22 research outputs found
Master Functional And Proper Formalism For Quantum Gauge Field Theory
We develop a general field-covariant approach to quantum gauge theories.
Extending the usual set of integrated fields and external sources to "proper"
fields and sources, which include partners of the composite fields, we define
the master functional Omega, which collects one-particle irreducible diagrams
and upgrades the usual Gamma-functional in several respects. The functional
Omega is determined from its classical limit applying the usual diagrammatic
rules to the proper fields. Moreover, it behaves as a scalar under the most
general perturbative field redefinitions, which can be expressed as linear
transformations of the proper fields. We extend the Batalin-Vilkovisky
formalism and the master equation. The master functional satisfies the extended
master equation and behaves as a scalar under canonical transformations. The
most general perturbative field redefinitions and changes of gauge-fixing can
be encoded in proper canonical transformations, which are linear and do not mix
integrated fields and external sources. Therefore, they can be applied as true
changes of variables in the functional integral, instead of mere replacements
of integrands. This property overcomes a major difficulty of the functional
Gamma. Finally, the new approach allows us to prove the renormalizability of
gauge theories in a general field-covariant setting. We generalize known
cohomological theorems to the master functional and show that when there are no
gauge anomalies all divergences can be subtracted by means of parameter
redefinitions and proper canonical transformations.Comment: 32 pages; v2: minor changes and proof corrections, EPJ
Consistent irrelevant deformations of interacting conformal field theories
I show that under certain conditions it is possible to define consistent
irrelevant deformations of interacting conformal field theories. The
deformations are finite or have a unique running scale ("quasi-finite"). They
are made of an infinite number of lagrangian terms and a finite number of
independent parameters that renormalize coherently. The coefficients of the
irrelevant terms are determined imposing that the beta functions of the
dimensionless combinations of couplings vanish ("quasi-finiteness equations").
The expansion in powers of the energy is meaningful for energies much smaller
than an effective Planck mass. Multiple deformations can be considered also. I
study the general conditions to have non-trivial solutions. As an example, I
construct the Pauli deformation of the IR fixed point of massless non-Abelian
Yang-Mills theory with N_c colors and N_f <~ 11N_c/2 flavors and compute the
couplings of the term F^3 and the four-fermion vertices. Another interesting
application is the construction of finite chiral irrelevant deformations of N=2
and N=4 superconformal field theories. The results of this paper suggest that
power-counting non-renormalizable theories might play a role in the description
of fundamental physics.Comment: 23 pages, 5 figures; reference updated - JHE
Cosmological Acceleration from Virtual Gravitons
Intrinsic properties of the space itself and quantum fluctuations of its
geometry are sufficient to provide a mechanism for the acceleration of
cosmological expansion (dark energy effect). Applying
Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy approach to self-consistent
equations of one-loop quantum gravity, we found exact solutions that yield
acceleration. The permanent creation and annihilation of virtual gravitons is
not in exact balance because of the expansion of the Universe. The excess
energy comes from the spontaneous process of graviton creation and is trapped
by the background. It provides the macroscopic quantum effect of cosmic
acceleration.Comment: 6 pages, REVTeX
A Master Functional For Quantum Field Theory
We study a new generating functional of one-particle irreducible diagrams in
quantum field theory, called master functional, which is invariant under the
most general perturbative changes of field variables. The usual functional
Gamma does not behave as a scalar under the transformation law inherited from
its very definition as the Legendre transform of W = ln Z, although it does
behave as a scalar under an unusual transformation law. The master functional,
on the other hand, is the Legendre transform of an improved functional W with
respect to the sources coupled to both elementary and composite fields. The
inclusion of certain improvement terms in W and Z is necessary to make the new
Legendre transform well defined. The master functional behaves as a scalar
under the transformation law inherited from its very definition. Moreover, it
admits a proper formulation, obtained extending the set of integrated fields to
so-called proper fields, which allows us to work without passing through Z, W
or Gamma. In the proper formulation the classical action coincides with the
classical limit of the master functional, and correlation functions and
renormalization are calculated applying the usual diagrammatic rules to the
proper fields. Finally, the most general change of field variables, including
the map relating bare and renormalized fields, is a linear redefinition of the
proper fields.Comment: 38 pages, 1 figure; v2: minor changes and proof corrections, EPJ
A General Field-Covariant Formulation Of Quantum Field Theory
In all nontrivial cases renormalization, as it is usually formulated, is not
a change of integration variables in the functional integral, plus parameter
redefinitions, but a set of replacements, of actions and/or field variables and
parameters. Because of this, we cannot write simple identities relating bare
and renormalized generating functionals, or generating functionals before and
