On the BV quantization of gauge gravitation theory

Using the Batalin-Vilkovisky technique and the background field method the proof of gauge invariant renormalizability is elaborated for a generic model of quantum gravity which is diffeomorphism invariant and has no other, potentially anomalous, symmetries. The gauge invariant renormalizability means that in all orders of loop expansion of the quantum effective action one can control deformations of the generators of gauge transformations which leave such an action invariant....

This is the first in a series of papers on an attempt to understand quantum field theory mathematically. In this paper we shall introduce and study BV QFT algebra and BV QFT as the proto-algebraic model of quantum field theory by exploiting Batalin-Vilkovisky quantization scheme. We shall develop a complete theory of obstruction (anomaly) to quantization of classical observables and propose that expectation value of quantized observable is certain quantum homotopy invariant. ...

Despite the fact that quantum gravity is non-renormalisable, a consistent and mathematically rigorous construction of a perturbation series is possible. This is based on the use of the Batalin-Vilkovisky-Becchi-Rouet-Stora-Tyutin formalism for gauge theories, the methods of perturbative algebraic quantum field theory and the principle of local covariance. The truncation of the series can be interpreted as an effective quantum field theory which provides predictions for obse...

This is a paper about geometry of (iterated) variations. We explain why no sources of divergence are built into the Batalin-Vilkovisky (BV) Laplacian, whence there is no need to postulate any ad hoc conventions such as "$\delta(0)=0$" and "$\log\delta(0)=0$" within BV-approach to quantisation of gauge systems. Remarkably, the geometry of iterated variations does not refer at all to the construction of Dirac's $\delta$-function as a limit of smooth kernels. We illustrate the r...

On the basis of dynamic quantization method we build in this paper a new mathematically correct quantization scheme of gravity. In the frame of this scheme we develop a canonical formalism in tetrad-connection variables in 4-D theory of pure gravity. In this formalism the regularized quantized fields corresponding to the classical tetrad and connection fields are constructed. It is shown, that the regularized fields satisfy to general covariant equations of motion, which ...

The current understanding of renormalization in quantum gravity (QG) is based on the fact that UV divergences of effective actions in the covariant QG models are covariant local expressions. This fundamental statement plays a central role in QG and, therefore, it is important to prove it for the widest possible range of the QG theories. Using the Batalin-Vilkovisky technique and the background field method, we elaborate the proof of gauge invariant renormalizability for a gen...

This survey article is an invited contribution to the Encyclopedia of Mathematical Physics, 2nd edition. We provide an accessible overview on relevant applications of higher and derived geometry to theoretical physics, including higher gauge theory, higher geometric quantization and Batalin-Vilkovisky formalism.

We generalize the method of superfield Lagrangian BRST quantization in the part of the gauge-fixing procedure and obtain a quantization method that can be considered as an alternative to the Batalin - Vilkovisky formalism.

The Batalin-Vilkovisky (BV) formalism is a powerful generalization of the BRST approach of gauge theories and allows to treat more general field theories. We will see how, starting from the case of a finite dimensional configuration space, we can see this formalism as a theory of integration for polyvectors over the shifted cotangent bundle of the configuration space, and arrive at a formula that admits a generalization to the infinite dimensional case. The process of gauge f...

This is the Preface to the special issue of 'International Journal of Geometric Methods in Modern Physics', v.3, N.1 (2006) dedicated to the 50th aniversary of gauge gravitation theory. It addresses the geometry underlying gauge gravitation theories, their higher-dimensional, supergauge and non-commutatuve extensions.