Related papers: Relativistic Harmonic Oscillator Revisited
We consider Polyakov theory of Bosonic strings in conformal gauge which are used to study conformal anomaly. However it exhibits ghost number anomaly. We show how this anomaly can be avoided by connecting this theory to that of in…
The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincar\'e symmetry of field theory can be extended to the larger conformal symmetry. We use…
Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables phi in R mod 2 pi and I > 0. But the symplectic transformation (\phi,I) to (q,p) is singular for (q,p) = (0,0). Globally {(q,p)} has…
In classical mechanics, the system of two coupled harmonic oscillators is shown to possess the symmetry of the Lorentz group O(3,3) applicable to a six-dimensional space consisting of three space-like and three time-like coordinates, or…
The effect on flavour oscillations of simple expanding background space-times, motivated by some D-particle foam models, is calculated for a toy-model of bosons with flavour degrees of freedom. The presence of D-particle defects in the…
The recent discoveries of new forms of quantum statistics require a close look at the under-lying Fock space structure. This exercise becomes all the more important in order to provide a general classification scheme for various forms of…
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…
We present a new approach to cosmological perturbations based on the theory of Lie groups and their representations. After re-deriving the standard covariant formalism from SO(3) considerations, we provide a new expansion of the perturbed…
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…
Complete description of the classical and quantum dynamics of a particle in an anisotropic, rotating, harmonic trap is given. The problem is studied in three dimensions and no restrictions on the geometry are imposed. In the generic case,…
In a recent article we showed that the analog of the cosmological constant in two spacetime dimensions for a wide variety of integrable quantum field theories has the form $\rho_{\rm vac} = - m^2 /2 \mathfrak{g} $ where $m$ is a physical…
According to Belinsky, Khalatnikov and Lifshitz, gravity near a space-like singularity reduces to a set of decoupled one-dimensional mechanical models at each point in space. We point out that these models fall into a class of conformal…
A free quantum field theory with Lorentz symmetry is derived for spin-half symplectic fermions in 2+1 dimensions. In particular, we show that fermionic spin-half fields may be canonically quantized in a free theory with a Klein-Gordon…
Supergravity theories in more than four dimensions with grand unified gauge symmetries are an important intermediate step towards the ultraviolet completion of the Standard Model in string theory. Using toric geometry, we classify and…
We calculate and identify the counterparts of zero-norm states in the old covariant first quantised (OCFQ) spectrum of open bosonic string in two other quantization schemes of string theory, namely the light-cone DDF zero-norm states and…
Vacuum static, axially symmetric space-times in $D$-dimensional general relativity with a Ricci-flat internal space are discussed. It is shown, in particular, that some of the monopole-type solutions are free of curvature singularities and…
False vacuum decay typically proceeds via the nucleation of spherical bubbles of true vacuum, described by $O(4)$ symmetric field configurations in Euclidean time. In this work, we investigate how the presence of cosmic strings can catalyze…
We investigate the simple harmonic oscillator in a 1-d box, and the 2-d isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the…
We realize the Weil representation of infinite dimensional symplectic group and spinor representation of infinite-dimensional group $GL$ by linear operators in the space of symmetric functions in infinite number of variables.
The structure of the state-vector space of identical bosons in noncommutative spaces is investigated. To maintain Bose-Einstein statistics the commutation relations of phase space variables should simultaneously include…