相关论文: Quantization of diffeomorphism invariant theories …

Quantization of diffeomorphism invariant theories of connections is studied. A solutions of the diffeomorphism constraints is found. The space of solutions is equipped with an inner product that is shown to satisfy the physical reality…

The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited. Such theories include general relativity described in terms of Ashtekar-Barbero variables and extension to Yang-Mills…

Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic…

We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices, one automatically takes care…

Given a symmetry group acting on a principal fibre bundle, symmetric states of the quantum theory of a diffeomorphism invariant theory of connections on this fibre bundle are defined. These symmetric states, equipped with a scalar product…

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…

In the canonical quantization of gravity in terms of the Ashtekar variables one uses paths in the 3-space to construct the quantum states. Usually, one restricts oneself to families of paths admitting only finite number of isolated…

Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical…

We investigate the action of diffeomorphisms in the context of Hamiltonian Gravity. By considering how the diffeomorphism-invariant Hilbert space of Loop Quantum Gravity should be constructed, we formulate a physical principle by demanding,…

Loop quantum gravity (LQG) is a quantization program for gravity based on the principles of QFT and general covariance of general relativity. Quantum states of LQG describe gravitational excitations based on graphs embedded in a spatial…

In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…

We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P -> Sigma be a principal G-bundle over space and let F be a vector bundle associated to P whose…

Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…

Several approaches to the dynamics of loop quantum gravity involve discretizing the equations of motion. The resulting discrete theories are known to be problematic since the first class algebra of constraints of the continuum theory…

We construct a space of quantum states and an algebra of quantum observables, over the set of all metrics of arbitrary but fixed signature, defined on a manifold. The construction is diffeomorphism invariant, and unique up to natural…

The notion of a measure on the space of connections modulo gauge transformations that is invariant under diffeomorphisms of the base manifold is important in a variety of contexts in mathematical physics and topology. At the formal level,…

This series of lectures gives a simple and self-contained introduction to the non-perturbative and background independent loop approach of canonical quantum gravity. The Hilbert space of kinematical quantum states is constructed and 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…

The conventional group of four-dimensional diffeomorphisms is not realizeable as a canonical transformation group in phase space. Yet there is a larger field-dependent symmetry transformation group which does faithfully reproduce 4-D…

We develop a general theory of `quantum' diffeomorphism groups based on the universal comeasuring quantum group $M(A)$ associated to an algebra $A$ and its various quotients. Explicit formulae are introduced for this construction, as well…