Related papers: St\"uckelberg Field Shiftting Quantization of Free…
We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in $D$ dimensions is possible only by converting the constraints to abelian gauge constraints, which are of first…
Cylindrically reduced Einstein gravity can be regarded as an $SL(2,R)/SO(2)$ sigma model coupled to 2D dilaton gravity. By using the corresponding 2D diffeomorphism algebra of constraints and the asymptotic behaviour of the Ernst equation…
We embed second class constrained systems by a formalism that combines concepts of the BFFT method and the unfixing gauge formalism. As a result, we obtain a gauge-invariant system where the introduction of the Wess-Zumino (WZ) field is…
We find two-dimensional free-field variables for D-dimensional general relativity on spacetimes with D-2 commuting spacelike Killing vector fields and non-compact spatial sections for D>4. We show that there is a canonical transformation…
The dimensional continuation approach to calculating the free energy of $d$-dimensional Euclidean CFT on the round sphere $S^d$ has been used to develop its $4-\epsilon$ expansion for a number of well-known non-supersymmetric theories, such…
We perform the momentum-space quantization of a spin-less particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using a non-canonical method entirely based on symmetry grounds. To achieve this…
We quantize the electromagnetic field in the presence of a nonmoving dielectric sphere in vacuum. The sphere is assumed to be lossless, dispersionless, isotropic, and homogeneous. The quantization is performed using normalized eigenmodes as…
The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…
We first study a free particle on an $(n-1)$-sphere in an extended phase space, where the originally second-class Hamiltonian and constraints are now in strong involution. This allows for a Schr\"odinger representation and a Hamilton-Jacobi…
We reconsider the problem of quantising a particle on the $D$-dimensional sphere. Adopting a Lagrangian method of reducing the degrees of freedom, the quantum Hamiltonian is found to be the usual Schr\"odinger operator without any boundary…
The Kepler problem concerns a point particle in an attractive inverse square force. After a brief review of the classical and quantum versions of this problem, focused on their hidden $\text{SU}(2) \times \text{SU}(2)$ symmetry, we discuss…
In this paper we propose an approach of obtaining of N-dimensional spherical harmonics based exclusively on the methods of solutions of differential equations and the use of the special functions properties. We deduce the Laplace-Beltrami…
In the framework of Dirac quantization with second class constraints, a free particle moving on the surface of a $(d-1)-$dimensional sphere has an ambiguity in the energy spectrum due to the arbitrary shift of canonical momenta. We…
D-theory is an alternative non-perturbative approach to quantum field theory formulated in terms of discrete quantized variables instead of classical fields. Classical scalar fields are replaced by generalized quantum spins and classical…
The problem of quantizing a particle on a 2-sphere has been treated by numerous approaches, including Isham's global method based on unitary representations of a symplectic symmetry group that acts transitively on the phase space. Here we…
We study perturbative behavior of free energies on a d-dimensional sphere S^d for theories with marginal interactions. The free energies are interpreted as the "dilaton effective action" with the dilaton having a nontrivial background…
We study the free energy of four-dimensional CFTs on deformed spheres. For generic nonsupersymmetric CFTs only the coefficient of the logarithmic divergence in the free energy is physical, which is an extremum for the round sphere. We then…
A model of Einstein-Hilbert action subject to the scale transformation is studied. By introducing a dilaton field as a means of scale transformation a new action is obtained whose Einstein field equations are consistent with traceless…
Free scalar field theory on 2 dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using LQG type `polymer' representations for the…
We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized…