155 research outputs found
Background field method, Batalin-Vilkovisky formalism and parametric completeness of renormalization
We investigate the background field method with the Batalin-Vilkovisky
formalism, to generalize known results, study parametric completeness and
achieve a better understanding of several properties. In particular, we study
renormalization and gauge dependence to all orders. Switching between the
background field approach and the usual approach by means of canonical
transformations, we prove parametric completeness without making use of
cohomological theorems, namely show that if the starting classical action is
sufficiently general all divergences can be subtracted by means of parameter
redefinitions and canonical transformations. Our approach applies to
renormalizable and non-renormalizable theories that are manifestly free of
gauge anomalies and satisfy the following assumptions: the gauge algebra is
irreducible and closes off shell, the gauge transformations are linear
functions of the fields, and closure is field-independent. Yang-Mills theories
and quantum gravity in arbitrary dimensions are included, as well as effective
and higher-derivative versions of them, but several other theories, such as
supergravity, are left out.Comment: 40 pages; v2: minor changes, PRD versio
Aspects of perturbative unitarity
We reconsider perturbative unitarity in quantum field theory and upgrade
several arguments and results. The minimum assumptions that lead to the largest
time equation, the cutting equations and the unitarity equation are identified.
Using this knowledge and a special gauge, we give a new, simpler proof of
perturbative unitarity in gauge theories and generalize it to quantum gravity,
in four and higher dimensions. The special gauge interpolates between the
Feynman gauge and the Coulomb gauge without double poles. When the Coulomb
limit is approached, the unphysical particles drop out of the cuts and the
cutting equations are consistently projected onto the physical subspace. The
proof does not extend to nonlocal quantum field theories of gauge fields and
gravity, whose unitarity remains uncertain.Comment: 37 pages, 9 figures; v2: minor changes, Phys. Rev.
Properties Of The Classical Action Of Quantum Gravity
The classical action of quantum gravity, determined by renormalization,
contains infinitely many independent couplings and can be expressed in
different perturbatively equivalent ways. We organize it in a convenient form,
which is based on invariants constructed with the Weyl tensor. We show that the
FLRW metrics are exact solutions of the field equations in arbitrary
dimensions, and so are all locally conformally flat solutions of the Einstein
equations. Moreover, expanding the metric tensor around locally conformally
flat backgrounds the quadratic part of the action is free of higher
derivatives. Black-hole solutions of Schwarzschild and Kerr type are modified
in a non-trivial way. We work out the first corrections to their metrics and
study their properties.Comment: 21 pages; v2: minor changes and proof corrections, JHE
Renormalization of gauge theories without cohomology
We investigate the renormalization of gauge theories without assuming
cohomological properties. We define a renormalization algorithm that preserves
the Batalin-Vilkovisky master equation at each step and automatically extends
the classical action till it contains sufficiently many independent parameters
to reabsorb all divergences into parameter-redefinitions and canonical
transformations. The construction is then generalized to the master functional
and the field-covariant proper formalism for gauge theories. Our results hold
in all manifestly anomaly-free gauge theories, power-counting renormalizable or
not. The extension algorithm allows us to solve a quadratic problem, such as
finding a sufficiently general solution of the master equation, even when it is
not possible to reduce it to a linear (cohomological) problem.Comment: 29 pages; v2: references updated, EPJ
Fakeons and the classicization of quantum gravity: the FLRW metric
Under certain assumptions, it is possible to make sense of higher derivative
theories by quantizing the unwanted degrees of freedom as fakeons, which are
later projected away. Then the true classical limit is obtained by classicizing
the quantum theory. Since quantum field theory is formulated perturbatively,
the classicization is also perturbative. After deriving a number of properties
in a general setting, we consider the theory of quantum gravity that emerges
from the fakeon idea and study its classicization, focusing on the FLRW metric.
We point out cases where the fakeon projection can be handled exactly, which
include radiation, the vacuum energy density and the combination of the two,
and cases where it cannot, which include dust. Generically, the classical limit
shares many features with the quantum theory it comes from, including the
impossibility to write down complete, "exact" field equations, to the extent
that asymptotic series and nonperturbative effects come into play.Comment: 27 pages, 3 figures; v2: typos corrected and refs. updated, JHE
Adler-Bardeen theorem and manifest anomaly cancellation to all orders in gauge theories
We reconsider the Adler-Bardeen theorem for the cancellation of gauge
anomalies to all orders, when they vanish at one loop. Using the
Batalin-Vilkovisky formalism and combining the dimensional-regularization
technique with the higher-derivative gauge invariant regularization, we prove
the theorem in the most general perturbatively unitary renormalizable gauge
theories coupled to matter in four dimensions, and identify the subtraction
scheme where anomaly cancellation to all orders is manifest, namely no
subtractions of finite local counterterms are required from two loops onwards.
