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

Azimuthal correlations of high transverse momentum jets at next-to-leading order in the parton branching method

AbstractThe azimuthal correlation, $$\Delta \phi _{12}$$ Δ ϕ 12 , of high transverse momentum jets in pp collisions at $$\sqrt{s}=13$$ 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 $$\Delta \phi _{12}$$ Δ ϕ 12 is observed. In the back-to-back region of $${\Delta \phi _{12}}\rightarrow \pi$$ Δ ϕ 12 → π , 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 $$\alpha _\mathrm {s}$$ 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 $$\Delta \phi _{12}$$ Δ ϕ 12 measurements are also compared with predictions using MCatNLO together Pythia8, illustrating the importance of details of the parton shower evolution.</jats:p