1,065 research outputs found

    Continuous point symmetries in Group Field Theories

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    We discuss the notion of symmetries in non-local field theories characterized by integro-differential equations of motion, from a geometric perspective. We then focus on Group Field Theory (GFT) models of quantum gravity and provide a general analysis of their continuous point symmetry transformations, including the generalized conservation laws following from them

    Generalised conservation laws in non-local field theories

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    We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalised conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalisation of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.Comment: 24 page

    Inequivalent coherent state representations in group field theory

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    In this paper we propose an algebraic formulation of group field theory and consider non-Fock representations based on coherent states. We show that we can construct representations with infinite number of degrees of freedom on compact base manifolds. We also show that these representations break translation symmetry. Since such representations can be regarded as quantum gravitational systems with an infinite number of fundamental pre-geometric building blocks, they may be more suitable for the description of effective geometrical phases of the theory

    Decomposition of L2L^{2}-vector fields on Lipschitz surfaces: characterization via null-spaces of the scalar potential

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    For ∂Ω\partial \Omega the boundary of a bounded and connected strongly Lipschitz domain in Rd\mathbb{R}^{d} with d≥3d\geq3, we prove that any field f∈L2(∂Ω;Rd)f\in L^{2} (\partial \Omega ; \mathbb{R}^{d}) decomposes, in an unique way, as the sum of three silent vector fields---fields whose magnetic potential vanishes in one or both components of Rd∖∂Ω\mathbb{R}^d\setminus\partial \Omega. Moreover, this decomposition is orthogonal if and only if ∂Ω\partial \Omega is a sphere. We also show that any ff in L2(∂Ω;Rd)L^{2} (\partial \Omega ; \mathbb{R}^{d}) is uniquely the sum of two silent fields and a Hardy function, in which case the sum is orthogonal regardless of ∂Ω\partial \Omega; we express the corresponding orthogonal projections in terms of layer potentials. When ∂Ω\partial \Omega is a sphere, both decompositions coincide and match what has been called the Hardy-Hodge decomposition in the literature

    Unique reconstruction of simple magnetizations from their magnetic potential

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    Inverse problems arising in (geo)magnetism are typically ill-posed, in particular {they exhibit non-uniqueness}. Nevertheless, there exist nontrivial model spaces on which the problem is uniquely solvable. Our goal is here to describe such spaces that accommodate constraints suited for applications. In this paper we treat the inverse magnetization problem on a Lipschitz domain with fairly general topology. We characterize the subspace of L2L^{2}-vector fields that causes non-uniqueness, and identify a subspace of harmonic gradients on which the inversion becomes unique. This classification has consequences for applications and we present some of them in the context of geo-sciences. In the second part of the paper, we discuss the space of piecewise constant vector fields. This vector space is too large to make the inversion unique. But as we show, it contains a dense subspace in L2L^2 on which the problem becomes uniquely solvable, i.e., magnetizations from this subspace are uniquely determined by their magnetic potential

    SOME CHANGES REQUIRED TO INCREASE THE PUBLIC'S UTILIZATION OF PREVENTIVE DENTISTRY *

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    Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65250/1/j.1752-7325.1968.tb03923.x.pd

    An experimental study of the behavior of supervisors given high and low power over their subordinates.