Our approach is based on an order-by-order analysis of renormalization, and,
differently from most derivations existing in the literature, does not make use
of arguments based on the properties of the renormalization group. As a
consequence, the proof we give also applies to conformal field theories and
finite theories.Comment: 43 pages; EPJ
On the quantum field theory of the gravitational interactions
We study the main options for a unitary and renormalizable, local quantum
field theory of the gravitational interactions. The first model is a Lee-Wick
superrenormalizable higher-derivative gravity, formulated as a nonanalytically
Wick rotated Euclidean theory. We show that, under certain conditions, the
matrix is unitary when the cosmological constant vanishes. The model is the
simplest of its class. However, infinitely many similar options are allowed,
which raises the issue of uniqueness. To deal with this problem, we propose a
new quantization prescription, by doubling the unphysical poles of the
higher-derivative propagators and turning them into Lee-Wick poles. The
Lagrangian of the simplest theory of quantum gravity based on this idea is the
linear combination of , , and the
cosmological term. Only the graviton propagates in the cutting equations and,
when the cosmological constant vanishes, the matrix is unitary. The theory
satisfies the locality of counterterms and is renormalizable by power counting.
It is unique in the sense that it is the only one with a dimensionless gauge
coupling.Comment: 23 pages, 1 figure; v2: minor changes, JHE
Fakeons, Microcausality And The Classical Limit Of Quantum Gravity
We elaborate on the idea of fake particle and study its physical
consequences. When a theory contains fakeons, the true classical limit is
determined by the quantization and a subsequent process of "classicization".
One of the major predictions due to the fake particles is the violation of
microcausality, which survives the classical limit. This fact gives hope to
detect the violation experimentally. A fakeon of spin 2, together with a scalar
field, is able to make quantum gravity renormalizable while preserving
unitarity. We claim that the theory of quantum gravity emerging from this
construction is the right one. By means of the classicization, we work out the
corrections to the field equations of general relativity. We show that the
finalized equations have, in simple terms, the form ,
where is an average that includes a little bit of "future".Comment: 27 pages, 4 figures; v2: expanded intro and bibliography, Class. Q.
Gra
Background field method and the cohomology of renormalization
Using the background field method and the Batalin-Vilkovisky formalism, we
prove a key theorem on the cohomology of perturbatively local functionals of
arbitrary ghost numbers, in renormalizable and nonrenormalizable quantum field
theories whose gauge symmetries are general covariance, local Lorentz symmetry,
non-Abelian Yang-Mills symmetries and Abelian gauge symmetries. Interpolating
between the background field approach and the usual, nonbackground approach by
means of a canonical transformation, we take advantage of the properties of
both approaches and prove that a closed functional is the sum of an exact
functional plus a functional that depends only on the physical fields and
possibly the ghosts. The assumptions of the theorem are the mathematical
versions of general properties that characterize the counterterms and the local
contributions to the potential anomalies. This makes the outcome a theorem on
the cohomology of renormalization, rather than the whole local cohomology. The
result supersedes numerous involved arguments that are available in the
literature.Comment: 27 pages; v2: more references, PRD versio
Weighted power counting and chiral dimensional regularization
We define a modified dimensional-regularization technique that overcomes
several difficulties of the ordinary technique, and is specially designed to
work efficiently in chiral and parity violating quantum field theories, in
arbitrary dimensions greater than 2. When the dimension of spacetime is
continued to complex values, spinors, vectors and tensors keep the components
they have in the physical dimension, therefore the matrices are the
standard ones. Propagators are regularized with the help of evanescent
higher-derivative kinetic terms, which are of the Majorana type in the case of
chiral fermions. If the new terms are organized in a clever way, weighted power
counting provides an efficient control on the renormalization of the theory,
and allows us to show that the resulting chiral dimensional regularization is
consistent to all orders. The new technique considerably simplifies the proofs
of properties that hold to all orders, and makes them suitable to be
generalized to wider classes of models. Typical examples are the
renormalizability of chiral gauge theories and the Adler-Bardeen theorem. The
difficulty of explicit computations, on the other hand, may increase.Comment: 41 pages; v2: minor changes, PRD versio
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