1,721,086 research outputs found
Geometry of nonlinear field theories
No full textThis book is an excellent elementary introduction to the modern geometric approach to the problem of a unitary description of field theory.
GENERAL-RELATIVITY AS A SOLDERED NON-LINEAR SIGMA MODEL
No full textIt is shown that the known analogies between general relativity and the nonlinear sigma models are not restricted to kinematics but extend also to the dynamics. Some comments are made on possible consequences of this point of view and on the so-called gauge theories of gravitatio
Some applications of the renormalization group involving gravity
No full textI describe the results of three calculations of running coupling constants in gravitation theory
On the Ultraviolet behaviour of Newton's constant
No full textWe clarify a point concerning the ultraviolet behaviour of the Quantum Field Theory of gravity, under the assumption of the existence of an ultraviolet Fixed Point. We explain why Newton's constant should to scale like the inverse of the square of the cutoff, even though it is technically inessential. As a consequence of this behaviour, the existence of an UV Fixed Point would seem to imply that gravity has a built-in UV cutoff when described in Planck units, but not necessarily in other units
SPONTANEOUS SOLDERING
No full textIt is proposed that the soldering form of general relativity be treated as a dynamical variable. This gives rise to the possibility of treating the linear connection on (n-dimensional) spacetime and an internal O(k)-Yang-Mills field as different components of the same O(N) gauge field (N=n+k). The distinction between gravitational and Yang-Mills interactions is due to a kind of Higgs mechanism driven by the vacuum expectation value of the soldering for
THE HIGGS PHENOMENON IN QUANTUM-GRAVITY
No full textThe Higgs phenomenon occurs in theories of gravity in which the connection is an independent dynamical variable. The role of order parameters is played by the soldering form and a fiber metric. The breaking of the original gauge symmetry is linked to the appearance of geometrical structures on space-time. These facts suggest certain modifications and generalizations of the theory. We propose a Higgs-like model which provides a dynamical explanation for the nondegeneracy of the metric and a framework for the unification of gravity with the other interactions
ON THE TOPOLOGICAL MASS IN 3-DIMENSIONAL GRAVITY
No full textIt is argued that, due to the existence of a previously unnoticed topological term, three dimensional gravity on R3 with asymptotically flat boundary conditions can be consistently quantized for any value of the topological mass. This is independent of the signature of the metric. The argument is based on the analogy with gauged non-linear sigma model
Renormalization group flow of Weyl invariant dilaton gravity
Full text linkAny theory can be made Weyl invariant by introducing a dilaton. It is shown here how to construct renormalization group equations for gravity that maintain this property. Explicit calculations are given only in the simplest approximation, namely for the one-loop beta functions of a dilaton conformally coupled to a dynamical metric, but the results have wider validity. This formalism could be used to define the meaning of a theory with a position-dependent cutoff: it is equivalent to a theory with a constant cutoff but a conformally related metric
Mixing internal and spacetime transformations: some examples and counterexamples
No full textThis note addresses the question whether in a gauge theory coupled to gravity internal and spacetime transformation can be mixed. It is shown that if the VEV of the gauge field is flat, the symmetry group is always a product of internal and spacetime symmetries. On the other hand, if the VEV of the gauge field is not flat it is impossible to properly define the notion of a ``spacetime'' transformation; as a consequence, if the symmetry group is nontrivial, mixing generically occurs
An introduction to covariant quantum gravity and asymptotic safety
No full textThis book covers recent developments in the covariant formulation of quantum gravity. Developed in the 1960s by Feynman and DeWitt, by the 1980s this approach seemed to lead nowhere due to perturbative non-renormalizability. The possibility of non-perturbative renormalizability or "asymptotic safety," originally suggested by Weinberg but largely ignored for two decades, was revived towards the end of the century by technical progress in the field of the renormalization group. It is now a very active field of research, providing an alternative to other approaches to quantum gravity. Written by one of the early contributors to this subject, this book provides a gentle introduction to the relevant ideas and calculational techniques. Several explicit calculations gradually bring the reader close to the current frontier of research. The main difficulties and present lines of development are also outlined
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