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We formulate scalar field theories coupled non-conformally to gravity in a manifestly frame-independent fashion. Physical quantities such as the $S$ matrix should be invariant under field redefinitions, and hence can be represented by the…
It is well known that general relativity (GR) does not possess any non-trivial local (in a precise standard sense) and diffeomorphism invariant observables. We propose a generalized notion of local observables, which retain the most…
In 1+1 dimensions, the Wheeler-DeWitt equation cannot be imposed owing to an anomaly in its commutator with the diffeomorphism constraint. A similar obstruction prevents also a semiclassical definition of a WKB local time. (Talk given at…
By a uniform and simple Weyl invariant coupling of scale and matter fields, we construct theories that unify massless, massive, and partially massless excitations. Masses are related to tractor Weyl weights, and Breitenlohner-Freedman…
We discuss some classical and quantum properties of 2d gravity models involving metric and a scalar field. Different models are parametrized in terms of a scalar potential. We show that a general Liouville-type model with exponential…
The cosmological constant problem is one of the long-standing issues of modern physics. While we can measure the value of the cosmological constant with great accuracy, we are not able to calculate it in a coherent theoretical framework. On…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
The gauge formulation of Einstein gravity in AdS$_3$ background leads to a boundary theory that breaks modular symmetry and loses the covariant form. We examine the Weyl anomaly for the cylinder and torus manifolds. The divergent term is…
We construct an $F(R)$ gravity theory corresponding to the Weyl invariant two scalar field theory. We investigate whether such $F(R)$ gravity can have the antigravity regions where the Weyl curvature invariant does not diverge at the Big…
We consider matter fields conformally coupled to a background metric and dilaton and describe in detail a quantization procedure and related renormalization group flow that preserve Weyl invariance. Even though the resulting effective…
A novel inhomogeneous gauge transformation law is proposed for a non-Abelian adjoint two-form in four dimensions. Rules for constructing actions invariant under this are given. The auxiliary vector field which appears in some of these…
We study the dynamics of Abelian gauge fields invariant under transverse diffeomorphisms (TDiff) in cosmological contexts. We show that in the geometric optics approximation, very much as for Diff invariant theories, the corresponding…
In the presence of a variable magnetic field, the Weyl pseudodifferential calculus must be modified. The usual modification, based on ``the minimal coupling principle'' at the level of the classical symbols, does not lead to gauge invariant…
We introduce a gauge and diffeomorphism invariant theory on the Yang-Mills phase space. The theory is well defined for an arbitrary gauge group with an invariant bilinear form, it contains only first class constraints, and the spacetime…
It is well known that one can parameterize 2-D Riemannian structures by conformal transformations and diffeomorphisms of fiducial constant curvature geometries; and that this construction has a natural setting in general relativity theory…
There are two covariant descriptions of massless spin-2 particles in $D=3+1$ via a symmetric rank-2 tensor: the linearized Einstein-Hilbert (LEH) theory and the Weyl plus transverse diffeomorphism (WTDIFF) invariant model. From the LEH…
We study classical solutions in the Weyl-transverse (WTDiff) gravity. The WTDiff gravity is invariant under both the local Weyl (conformal) transformation and the volume preserving diffeormorphisms (transverse diffeomorphisms) and is known…
The traditional presentation of Unimodular Gravity (UG) consists on indicating that it is an alternative theory of gravity that restricts the generic diffeomorphism invariance of General Relativity. In particular, as often encountered in…
Weyl consistency conditions have been used in unitary relativistic quantum field theory to impose constraints on the renormalization group flow of certain quantities. We classify the Weyl anomalies and their renormalization scheme…
The mathematical structure of the temporal gauge of QED is critically examined in both the alternative formulations characterized by either positivity or regularity of the Weyl algebra. The conflict between time translation invariance and…