43 research outputs found
Hamiltonian Multivector Fields and Poisson Forms in Multisymplectic Field Theory
We present a general classification of Hamiltonian multivector fields and of
Poisson forms on the extended multiphase space appearing in the geometric
formulation of first order classical field theories. This is a prerequisite for
computing explicit expressions for the Poisson bracket between two Poisson
forms.Comment: 50 page
Black Hole Entropy in the presence of Chern-Simons Terms
We derive a formula for the black hole entropy in theories with gravitational
Chern-Simons terms, by generalizing Wald's argument which uses the Noether
charge. It correctly reproduces the entropy of three-dimensional black holes in
the presence of Chern-Simons term, which was previously obtained via indirect
methods.Comment: v2: 12 pages, added reference
Kinetic Terms for 2-Forms in Four Dimensions
We study the general form of the possible kinetic terms for 2-form fields in
four dimensions, under the restriction that they have a semibounded energy
density. This is done by using covariant symplectic techniques and generalizes
previous partial results in this direction.Comment: 20 pages, REVTEX, accepted for publication in Phys. Rev.
BF Actions for the Husain-Kuchar Model
We show that the Husain-Kuchar model can be described in the framework of BF
theories. This is a first step towards its quantization by standard
perturbative QFT techniques or the spin-foam formalism introduced in the
space-time description of General Relativity and other diff-invariant theories.
The actions that we will consider are similar to the ones describing the
BF-Yang-Mills model and some mass generating mechanisms for gauge fields. We
will also discuss the role of diffeomorphisms in the new formulations that we
propose.Comment: 21 pages (in DIN A4 format), minor typos corrected; to appear in
Phys. Rev.
Generating Functionals and Lagrangian PDEs
We introduce the concept of Type-I/II generating functionals defined on the
space of boundary data of a Lagrangian field theory. On the Lagrangian side, we
define an analogue of Jacobi's solution to the Hamilton-Jacobi equation for
field theories, and we show that by taking variational derivatives of this
functional, we obtain an isotropic submanifold of the space of Cauchy data,
described by the so-called multisymplectic form formula. We also define a
Hamiltonian analogue of Jacobi's solution, and we show that this functional is
a Type-II generating functional. We finish the paper by defining a similar
framework of generating functions for discrete field theories, and we show that
for the linear wave equation, we recover the multisymplectic conservation law
of Bridges.Comment: 31 pages; 1 figure -- v2: minor change
Background-Independence
Intuitively speaking, a classical field theory is background-independent if
the structure required to make sense of its equations is itself subject to
dynamical evolution, rather than being imposed ab initio. The aim of this paper
is to provide an explication of this intuitive notion. Background-independence
is not a not formal property of theories: the question whether a theory is
background-independent depends upon how the theory is interpreted. Under the
approach proposed here, a theory is fully background-independent relative to an
interpretation if each physical possibility corresponds to a distinct spacetime
geometry; and it falls short of full background-independence to the extent that
this condition fails.Comment: Forthcoming in General Relativity and Gravitatio
Expression of inhibitor of apoptosis protein Livin in renal cell carcinoma and non-tumorous adult kidney
The antiapoptotic Livin/ML-IAP gene has recently gained much attention as a potential new target for cancer therapy. Reports indicating that livin is expressed almost exclusively in tumours, but not in the corresponding normal tissue, suggested that the targeted inhibition of livin may present a novel tumour-specific therapeutic strategy. Here, we compared the expression of livin in renal cell carcinoma and in non-tumorous adult kidney tissue by quantitative real-time reverse transcription-PCR, immunoblotting, and immunohistochemistry. We found that livin expression was significantly increased in tumours (P=0.0077), but was also clearly detectable in non-tumorous adult kidney. Transcripts encoding Livin isoforms α and β were found in both renal cell carcinoma and normal tissue, without obvious qualitative differences. Livin protein in renal cell carcinoma samples exhibited cytoplasmic and/or nuclear staining. In non-tumorous kidney tissue, Livin protein expression was only detectable in specific cell types and restricted to the cytoplasm. Thus, whereas the relative overexpression of livin in renal cell carcinoma indicates that it may still represent a therapeutic target to increase the apoptotic sensitivity of kidney cancer cells, this strategy is likely to be not tumour-specific
A Matrix Integral Solution to [P,Q]=P and Matrix Laplace Transforms
In this paper we solve the following problems: (i) find two differential
operators P and Q satisfying [P,Q]=P, where P flows according to the KP
hierarchy \partial P/\partial t_n = [(P^{n/p})_+,P], with p := \ord P\ge 2;
(ii) find a matrix integral representation for the associated \t au-function.
