin foam quantization of the theory once the simplicity constraints are solved at the classical level, and to compare this result with the various models that have been proposed for the implementation of the constraints after quantization. In particular, we impose the simplicity constraints following the prescriptions of the so-called BC and EPRL models. We observe that the BC prescription cannot lead to the proper vertex amplitude. The EPRL prescription allows us to recover the expected result when, in this three-dimensional model, it is supplemented with additional secondary second class constraints.

Spontaneously broken Lorentz symmetry for Hamiltonian gravity

In Ashtekar's Hamiltonian formulation of general relativity, and in loop quantum gravity, Lorentz covariance is a subtle issue that has been strongly debated. Maintaining manifest Lorentz covariance seems to require introducing either complex-valued fields, presenting a significant obstacle to quantization, or additional (usually second class) constraints whose solution renders the resulting phase space variables harder to interpret in a spacetime picture. After reviewing the sources of difficulty, we present a Lorentz covariant, real formulation in which second class constraints never arise. Rather than a foliation of spacetime, we use a gauge field y, interpreted as a field of observers, to break the SO(3,1) symmetry down to a subgroup SO(3)_y. This symmetry breaking plays a role analogous to that in MacDowell-Mansouri gravity, which is based on Cartan geometry, leading us to a picture of gravity as 'Cartan geometrodynamics.' We study both Lorentz gauge transformations and transformations of the observer field to show that the apparent breaking of SO(3,1) to SO(3) is not in conflict with Lorentz covariance.

EMBEDDING OF NONCOMMUTATIVE MASSIVE QED

In this paper, BFT formalism of Proca model in noncommutative space is investigated. Considering that all theories with first class constraint are gauge theories, Proca model in noncommutative space is not a gauge theory in general due to the appearance of second class constraints in it. In present research, the Proca model is converted into a gauge theory using BFT approach by introducing several auxiliary variables which in turn manage to convert the second class constraints to first class ones. Consequently, we apply modified BFT that preserve the chain structure of constraints. Modified BFT has the benefit that it gives less number of independent gauge parameters and we obtain gauge generating function and infinitesimal gauge variation of fields in Proca model. As results, we investigate partition function of this model and embedded noncommutative Proca is ready to quantize in usual way.

SYMPLECTIC QUANTIZATION OF MASSIVE BOSONIC STRING IN BACKGROUND B-FIELD

We give the details of symplectic quantization for a system containing second class constraints. This method is appropriate for imposing infinite series of constraints due to the boundary conditions. We use this method for massive bosonic strings in a background B-field and find the correct expansions of the fields in terms of the physical modes. We have found a canonical basis for this model.

Covariant gauge fixing and canonical quantization

Theories that contain first class constraints possess gauge invariance which results in the necessity of altering the measure in the associated quantum mechanical path integral. If the path integral is derived from the canonical structure of the theory, then the choice of gauge conditions used in constructing Faddeev's measure cannot be covariant. This shortcoming is normally overcome either by using the "Faddeev-Popov" quantization procedure, or by the approach of Batalin-Fradkin-Fradkina-Vilkovisky, and then demonstrating that these approaches are equivalent to the path integral constructed from the canonical approach with Faddeev's measure. We propose in this paper an alternate way of defining the measure for the path integral when it is constructed using the canonical procedure for theories containing first class constraints and that this new approach can be used in conjunction with covariant gauges. This procedure follows the Faddeev-Popov approach, but rather than working with the form of the gauge transformation in configuration space, it employs the generator of the gauge transformation in phase space. We demonstrate this approach to the path integral by applying it to Yang-Mills theory, a spin-two field and the first order Einstein-Hilbert action in two dimensions. The problems associated with defining the measure for theories containing second-class constraints and ones in which there are fewer secondary first class constraints than primary first class constraints are discussed.

CANONICAL TENSOR MODELS WITH LOCAL TIME

It is an intriguing question how local time can be introduced in the emergent picture of space–time. In this paper, this problem is discussed in the context of tensor models. To consistently incorporate local time into tensor models, a rank-three tensor model with first class constraints in Hamilton formalism is presented. In the limit of usual continuous spaces, the algebra of constraints reproduces that of general relativity in Hamilton formalism. While the momentum constraints can be realized rather easily by the symmetry of the tensor models, the form of the Hamiltonian constraints is strongly limited by the condition of the closure of the whole constraint algebra. Thus the Hamiltonian constraints have been determined on the assumption that they are local and at most cubic in canonical variables. The form of the Hamiltonian constraints has similarity with the Hamiltonian in the c < 1 string field theory, but it seems impossible to realize such a constraint algebras in the framework of vector or matrix models. Instead these models are rather useful as matter theories coupled with the tensor model. In this sense, a three-index tensor is the minimum-rank dynamical variable necessary to describe gravity in terms of tensor models.

