Faddeev–Jackiw approach of noncommutative space–time electromagnetic theories

The interest in higher derivatives field theories has its origin mainly in their influence concerning the renormalization properties of physical models and to remove ultraviolet divergences. The noncommutative Podolsky theory is a constrained system that cannot be directly quantized by the canonical way. In this work, we have used the Faddeev–Jackiw method in order to obtain the Dirac brackets of the NC space–time Maxwell, Proca and Podolsky theories.

A BRST formulation for the conic constrained particle

We describe the gauge invariant BRST formulation of a particle constrained to move in a general conic. The model considered constitutes an explicit example of an originally second-class system which can be quantized within the BRST framework. We initially impose the conic constraint by means of a Lagrange multiplier leading to a consistent second-class system which generalizes previous models studied in the literature. After calculating the constraint structure and the corresponding Dirac brackets, we introduce a suitable first-order Lagrangian, the resulting modified system is then shown to be gauge invariant. We proceed to the extended phase space introducing fermionic ghost variables, exhibiting the BRST symmetry transformations and writing the Green’s function generating functional for the BRST quantized model.

Light-front quantization with the light cone gauge

The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first-class constraints that arise and the resulting Dirac brackets are found. These gauge conditions are not used to eliminate degrees of freedom from the action prior to applying the Dirac constraint procedure. This approach is illustrated by considering Yang–Mills theory and the superparticle in a 2+1-dimensional target space.

Quaternionic quantization principle in general relativity and supergravity

A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta referring to other space–time directions. The corresponding commutation relations are formulated by using quaternions. At the beginning, this extended quantization concept is applied to the variables of quantum mechanics. The resulting Dirac equation and the corresponding generalized expression for plane waves are formulated and some consequences for quantum field theory are considered. Later, the quaternionic quantization principle is transferred to canonical quantum gravity. Within quantum geometrodynamics as well as the Ashtekar formalism, the generalized algebraic properties of the operators describing the gravitational observables and the corresponding quantum constraints implied by the generalized representations of these operators are determined. The generalized algebra also induces commutation relations of the several components of the quantized variables with each other. Finally, the quaternionic quantization procedure is also transferred to [Formula: see text] supergravity. Accordingly, the quantization principle has to be generalized to be compatible with Dirac brackets, which appear in canonical quantum supergravity.

Hamiltonian dynamics of 5D Kalb–Ramond theories with a compact extra dimension

A detailed Hamiltonian analysis for a 5D Kalb–Ramond, massive Kalb–Ramond and Stüeckelberg Kalb–Ramond theories with an extra compact dimension is performed. We develop a complete constraint program, then we quantize the theory by constructing the Dirac brackets. From the gauge transformations of the theories, we fix a particular gauge and we find pseudo-Goldstone bosons in Kalb–Ramond and Stüeckelberg Kalb–Ramond systems. Finally we discuss some remarks and prospects.

CLASSICAL AND QUANTUM ASPECTS OF FIVE-DIMENSIONAL CHERN–SIMONS GAUGE THEORY

In this paper, we investigate the classical and quantum aspects of five-dimensional Chern–Simons theory. As a constrained Hamiltonian system we compute the Dirac brackets among the canonical variables for the Abelian case. In terms of the Batalin–Vilkovisky formalism, we show that the classical master equation leads to new algebraic constraints on the Lie algebra. Finally, partition function and geometric quantization of the theory have been also discussed.

REMARKS ON GENERALIZED UNCERTAINTY PRINCIPLE INDUCED FROM CONSTRAINT SYSTEM

The extended commutation relations for generalized uncertainty principle (GUP) have been based on the assumption of the minimal length in position. Instead of this assumption, we start with a constrained Hamiltonian system described by the conventional Poisson algebra and then impose appropriate second class constraints to this system. Consequently, we can show that the consistent Dirac brackets for this system are nothing, but the extended commutation relations describing the GUP.