Gauge symmetry and W-algebra in higher derivative systems

The problem of gauge symmetry in higher derivative Lagrangian systems is discussed from a Hamiltonian point of view. The number of independent gauge parameters is shown to be in general {\it{less}} than the number of independent primary first class constraints, thereby distinguishing it from conventional first order systems. Different models have been considered as illustrative examples. In particular we show a direct connection between the gauge symmetry and the W-algebra for the rigid relativistic particle.Comment: 1+22 pages, 1 figure, LaTeX, v2; title changed, considerably expanded version with new results, to appear in JHE

An inhomogeneous toy-model of the quantum gravity with explicitly evolvable observables

An inhomogeneous (1+1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating against some curved background space. The quantization scheme including the Wheeler-DeWitt equation and the "particle on a sphere" type of the gauge condition is suggested. In the quantization scheme considered, the "problem of time" is solved by building of the quasi-Heisenberg operators acting in a space of solutions of the Wheeler-DeWitt equation and the normalization of the wave function corresponds to the Klein-Gordon type. To analyze the physical consequences of the scheme, a (1+1)-dimensional background space is considered for which a classical solution is found and quantized. The obtained estimations show the way to solution of the cosmological constant problem, which consists in compensation of the zero-point oscillations of the matter fields by the quantum oscillations of the scale factor. Along with such a compensation, a slow global evolution of a background corresponding to an universe expansion exists.Comment: 18 page

Parent formulation at the Lagrangian level

The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigma model. The proposed formulation can be also seen as a Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV--BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic particle, Yang--Mills theory, and gravity.Comment: 26 pages, discussion of the truncation extended, typos corrected, references adde

Maxwell-like Lagrangians for higher spins

We show how implementing invariance under divergence-free gauge transformations leads to a remarkably simple Lagrangian description of massless bosons of any spin. Our construction covers both flat and (A)dS backgrounds and extends to tensors of arbitrary mixed-symmetry type. Irreducible and traceless fields produce single-particle actions, while whenever trace constraints can be dispensed with the resulting Lagrangians display the same reducible, multi-particle spectra as those emerging from the tensionless limit of free open-string field theory. For all explored options the corresponding kinetic operators take essentially the same form as in the spin-one, Maxwell case.Comment: 77 pages, revised version. Erroneous interpretation and proof of the gauge-fixing procedure for mixed-symmetry fields corrected. As a consequence, the mixed-symmetry, one-particle Lagrangians are to be complemented with conditions on the divergences of the fields; all other conclusions unchanged. Additional minor changes including references added. To appear in JHE

Point massive particle in General Relativity

It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle. Nevertheless, what is the exact solution of Einstein's equations with $\delta$-type source corresponding to a point particle is not known. In the present paper, we prove that the Schwarzschild solution in isotropic coordinates is the asymptotically flat static spherically symmetric solution of Einstein's equations with $\delta$-type energy-momentum tensor corresponding to a point particle. Solution of Einstein's equations is understood in the generalized sense after integration with a test function. Metric components are locally integrable functions for which nonlinear Einstein's equations are mathematically defined. The Schwarzschild solution in isotropic coordinates is locally isometric to the Schwarzschild solution in Schwarzschild coordinates but differs essentially globally. It is topologically trivial neglecting the world line of a point particle. Gravity attraction at large distances is replaced by repulsion at the particle neighbourhood.Comment: 15 pages, references added, 1 figur

Cellular mechanisms by which proinsulin C-peptide prevents insulin-induced neointima formation in human saphenous vein

AIMS/HYPOTHESIS: Endothelial cells (ECs) and smooth muscle cells (SMCs) play key roles in the development of intimal hyperplasia in saphenous vein (SV) bypass grafts. In diabetic patients, insulin administration controls hyperglycaemia but cardiovascular complications remain. Insulin is synthesised as a pro-peptide, from which C-peptide is cleaved and released into the circulation with insulin; exogenous insulin lacks C-peptide. Here we investigate modulation of human SV neointima formation and SV-EC and SV-SMC function by insulin and C-peptide. METHODS: Effects of insulin and C-peptide on neointima formation (organ cultures), EC and SMC proliferation (cell counting), EC migration (scratch wound), SMC migration (Boyden chamber) and signalling (immunoblotting) were examined. A real-time RT-PCR array identified insulin-responsive genes, and results were confirmed by real-time RT-PCR. Targeted gene silencing (siRNA) was used to assess functional relevance. RESULTS: Insulin (100 nmol/l) augmented SV neointimal thickening (70% increase, 14 days), SMC proliferation (55% increase, 7 days) and migration (150% increase, 6 h); effects were abrogated by 10 nmol/l C-peptide. C-peptide did not affect insulin-induced Akt or extracellular signal-regulated kinase signalling (15 min), but array data and gene silencing implicated sterol regulatory element binding transcription factor 1 (SREBF1). Insulin (1-100 nmol/l) did not modify EC proliferation or migration, whereas 10 nmol/l C-peptide stimulated EC proliferation by 40% (5 days). CONCLUSIONS/INTERPRETATION: Our data support a causative role for insulin in human SV neointima formation with a novel counter-regulatory effect of proinsulin C-peptide. Thus, C-peptide can limit the detrimental effects of insulin on SMC function. Co-supplementing insulin therapy with C-peptide could improve therapy in insulin-treated patients