We develop elementary canonical methods for the quantization of abelian and nonabelian Chern-Simons actions using well known ideas in gauge theories and quantum gravity. Our approach does not involve choice of gauge or clever manipulations of functional integrals. When the spatial slice is a disc, it yields Witten's edge states carrying a representation of the Kac-Moody algebra. The canonical expression for the generators of diffeomorphisms on the boundary of the disc are also found, and it is established that they are the Chern-Simons version of the Sugawara construction. This paper is a prelude to our future publications on edge states, sources, vertex operators, and their spin and statistics in 3d and 4d topological field theories.

We construct a perturbative solution to classical noncommutative gauge theory on R 3 minus the origin using the Groenewald-Moyal star product. The result describes a noncommutative point charge. Applying it to the quantum mechanics of the noncommutative hydrogen atom gives shifts in the 1S hyperfine splitting which are first order in the noncommutativity parameter.

Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no further major axiom in quantum physics than those formulated for example in Dirac's 'Quantum Mechanics', then a quantum physicist would not be able to tell a torus from a hole in the ground. We argue that there are indeed such axioms involving observables with smooth time evolution: they contain commutative subalgebras from which the spatial slice of spacetime with its topology (and with further refinements of the axiom, its C K − and C ∞ − structures) can be reconstructed using Gel'fand -Naimark theory and its extensions. Classical topology is an attribute of only certain quantum observables for these axioms, the spatial slice emergent from quantum physics getting progressively less differentiable with increasingly higher excitations of energy and eventually altogether ceasing to exist. After formulating these axioms, we apply them to show the possibility of topology change and to discuss quantized fuzzy topologies. Fundamental issues concerning the role of time in quantum physics are also addressed.

A new Lagrangian L is proposed for the description of a particle with a non-Abelian charge in interaction with aYang-Mills field. The canonical quantization of L is discussed. At the quantum level L leads t o both irreducible and reducible multiplets of the particle depending upon which of the parameters in L are regarded as dynamical.The case which leads to the irreducible multiplet is the minimal non-Abelian generalization of the usual Lagrangian for a charged point particle in an electromagnetic field. Some of the Lagrangians proposed before for such systems are either special cases of ours or can be obtained from ours by simple modifications. Our formulation bears some resemblance t o Dirac's theory of magnetic monopoles in the following respects: (1) Quantization is possible only if the values of certain parameters in L are restricted to a certain discrete set, this is analogous to the Dirac quantization condition; (2) in certain cases, L depends on external (nondynamical) directions in the internal-symmetry space. This is analogous to the dependence of the magnetic-monopole Lagran'gian on the direction of the Dirac string.

It shown that the chiral model with SU(3) flavor symmetry predicts a dibaryon state of low mass M (M^2.2 GeV). It is electrically neutral and is an SU(3) singlet with J p =0 + .It corresponds to a six-quark state found in the MIT bag model by Jaffe. It is also shown that there is no stable particlelike state of baryon number 2 which is based on Skyrme's spherically symmetric Ansatz for the chiral field.PACS numbers: ll.30. Rd, 12.35.Ht, 14.20.Pt It is believed that the low-energy properties of QCD are effectively reproduced by the chiral model. The order parameter in this model when we consider only the light quarks is a field U where U(x) is a 3x3 SU(3) matrix. Skyrme pointed out many years ago 1 that this model admits solitons characterized by an integer-valued topological number and proposed to interpret the states with the unit value of this number as the nucleon and its excitations. He also suggested that the topological number t is the baryon number B of the nucleon. This conjecture was confirmed in all essential respects by Balachandran, Nair, Rajeev, and Stern 2 ' 3 who showed that b = const x t, where the constant is completely determined by the detailed assumptions in the treatment of the fermions in the model. Further studies of the chiral model 4,5 which include in particular the topological effects of the Wess-Zumino term also suggest that the \tI = 1 states are indeed fermions. There is thus good support to Skyrme's conjecture that the 1*1 = 1 solitons are baryons and t is related to the baryon number. The conservative assumption at this point would be to identify these states with the baryon octet and assume that t is exactly equal to B. Following Skyrme 1 and Witten, 4 we shall adopt this interpreta-tion for the purposes of this paper 6 ; our conclusions can, however, be readily modified if, as has been suggested, 2 the topological excitations represent a novel family of states.The stable static solutions with |2?| = 1 in the Skyrme model are described by a "spherically symmetric' ' configuration. In this context, spherical symmetry is understood in a generalized sense and depends on the choice of an SU(2) subgroup of the flavor SU(3). There are, however, spherically symmetric configurations which involve instead the SO (3) subgroup of real orthogonal matrices of SU(3) 7 and the major results of this note pertain to these configurations. The associated topological excitations are characterized by \B| = 0,2,4, ... . We show in this note that the lightest dibaryon states in this sequence with B = ± 2 have a mass of the order of 2.2 GeV. They are also expected to be SU(3) singlets with J p =0 + . In this note, we shall also briefly study the \B\ = 2 states based on the SU(2) subgroup and show that the corresponding static configurations are not stable even classically. Therefore we do not expect a dibaryon resonance identifiable with such a configuration. 8 We shall first briefly review the relevant aspects of Skyrme's model for three flavors. It is based on the Lagrangian density J?= -jflTrid^d^U...