1,572 research outputs found
Implication of Compensator Field and Local Scale Invariance in the Standard Model
We introduce Weyl's scale symmetry into the standard model (SM) as a local
symmetry. This necessarily introduces gravitational interactions in addition to
the local scale invariance group \tilde U(1) and the SM groups SU(3) X SU(2) X
U(1). The only other new ingredients are a new scalar field \sigma and the
gauge field for \tilde U(1) we call the Weylon. A noteworthy feature is that
the system admits the St\" uckelberg-type compensator. The \sigma couples to
the scalar curvature as (-\zeta/2) \sigma^2 R, and is in turn related to a St\"
uckelberg-type compensator \varphi by \sigma \equiv M_P e^{-\varphi/M_P} with
the Planck mass M_P. The particular gauge \varphi = 0 in the St\" uckelberg
formalism corresponds to \sigma = M_P, and the Hilbert action is induced
automatically. In this sense, our model presents yet another mechanism for
breaking scale invariance at the classical level. We show that our model
naturally accommodates the chaotic inflation scenario with no extra field.Comment: This work is to be read in conjunction with our recent comments
hep-th/0702080, arXiv:0704.1836 [hep-ph] and arXiv:0712.2487 [hep-ph]. The
necessary ingredients for describing chaotic inflation in the SM as
entertained by Bezrukov and Shaposhnikov [17] have been provided by our
original model [8]. We regret their omission in citing our original model [8
The C-metric as a colliding plane wave space-time
It is explicitly shown that part of the C-metric space-time inside the black
hole horizon may be interpreted as the interaction region of two colliding
plane waves with aligned linear polarization, provided the rotational
coordinate is replaced by a linear one. This is a one-parameter generalization
of the degenerate Ferrari-Ibanez solution in which the focussing singularity is
a Cauchy horizon rather than a curvature singularity.Comment: 6 pages. To appear in Classical and Quantum Gravit
The inception of Symplectic Geometry: the works of Lagrange and Poisson during the years 1808-1810
The concept of a symplectic structure first appeared in the works of Lagrange
on the so-called "method of variation of the constants". These works are
presented, together with those of Poisson, who first defined the composition
law called today the "Poisson bracket". The method of variation of the
constants is presented using today's mathematical concepts and notations.Comment: Presented at the meeting "Poisson 2008" in Lausanne, July 2008.
Published in Letters in Mathematical Physics. 22 page
Accelerated black holes in an anti-de Sitter universe
The C-metric is one of few known exact solutions of Einstein's field
equations which describes the gravitational field of moving sources. For a
vanishing or positive cosmological constant, the C-metric represents two
accelerated black holes in asymptotically flat or de Sitter spacetime. For a
negative cosmological constant the structure of the spacetime is more
complicated. Depending on the value of the acceleration, it can represent one
black hole or a sequence of pairs of accelerated black holes in the spacetime
with an anti-de Sitter-like infinity. The global structure of this spacetime is
analyzed and compared with an empty anti-de Sitter universe. It is illustrated
by 3D conformal-like diagrams.Comment: 14 pages, 17 figures [see
http://utf.mff.cuni.cz/~krtous/physics/CADS/ for the version with the high
quality figures and for related animations and interactive 3D diagrams
Self-adjoint symmetry operators connected with the magnetic Heisenberg ring
We consider symmetry operators a from the group ring C[S_N] which act on the
Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We
investigate such symmetry operators a which are self-adjoint (in a sence
defined in the paper) and which yield consequently observables of the
Heisenberg model. We prove the following results: (i) One can construct a
self-adjoint idempotent symmetry operator from every irreducible character of
every subgroup of S_N. This leads to a big manifold of observables. In
particular every commutation symmetry yields such an idempotent. (ii) The set
of all generating idempotents of a minimal right ideal R of C[S_N] contains one
and only one idempotent which ist self-adjoint. (iii) Every self-adjoint
idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k
which are also self-adjoint and pairwise orthogonal. We give a computer
algorithm for the calculation of such decompositions. Furthermore we present 3
additional algorithms which are helpful for the calculation of self-adjoint
operators by means of discrete Fourier transforms of S_N. In our investigations
we use computer calculations by means of our Mathematica packages PERMS and
HRing.Comment: 13 page
An alternative formulation of classical electromagnetic duality
By introducing a doublet of electromagnetic four dimensional vector
potentials, we set up a manifestly Lorentz covariant and SO(2) duality
invariant classical field theory of electric and magnetic charges. In our
formulation one does not need to introduce the concept of Dirac string.Comment: 14 pages, no figures, Latex, minor corrections, references and
acknowledgements adde
Periodic and discrete Zak bases
Weyl's displacement operators for position and momentum commute if the
product of the elementary displacements equals Planck's constant. Then, their
common eigenstates constitute the Zak basis, each state specified by two phase
parameters. Upon enforcing a periodic dependence on the phases, one gets a
one-to-one mapping of the Hilbert space on the line onto the Hilbert space on
the torus. The Fourier coefficients of the periodic Zak bases make up the
discrete Zak bases. The two bases are mutually unbiased. We study these bases
in detail, including a brief discussion of their relation to Aharonov's modular
operators, and mention how they can be used to associate with the single degree
of freedom of the line a pair of genuine qubits.Comment: 15 pages, 3 figures; displayed abstract is shortened, see the paper
for the complete abstrac
Measuring the parity of an -qubit state
We present a scheme for a projective measurement of the parity operator
of -qubits. Our protocol uses a single
ancillary qubit, or a probe qubit, and involves manipulations of the total spin
of the qubits without requiring individual addressing. We illustrate our
protocol in terms of an experimental implementation with atomic ions in a
two-zone linear Paul trap, and further discuss its extensions to several more
general cases.Comment: 4 pages, 2 figure
Interpreting the C-metric
The basic properties of the C-metric are well known. It describes a pair of
causally separated black holes which accelerate in opposite directions under
the action of forces represented by conical singularities. However, these
properties can be demonstrated much more transparently by making use of
recently developed coordinate systems for which the metric functions have a
simple factor structure. These enable us to obtain explicit
Kruskal-Szekeres-type extensions through the horizons and construct
two-dimensional conformal Penrose diagrams. We then combine these into a
three-dimensional picture which illustrates the global causal structure of the
space-time outside the black hole horizons. Using both the weak field limit and
some invariant quantities, we give a direct physical interpretation of the
parameters which appear in the new form of the metric. For completeness,
relations to other familiar coordinate systems are also discussed.Comment: 22 pages, 14 figures (low-resolution figures; for the version with
high-resolution figures see http://utf.mff.cuni.cz/~krtous/papers/ or
http://www-staff.lboro.ac.uk/~majbg/
The Post-Newtonian Limit of f(R)-gravity in the Harmonic Gauge
A general analytic procedure is developed for the post-Newtonian limit of
-gravity with metric approach in the Jordan frame by using the harmonic
gauge condition. In a pure perturbative framework and by using the Green
function method a general scheme of solutions up to order is shown.
Considering the Taylor expansion of a generic function it is possible to
parameterize the solutions by derivatives of . At Newtonian order,
, all more important topics about the Gauss and Birkhoff theorem are
discussed. The corrections to "standard" gravitational potential
(-component of metric tensor) generated by an extended uniform mass
ball-like source are calculated up to order. The corrections, Yukawa
and oscillating-like, are found inside and outside the mass distribution. At
last when the limit is considered the -gravity converges
in General Relativity at level of Lagrangian, field equations and their
solutions.Comment: 16 pages, 10 figure
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