Related papers: Operatorial quantization of Born-Infeld Skyrmions
We propose a natural family of higher-order partial differential equations generalizing the second-order Klein-Gordon equation. We characterize the associated model by means of a generalized action for a scalar field, containing…
We examine the mechanical matrix model that can be derived from the SU(2) Yang-Mills light-cone field theory by restricting the gauge fields to depend on the light-cone time alone. We use Dirac's generalized Hamiltonian approach. In…
We obtain a new symplectic Lagrangian density and deduce Faddeev-Jackiw (FJ) generalized brackets of the gauge invariant self-dual fields interacting with gauge fields. We further give FJ quantization of this system. Furthermore, the FJ…
We consistently quantize a class of relativistic non-local field equations characterized by a non-local kinetic term in the lagrangian. We solve the classical non-local equations of motion for a scalar field and evaluate the on-shell…
We construct Hermitian representations of Lie algebroids and associated unitary representations of Lie groupoids by a geometric quantization procedure. For this purpose we introduce a new notion of Hamiltonian Lie algebroid actions. The…
In our work we extend the ideas of the derivation of the chiral effective theory from the lattice QCD [1] to the case of the random lattice regularization of QCD. Such procedure allows in principle to find contribution of any order into the…
It is well known that the integrable Hamiltonian systems defined by the Adler-Kostant-Symes construction correspond via Hamiltonian reduction to systems on cotangent bundles of Lie groups. Generalizing previous results on Toda systems, here…
We accomplish the quantization of a few classical constrained systems \`a la (modified) Faddeev-Jackiw formalism. We analyze the constraint structure and obtain basic brackets of the theory. In addition, we disclose the gauge symmetries…
The mathematical framework for an exact quantization of the two-dimensional coset space sigma-models coupled to dilaton gravity, that arise from dimensional reduction of gravity and supergravity theories, is presented. Extending previous…
We perform a deformation quantization of the classical isotropic rigid rotator. The resulting quantum system is not invariant under the usual $SU(2)\times SU(2)$ chiral symmetry, but instead $SU_{q^{-1}}(2) \times SU_q(2)$.
In view of growing interest in tensor modes and their possible detection, we clarify the definition of tensor modes up to 2nd order in perturbation theory within the Hamiltonian formalism. Like in gauge theory, in cosmology the Hamiltonian…
We perform, in a manifestly $SO(n-1,1)$ [$SO(n)$] covariant fashion, the Hamiltonian analysis of general relativity in $n$ dimensions written as a constrained $BF$ theory. We solve the constraint on the $B$ field in a way naturally adapted…
We analyze a structure of the singular Lagrangian $L$ with first and second class constraints of an arbitrary stage. We show that there exist an equivalent Lagrangian (called the extended Lagrangian $\tilde L$) that generates all the…
Recently the Hamilton-Jacobi formulation for first order constrained systems has been developed. In such formalism the equations of motion are written as total differential equations in many variables. We generalize the Hamilton-Jacobi…
Two numerical algorithms for the computation of eigenvalues of Dirac operators in lattice gauge theories are described: one is an accelerated conjugate gradient method, the other one a standard Lanczos method. Results obtained by Cullum's…
Global quantization of pseudo-differential operators on compact Lie groups is introduced relying on the representation theory of the group rather than on expressions in local coordinates. Operators on the 3-dimensional sphere and on group…
Quantum mechanics of models is considered which are constructed in spaces with Lie algebra type commutation relations between spatial coordinates. The case is specialized to that of the group SU(2), for which the formulation of the problem…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…
The nonholonomic constrained system with second-class constraints is investigated using the Hamilton-Jacobi (HJ) quantization scheme to yield the complete equations of motion of the system. Although the integrability conditions in the HJ…
We discuss the quantization of the restricted gauge theory of SU(2) QCD regarding it as a second-class constraint system, and construct the BRST symmetry of the constrained system in the framework of the improved Dirac quantization scheme.…