Topological parameters in gravity

We present the Hamiltonian analysis of the theory of gravity based on a Lagrangian density containing Hilbert-Palatini term along with three topological densities, Nieh-Yan, Pontryagin and Euler. The addition of these topological terms modifies the symplectic structure non-trivially. The resulting canonical theory develops a dependence on three parameters which are coefficients of these terms. In the time gauge, we obtain a real SU (2) gauge theoretic description with a set of seven first class constraints corresponding to three SU (2) rotations, three spatial diffeomorphism and one to evolution in a timelike direction. Inverse of the coefficient of Nieh-Yan term, identified as Barbero-Immirzi parameter, acts as the coupling constant of the gauge theory.

Note about Hamiltonian structure of non-linear massive gravity

We perform the Hamiltonian analysis of non-linear massive gravity action studied recently in arXiv:1106.3344 [hep-th]. We show that the Hamiltonian constraint is the second class constraint. As a result the theory possesses an odd number of the second class constraints and hence all non physical degrees of freedom cannot be eliminated.

GAUGE-INVARIANT EXTENSION OF LINEARIZED HORAVA GRAVITY

In this paper we have constructed a gauge-invariant extension of a generic Horava Gravity (HG) model (with quadratic curvature terms) in linearized version in a systematic procedure. No additional fields are introduced. The linearized HG model is explicitly shown to be a gauge fixed version of the Einstein Gravity (EG) thus proving the Bellorin–Restuccia conjecture in a robust way. In the process we have explicitly computed the correct Hamiltonian dynamics using Dirac Brackets appearing from the Second Class Constraints present in the HG model. We comment on applying this scheme to the full nonlinear HG.

Editor's Note

Editor's Note

An analytical description of the evolution of binary orbital-parameter distributions in N-body computations of star clusters

A new method is presented to describe the evolution of the orbital-parameter distributions for an initially universal binary population in star clusters by means of the currently largest existing library of N-body models. It is demonstrated that a stellar-dynamical operator exists, which uniquely transforms an initial orbital parameter distribution function for binaries into a new distribution depending on the initial cluster mass and half-mass radius, after some time of dynamical evolution. For the initial distribution the distribution functions derived by Kroupa (1995a,b) are used, which are consistent with constraints for pre-main sequence and Class I binary populations. Binaries with a lower energy and a higher reduced-mass are dissolved preferentially. The stellar-dynamical operator can be used to efficiently calculate and predict binary properties in clusters and whole galaxies without the need for further N-body computations. For the present set of N-body models it is found that the binary populations change their properties on a crossing time-scale such that the stellar dynamical operator can be well parametrized as a function of the initial cluster density. Furthermore it is shown that the binary-fraction in clusters with similar initial velocity dispersions follows the same evolutionary tracks as a function of the passed number of relaxation-times. Present-day observed binary populations in star clusters put constraints on their initial stellar densities which are found to be in the range 10^2 - 2x10^5 M_sun pc^-3 for open clusters and a few x 10^3 - 10^8 M_sun pc^-3 for globular clusters, respectively.

Consistency of canonical formulation of Horava gravity

Both the non-projectable and projectable version of Horava gravity face serious challenges. In the non-projectable version, the constraint algebra is seemingly inconsistent. The projectable version lacks a local Hamiltonian constraint, thus allowing for an extra graviton mode which can be problematic. A new formulation (based on arXiv:1007.1563) of Horava gravity which is naturally realized as a representation of the master constraint algebra (instead of the Dirac algebra) studied by loop quantum gravity researchers is presented. This formulation yields a consistent canonical theory with first class constraints; and captures the essence of Horava gravity in retaining only spatial diffeomorphisms as the physically relevant non-trivial gauge symmetry. At the same time the local Hamiltonian constraint is equivalently enforced by the master constraint.

Women Psychologists

Six women from the same graduate school of psychology, one faculty member and one student from each year of the doctoral program, came together to learn about each other, the developmental experiences of women psychologists, and to supplement the largely overlooked documented histories of women psychologists. As a result, these women, whose personal histories differed greatly, began a project to record their individual and collective life and career development experiences with the ultimate goals of (a) identifying predominant characteristics of the first women psychologists, (b) comparing their paths with those who led the way for women entering the profession, and (c) elucidating for today’s women psychologists the rich legacy of the pioneers in the field, including the familiar challenges of balancing life and work. A review of the literature was undertaken and the consensual qualitative research model was used to analyze data. The core themes revealed were (a) spirited personality traits; (b) constraints of culture, gender, race, and social class; and (c) development influenced by relationships and role models. These themes echoed the experiences of the earliest women psychologists who came from privileged backgrounds; the current women psychologists were from more diverse backgrounds and are seen as women of opportunity.