In this paper DeWitt's formalism for field theories is presented; it provides a framework in which the quantization of fields possessing infinite dimensional invariance groups may be carried out manifestly covariant (non-Hamiltonian) fashion, even curved space-time. Another important virtue approach that emphasizes common features apparently very different such as Yang-Mills and General Relativ...

We discuss the relation between space–time diffeomorphisms and gauge transformations in theories of the Yang–Mills type coupled with Einstein’s general relativity. We show that local symmetries of the Hamiltonian and Lagrangian formalisms of these generally covariant gauge systems are equivalent when gauge transformations are required to induce transformations which are projectable under the Le...

It is our goal to study the influence of the structure of the configuration space on the SU(2) glueball spectrum. The method we use consists of putting the theory in a finite spatial volume and reducing the full dynamics to an effective theory of a finite number of degrees of freedom [1,2]. Asymptotic freedom implies that a small volume corresponds to a small coupling constant. Hence changing t...

In a quantum mechanical treatment of gauge theories (including general relativity), one is led to consider a certain completion, A/G, of the space A/G of gauge equivalent connections. This space serves as the quantum configuration space, or, as the space of all Euclidean histories over which one must integrate in the quantum theory. A/G is a very large space and serves as a “universal home” for...

We prove that magnetic charge does not exist as a physical observable on the physical Hilbert space of the pure SU(2) gauge theory. The abelian magnetic monopoles seen in lattice simulations are then interpreted as artifacts of gauge fixing. The apparent physical scaling properties of the monopole density in the continuum limit observed on the lattice are attributed to the correct scaling prope...

Lattice Gauge Theory in 4-dimensional Euclidean space-time is generalized to ribbon categories which replace the category of representations of the gauge group. This provides a framework in which the gauge group becomes a quantum group while space-time is still given by the ‘classical’ lattice. At the technical level, this construction generalizes the Spin Foam Model dual to Lattice Gauge Theor...

A consistent framework has been put forward to quantize the isentropic, compressible and inviscid fluid model in the Hamiltonian framework, using the Clebsch parameterization. The naive quantization is hampered by the non-canonical (in particular field dependent) Poisson Bracket algebra. To overcome this problem, the Batalin-Tyutin [11] quantization formalism is adopted in which the original sy...

Long ago, Bergshoeff, Sezgin, Tanni and Townsend have shown that the light-cone gauge-fixed action of a super p-brane belongs to a new kind of supersymmetric gauge theory of p-volume preserving diffeomorphisms (diffs) associated with the p-spatial dimensions of the extended object. These authors conjectured that this new kind of supersymmetric gauge theory must be related to an infinite-dim non...