after nonlinear changes of field variables. In this paper we investigate this
issue and work out a general field-covariant approach to quantum field theory,
which allows us to treat all perturbative changes of field variables, including
the relation between bare and renormalized fields, as true changes of variables
in the functional integral, under which the functionals Z and W = ln Z behave
as scalars. We investigate the relation between composite fields and changes of
field variables, and show that, if J are the sources coupled to the elementary
fields, all changes of field variables can be expressed as J-dependent
redefinitions of the sources L coupled to the composite fields. We also work
out the relation between the renormalization of variable-changes and the
renormalization of composite fields. Using our transformation rules it is
possible to derive the renormalization of a theory in a new variable frame from
the renormalization in the old variable frame, without having to calculate it
anew. We define several approaches, useful for different purposes, in
particular a linear approach where all variable changes are described as linear
source redefinitions. We include a number of explicit examples.Comment: 36 pages, 2 figures; v2: minor changes and proof corrections, EPJ
Massive gravity as a quantum gauge theory
We present a new point of view on the quantization of the massive
gravitational field, namely we use exclusively the quantum framework of the
second quantization. The Hilbert space of the many-gravitons system is a Fock
space where the one-particle Hilbert
space carries the direct sum of two unitary irreducible
representations of the Poincar\'e group corresponding to two particles of mass
and spins 2 and 0, respectively. This Hilbert space is canonically
isomorphic to a space of the type where is a gauge charge
defined in an extension of the Hilbert space
generated by the gravitational field and some ghosts fields
(which are vector Fermi fields) and (which
are vector field Bose fields.)
Then we study the self interaction of massive gravity in the causal
framework. We obtain a solution which goes smoothly to the zero-mass solution
of linear quantum gravity up to a term depending on the bosonic ghost field.
This solution depends on two real constants as it should be; these constants
are related to the gravitational constant and the cosmological constant. In the
second order of the perturbation theory we do not need a Higgs field, in sharp
contrast to Yang-Mills theory.Comment: 35 pages, no figur
On the perturbative expansion of a quantum field theory around a topological sector
The idea of treating general relativistic theories in a perturbative
expansion around a topological theory has been recently put forward in the
quantum gravity literature. Here we investigate the viability of this idea, by
applying it to conventional Yang--Mills theory on flat spacetime. We find that
the expansion around the topological theory coincides with the usual expansion
around the abelian theory, though the equivalence is non-trivial. In this
context, the technique appears therefore to be viable, but not to bring
particularly new insights. Some implications for gravity are discussed.Comment: 7 page
Gauge Formulation for Higher Order Gravity
This work is an application of the second order gauge theory for the Lorentz
group, where a description of the gravitational interaction is obtained which
includes derivatives of the curvature. We analyze the form of the second field
strenght, , in terms of geometrical variables. All possible
independent Lagrangians constructed with quadratic contractions of and
quadratic contractions of are analyzed. The equations of motion for a
particular Lagrangian, which is analogous to Podolsky's term of his Generalized
Electrodynamics, are calculated. The static isotropic solution in the linear
approximation was found, exhibiting the regular Newtonian behaviour at short
distances as well as a meso-large distance modification.Comment: Published versio
Quantum Gravitational Corrections to the Nonrelativistic Scattering Potential of Two Masses
We treat general relativity as an effective field theory, obtaining the full
nonanalytic component of the scattering matrix potential to one-loop order. The
lowest order vertex rules for the resulting effective field theory are
presented and the one-loop diagrams which yield the leading nonrelativistic
post-Newtonian and quantum corrections to the gravitational scattering
amplitude to second order in G are calculated in detail. The Fourier
transformed amplitudes yield a nonrelativistic potential and our result is
discussed in relation to previous calculations. The definition of a potential
is discussed as well and we show how the ambiguity of the potential under
coordinate changes is resolved.Comment: 27 pages, 17 figure
String Theory, Unification and Quantum Gravity
An overview is given of the way in which the unification program of particle
physics has evolved into the proposal of superstring theory as a prime
candidate for unifying quantum gravity with the other forces and particles of
nature. A key concern with quantum gravity has been the problem of ultraviolet
divergences, which is naturally solved in string theory by replacing particles
with spatially extended states as the fundamental excitations. String theory
turns out, however, to contain many more extended-object states than just
strings. Combining all this into an integrated picture, called M-theory,
requires recognition of the r\^ole played by a web of nonperturbative duality
symmetries suggested by the nonlinear structures of the field-theoretic
supergravity limits of string theory.Comment: 29 pages, 13 figures, 3 tables; Lectures given at the 6th Aegean
Summer School "Quantum Gravity and Quantum Cosmology", Chora, Naxos Island,
Greece, 12-17 September 201