15 research outputs found
From massive gravity to modified general relativity II
We continue our investigation of massive gravity in the massless limit of
vanishing graviton mass. From gauge invariance we derive the most general
coupling between scalar matter and gravity. We get further couplings beside the
standard coupling to the energy-momentum tensor. On the classical level this
leads to a further modification of general relativity.Comment: 12 pages, no figur
Massive gravity from descent equations
Both massless and massive gravity are derived from descent equations
(Wess-Zumino consistency conditions). The massive theory is a continuous
deformation of the massless one.Comment: 8 pages, no figur
The Interaction of Quantum Gravity with Matter
The interaction of (linearized) gravitation with matter is studied in the
causal approach up to the second order of perturbation theory. We consider the
generic case and prove that gravitation is universal in the sense that the
existence of the interaction with gravitation does not put new constraints on
the Lagrangian for lower spin fields. We use the formalism of quantum off-shell
fields which makes our computation more straightforward and simpler.Comment: 25 page
The Standard Model and its Generalizations in Epstein-Glaser Approach to Renormalization Theory II: the Fermion Sector and the Axial Anomaly
We complete our study of non-Abelian gauge theories in the framework of
Epstein-Glaser approach to renormalization theory including in the model an
arbitrary number of Dirac Fermions. We consider the consistency of the model up
to the third order of the perturbation theory. In the second order we obtain
pure group theoretical relations expressing a representation property of the
numerical coefficients appearing in the left and right handed components of the
interaction Lagrangian. In the third order of the perturbation theory we obtain
the the condition of cancellation of the axial anomaly.Comment: 38 pages, LATEX 2e, extensive rewritting, some errors eliminate
Perturbative Gravity in the Causal Approach
Quantum theory of the gravitation in the causal approach is studied up to the
second order of perturbation theory. We prove gauge invariance and
renormalizability in the second order of perturbation theory for the pure
gravity system (massless and massive). Then we investigate the interaction of
massless gravity with matter (described by scalars and spinors) and massless
Yang-Mills fields. We obtain a difference with respect to the classical field
theory due to the fact that in quantum field theory one cannot enforce the
divergenceless property on the vector potential and this spoils the
divergenceless property of the usual energy-momentum tensor. To correct this
one needs a supplementary ghost term in the interaction Lagrangian.Comment: 50 pages, no figures, some changes in the last sectio
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
Massive Vector Mesons and Gauge Theory
We show that the requirements of renormalizability and physical consistency
imposed on perturbative interactions of massive vector mesons fix the theory
essentially uniquely. In particular physical consistency demands the presence
of at least one additional physical degree of freedom which was not part of the
originally required physical particle content. In its simplest realization
(probably the only one) these are scalar fields as envisaged by Higgs but in
the present formulation without the ``symmetry-breaking Higgs condensate''. The
final result agrees precisely with the usual quantization of a classical gauge
theory by means of the Higgs mechanism. Our method proves an old conjecture of
Cornwall, Levin and Tiktopoulos stating that the renormalization and
consistency requirements of spin=1 particles lead to the gauge theory structure
(i.e. a kind of inverse of 't Hooft's famous renormalizability proof in
quantized gauge theories) which was based on the on-shell unitarity of the
-matrix. We also speculate on a possible future ghostfree formulation which
avoids ''field coordinates'' altogether and is expected to reconcile the
on-shell S-matrix point of view with the off-shell field theory structure.Comment: 53 pages, version to appear in J. Phys.
Renormalized Quantum Yang-Mills Fields in Curved Spacetime
We present a proof that quantum Yang-Mills theory can be consistently defined
as a renormalized, perturbative quantum field theory on an arbitrary globally
hyperbolic curved, Lorentzian spacetime. To this end, we construct the
non-commutative algebra of observables, in the sense of formal power series, as
well as a space of corresponding quantum states. The algebra contains all gauge
invariant, renormalized, interacting quantum field operators (polynomials in
the field strength and its derivatives), and all their relations such as
commutation relations or operator product expansion. It can be viewed as a
deformation quantization of the Poisson algebra of classical Yang-Mills theory
equipped with the Peierls bracket. The algebra is constructed as the cohomology
of an auxiliary algebra describing a gauge fixed theory with ghosts and
anti-fields. A key technical difficulty is to establish a suitable hierarchy of
Ward identities at the renormalized level that ensure conservation of the
interacting BRST-current, and that the interacting BRST-charge is nilpotent.
The algebra of physical interacting field observables is obtained as the
cohomology of this charge. As a consequence of our constructions, we can prove
that the operator product expansion closes on the space of gauge invariant
operators. Similarly, the renormalization group flow is proved not to leave the
space of gauge invariant operators.Comment: Latex 144pp, no figures, review style presentation; v2: equations
corrected, details in proof of Ward-identity added, discussion of state
space, refs. added; v3: typos corrected, details added in renormalization
section, one subsection removed; v4 BRST-invariant state, typos corrected,
background field discussion clarified, hyperref feature adde