1,070 research outputs found
Continuous point symmetries in Group Field Theories
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
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
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 -vector fields on Lipschitz surfaces: characterization via null-spaces of the scalar potential
For the boundary of a bounded and connected strongly
Lipschitz domain in with , we prove that any field
decomposes, in an unique way,
as the sum of three silent vector fields---fields whose magnetic potential
vanishes in one or both components of .
Moreover, this decomposition is orthogonal if and only if is
a sphere. We also show that any in is uniquely the sum of two silent fields and a Hardy function,
in which case the sum is orthogonal regardless of ; we express
the corresponding orthogonal projections in terms of layer potentials. When
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
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 -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 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 *
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.
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
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
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
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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