Self-dual formulations of d=3 gravity theories in the path-integral framework

We study the connection, at the quantum level, between d=2+1 dimensional self-dual models with actions of growing (from first to fourth) order, governing the dynamics of helicity +2 (or -2) massive excitations. We obtain identities between generating functionals of the different models using the path-integral framework, this allowing to establish dual maps among relevant vacuum expectation values. We check consistency of these v.e.v.'s with the gauge invariance gained in each mapping.Comment: 26 pages. LaTeX. Minor changes. Published in Int. J Modern Phys. A; http://www.worldscinet.com/ijmp

Spacetime locality in Sp(2) symmetric lagrangian formalism

The existence of a local solution to the Sp(2) master equation for gauge field theory is proven in the framework of perturbation theory and under standard assumptions on regularity of the action. The arbitrariness of solutions to the Sp(2) master equation is described, provided that they are proper. It is also shown that the effective action can be chosen to be Sp(2) and Lorentz invariant (under the additional assumption that the gauge transformation generators are Lorentz tensors).Comment: LaTeX, 13 pages, minor misprints correcte

On the correspondence between the classical and quantum gravity

The relationship between the classical and quantum theories of gravity is reexamined. The value of the gravitational potential defined with the help of the two-particle scattering amplitudes is shown to be in disagreement with the classical result of General Relativity given by the Schwarzschild solution. It is shown also that the potential so defined fails to describe whatever non-Newtonian interactions of macroscopic bodies. An alternative interpretation of the $\hbar^0$-order part of the loop corrections is given directly in terms of the effective action. Gauge independence of that part of the one-loop radiative corrections to the gravitational form factors of the scalar particle is proved, justifying the interpretation proposed.Comment: Latex 2.09, 3 ps. figures, 17 page

Self-adjoint extensions and spectral analysis in Calogero problem

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential $\alpha x^{-2}$. Although the problem is quite old and well-studied, we believe that our consideration, based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some "paradoxes" inherent in the "naive" quantum-mechanical treatment. We study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In addition, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.Comment: 39 page

Gauge and parametrization dependence in higher derivative quantum gravity

The structure of counterterms in higher derivative quantum gravity is reexamined. Nontrivial dependence of charges on the gauge and parametrization is established. Explicit calculations of two-loop contributions are carried out with the help of the generalized renormgroup method demonstrating consistency of the results obtained.Comment: 22 pages, Latex, no figure

Once again on the equivalence theorem

We present the proof of the equivalence theorem in quantum field theory which is based on a formulation of this problem in the field-antifield formalism. As an example, we consider a model in which a different choices of natural finite counterterms is possible, leading to physically non-equivalent quantum theories while the equivalent theorem remains valid.Comment: 12 pages, LATEX, report number was correcte

Ostrogradsky's Hamilton formalism and quantum corrections

By means of a simple scalar field theory it is demonstrated that the Lagrange formalism and Ostrogradsky's Hamilton formalism in the presence of higher derivatives, in general, do not lead to the same results. While the two approaches are equivalent at the classical level, differences appear due to the quantum corrections.Comment: 10 pages, 1 figure, REVTeX