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    Thesis (Ph.D.)--Boston University N.B.: page 73 appear to be missing from the physical thesis. We believe that this is a page numbering error on the author's part, and no actual content is missing.An experimental study of the behavior of supervisors given high and low power over their subordinates This study permitted an exploration under specific conditions of the behavior of persons with high power. The definition of power used here was first formulated by Hymovitch, as: the ability of any person in an interpersonal relationship to reward or punish the other person in the relationship in some particular way in some particular situation. Focal points for the theory were two constructs, (1) the power-ratio, within any two person relationship, defined as: the power of one person over a second as compared in some way to the power of the second over the fist, and (2) the maximal-needed power, defined as:a state where an individual higher in the power-ratio perceives that all of his needs, over which the person lower has control, are being satisfied by the person lower in the power-ratio. Theoretical considerations seemed to indicate that persons who varied in distance from the maximal-needed power would accordingly vary in their behavior toward subordinates. An experiment was designed to test formulations about the behavior of persons with high power. In the experimental situation, subjects met in fifteen groups of four and were told they were to work on a problem involving the assessment of persons from autobiographical sketches. They were told that one of them was to be selected on a chance basis as supervisor, the other three would serve as subordinates. They were further instructed that in some of these experiments the supervisor would have high power to recommend rewards for subordinates, while in other experiments he would have low power. In each group, the four subjects were then separated for the remainder of the experiment, and each received instructions that telling them they had high power to recommend rewards for the subordinates; the other two were told they had low power. Each subject then received notes apparently written by each of his subordinates but actually prepared in advance by the experimenter. The notes he received were a hostile notes, a praise note and a neutral note, each coupled with equally inaccurate evaluations of the characters described in the autographical sketches. The supervisor (i.e., each subject) according to instructions, compared these evaluations with "correct" evaluations, and then answered each supposed subordinate. After the experiment, each subject was asked through a questionaire to recommend each subordinate for financial rewards to which he felt the subordinate was entitled. The size of the reward varied between zero and ten dollars. Several weeks after the experimental session, subjects were requested to fill out an autocratic-democratic ideology scale. The data for the experiment were tabulated from (1) a codification of the analysis of notes communicated by all subjects and (2) an analysis of the questionaire. [Truncated

    Exact solutions for shells collapsing towards a pre-existing black hole

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    The gravitational collapse of a star is an important issue both for general relativity and astrophysics, which is related to the well known "frozen star" paradox. This paradox has been discussed intensively and seems to have been solved in the comoving-like coordinates. However, to a real astrophysical observer within a finite time, this problem should be discussed in the point of view of the distant rest-observer, which is the main purpose of this paper. Following the seminal work of Oppenheimer and Snyder (1939), we present the exact solution for one or two dust shells collapsing towards a pre-existing black hole. We find that the metric of the inner region of the shell is time-dependent and the clock inside the shell becomes slower as the shell collapses towards the pre-existing black hole. This means the inner region of the shell is influenced by the property of the shell, which is contrary to the result in Newtonian theory. It does not contradict the Birkhoff's theorem, since in our case we cannot arbitrarily select the clock inside the shell in order to ensure the continuity of the metric. This result in principle may be tested experimentally if a beam of light travels across the shell, which will take a longer time than without the shell. It can be considered as the generalized Shapiro effect, because this effect is due to the mass outside, but not inside as the case of the standard Shapiro effect. We also found that in real astrophysical settings matter can indeed cross a black hole's horizon according to the clock of an external observer and will not accumulate around the event horizon of a black hole, i.e., no "frozen star" is formed for an external observer as matter falls towards a black hole. (abridged)Comment: 18 pages, 6 figures. Accepted for publication in Physics Letters

    Robertson-Walker fluid sources endowed with rotation characterised by quadratic terms in angular velocity parameter

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    Einstein's equations for a Robertson-Walker fluid source endowed with rotation Einstein's equations for a Robertson-Walker fluid source endowed with rotation are presented upto and including quadratic terms in angular velocity parameter. A family of analytic solutions are obtained for the case in which the source angular velocity is purely time-dependent. A subclass of solutions is presented which merge smoothly to homogeneous rotating and non-rotating central sources. The particular solution for dust endowed with rotation is presented. In all cases explicit expressions, depending sinusoidally on polar angle, are given for the density and internal supporting pressure of the rotating source. In addition to the non-zero axial velocity of the fluid particles it is shown that there is also a radial component of velocity which vanishes only at the poles. The velocity four-vector has a zero component between poles

    Slowly, rotating non-stationary, fluid solutions of Einstein's equations and their match to Kerr empty space-time

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    A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in angular speed parameter. It is shown that the match applies to any previously known non-rotating fluid source made to rotate slowly for which a zero pressure boundary surface exists. The method is applied to the dust source of Robertson-Walker and in outline to an interior solution due to McVittie describing gravitational collapse. The applicability of the method to additional examples is transparent. The differential angular velocity of the rotating systems is determined and the induced rotation of local inertial frame is exhibited
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