First we construct an infinite dimensional space {\cal W}=\Span_\BC
\{\psi_0(z),\psi_1(z),... \} of functions of z\in\BC invariant under the action
of two operators, multiplication by z^p and A_c:= z \partial/\partial z - z +
c. This requirement is satisfied, for arbitrary p, if \psi_0 is a certain
function generalizing the classical H\"ankel function (for p=2); our
representation of the generalized H\"ankel function as a double Laplace
transform of a simple function, which was unknown even for the p=2 case,
enables us to represent the \tau-function associated with the KP time evolution
of the space \cal W as a ``double matrix Laplace transform'' in two different
ways. One representation involves an integration over the space of matrices
whose spectrum belongs to a wedge-shaped contour \gamma := \gamma^+ + \gamma^-
\subset\BC defined by \gamma^\pm=\BR_+\E^{\pm\pi\I/p}. The new integrals above
relate to the matrix Laplace transforms, in contrast with the matrix Fourier
transforms, which generalize the Kontsevich integrals and solve the operator
equation [P,Q]=1.Comment: 27 pages, LaTeX, 1 figure in PostScrip
Mass and Angular Momentum in General Relativity
We present an introduction to mass and angular momentum in General
Relativity. After briefly reviewing energy-momentum for matter fields, first in
the flat Minkowski case (Special Relativity) and then in curved spacetimes with
or without symmetries, we focus on the discussion of energy-momentum for the
gravitational field. We illustrate the difficulties rooted in the Equivalence
Principle for defining a local energy-momentum density for the gravitational
field. This leads to the understanding of gravitational energy-momentum and
angular momentum as non-local observables that make sense, at best, for
extended domains of spacetime. After introducing Komar quantities associated
with spacetime symmetries, it is shown how total energy-momentum can be
unambiguously defined for isolated systems, providing fundamental tests for the
internal consistency of General Relativity as well as setting the conceptual
basis for the understanding of energy loss by gravitational radiation. Finally,
several attempts to formulate quasi-local notions of mass and angular momentum
associated with extended but finite spacetime domains are presented, together
with some illustrations of the relations between total and quasi-local
quantities in the particular context of black hole spacetimes. This article is
not intended to be a rigorous and exhaustive review of the subject, but rather
an invitation to the topic for non-experts. In this sense we follow essentially
the expositions in Szabados 2004, Gourgoulhon 2007, Poisson 2004 and Wald 84,
and refer the reader interested in further developments to the existing
literature, in particular to the excellent and comprehensive review by Szabados
(2004).Comment: 41 pages. Notes based on the lecture given at the C.N.R.S. "School on
Mass" (June 2008) in Orleans, France. To appear as proceedings in the book
"Mass and Motion in General Relativity", eds. L. Blanchet, A. Spallicci and
B. Whiting. Some comments and references added
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Azimuthal correlations of high transverse momentum jets at next-to-leading order in the parton branching method
AbstractThe azimuthal correlation,
Δ
Ď•
12
, of high transverse momentum jets in pp collisions at
s
=
13
 TeV is studied by applying PB-TMD distributions to NLO calculations via MCatNLO together with the PB-TMD parton shower. A very good description of the cross section as a function of
Δ
Ď•
12
is observed. In the back-to-back region of
Δ
Ď•
12
→
Ď€
, a very good agreement is observed with the PB-TMD Set 2 distributions while significant deviations are obtained with the PB-TMD Set 1 distributions. Set 1 uses the evolution scale while Set 2 uses transverse momentum as an argument in
α
s
, and the above observation therefore confirms the importance of an appropriate soft-gluon coupling in angular ordered parton evolution. The total uncertainties of the predictions are dominated by the scale uncertainties of the matrix element, while the uncertainties coming from the PB-TMDs and the corresponding PB-TMD shower are very small. The
Δ
Ď•
12
measurements are also compared with predictions using MCatNLO together Pythia8, illustrating the importance of details of the parton shower evolution.</jats:p