arXiv subjects

Petre Diţă

Publications and source records attributed to Petre Diţă.

4 recordsLinked to original sources

arXiv2014

Complex Hadamard matrices for prime number

In this paper we disprove the Haagerup statement that all complex Hadamard matrices of order five are equivalent with the Fourier matrix $F_5$ by constructing circulant matrices that lead to new Hadamard matrices. An important item is the construction of new mutually unbiased bases that are a basic concept of quantum theory and play an essential role in quantum tomography, quantum cryptografy, teleportation, construction of dense coding schemes, classical signal proccesing, etc.

quant-ph↗

arXiv1998

Poisson-Lie Structures and Quantisation with Constraints

We develop here a simple quantisation formalism that make use of Lie algebra properties of the Poisson bracket. When the brackets $\{H,ϕ_i\}$ and $\{ϕ_i,ϕ_j\}$, where $H$ is the Hamiltonian and $ϕ_i$ are primary and secondary constraints, can be expressed as functions of $H$ and $ϕ_i$ themselves, the Poisson bracket defines a Poisson-Lie structure. When this algebra has a finite dimension a system of first order partial differential equations is established whose solutions are the observables of the theory. The method is illustrated with a few examples.

quant-ph↗

arXiv1998

Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes

We test the positivity property of the chiral perturbation theory (ChPT) pion-pion scattering amplitudes within the Mandelstam triangle. In the one-loop approximation, ${\cal O}(p^4)$, the positivity constrains only the coefficients $b_3$ and $b_4$, namely one obtains that $b_4$ and the linear combination $b_3+3 b_4$ are positive quantities. The two-loops approximation gives inequalities involving all the six arbitrary parameters entering ChPT amplitude, but the corrections to the one-loop approximation results are small. ChPT amplitudes pass unexpectedly well all the positivity tests giving strong support to the idea that ChPT is the good theory of the low energy pion-pion scattering.

hep-ph↗

arXiv1997

Quantization of the Particle Motion on the $n$-Dimensional Sphere

We develop here a simple formalism that converts the second-class constraints into first-class ones for a particle moving on the $n$-dimensional sphere. The Poisson algebra generated by the Hamiltonian and the constraints closes and by quantization transforms into a Lie algebra. The observable of the theory is given by the Casimir operator of this algebra and coincides with the square of the angular momentum.

hep-th↗