Related papers: Diffeomorphisms of quantum fields
Gravitational theories with fixed background fields break diffeomorphism invariance. This breaking can be spontaneous or explicit. A brief summary of the main consequences of these types of breaking is presented.
The issue of field redefinition invariance of path integrals in quantum field theory is reexamined. A ``paradox'' is presented involving the reduction to an effective quantum-mechanical theory of a $(d+1)$-dimensional free scalar field in a…
Recent progress in the quantization of nonrenormalizable scalar fields has found that a suitable non-classical modification of the ground state wave function leads to a result that eliminates term-by-term divergences that arise in a…
Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with…
Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to…
We propose a local renormalization group procedure where length scale is changed in spacetime dependent way. Combining this scheme with an earlier observation that high energy modes in renormalization group play the role of dynamical…
We are concerned with the issue of quantization of a scalar field in a diffeomorphism invariant manner. We apply the method used in Loop Quantum Gravity. It relies on the specific choice of scalar field variables referred to as the polymer…
The problem of observables in classical and quantum gravity is a long-standing one. It is sometimes argued that observable quantities should be diffeomorphsm invariant, following the philosophy of Dirac. We argue that diffeomorphism…
We discuss quantum theory of fields \phi defined on (d+1)-dimensional manifold {\cal M} with a boundary {\cal B}. The free action W_{0}(\phi) which is a bilinear form in \phi defines the Gaussian measure with a covariance (Green function)…
For a variety of diffeomorphism-invariant field theories describing hypersurface motions (such as relativistic M-branes in space-time dimension M+2) we perform a Hamiltonian reduction ``at level 0'', showing that a simple algebraic function…
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…
The usual mathematical formalism of quantum field theory is non-rigorous because it contains divergences that can only be renormalized by non-rigorous mathematical methods. The purpose of this paper is to present a method of subtraction of…
We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be…
Let $F$ be an algebraically closed field. We show that if a quantum formal deformation $A$ of a commutative domain $A_0$ over $F$ is a PI algebra, then $A$ is commutative if ${\rm char}(F)=0$, and has PI degree a power of $p$ if ${\rm…
A quantum hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop representation, and is shown to be finite and…
We extend the recently developed kinematical framework for diffeomorphism invariant theories of connections for compact gauge groups to the case of a diffeomorphism invariant quantum field theory which includes besides connections also…
We discuss a D-dimensional Euclidean scalar field interacting with a scale invariant quantized metric. We assume that the metric depends on d-dimensional coordinates where d<D. We show that the interacting quantum fields have more regular…
We are concerned with the issue of quantization of a scalar field in a diffeomorphism invariant manner. We apply the method used in Loop Quantum Gravity. It relies on the specific choice of scalar field variables referred to as the polymer…
The scaling properties of quantum gravity are discussed by employing a class of proper-time regulators in the functional flow equation for the conformal factor within the formalism of the background field method. Renormalization group…
The local limit of a quantum field theory on the loop space is studied. It is proved that the invariance of the theory with respect to the group of diffeomorphisms leads to Feynman diagrams convergence in the local limit.