Related papers: Relativistic Gamow Vectors
Correlation functions involving products and ratios of half-integer powers of characteristic polynomials of random matrices from the Gaussian Orthogonal Ensemble (GOE) frequently arise in applications of Random Matrix Theory (RMT) to…
The non energy-weighted Gamow-Teller(GT) sum rule is satisfied in relativistic models, when all nuclear density-dependent terms, including Pauli blocking terms from nucleon-antinucleon excitations, are taken into account in the RPA…
A Gelfand triplet for the Hamiltonian H of the infinite-dimensional Friedrichs model on the positive half line with Hilbert-Schmidt perturbations is constructed such that exactly the resonances (poles of the inverse of the Livsic-matrix)…
Symmetries in quantum mechanics are realized by the projective representations of the Lie group as physical states are defined only up to a phase. A cornerstone theorem shows that these representations are equivalent to the unitary…
The Gamow states describe the quasinormal modes of quantum systems. It is shown that the resonance amplitude associated with the Gamow states is given by the complex delta function. It is also shown that under the near-resonance…
By means of expressing volumes in phase space in terms of traces of quantum operators, a relationship between the Hamiltonian poles and the Lyapunov exponents in a non Hermitian quantum dynamics, is presented. We illustrate the formalism by…
The eigenvalues of the Dirac operator on a curved spacetime are diffeomorphism-invariant functions of the geometry. They form an infinite set of ``observables'' for general relativity. Recent work of Chamseddine and Connes suggests that…
We consider eigenvectors of the Hamiltonian $H_0$ perturbed by a generic perturbation $V$ modelled by a random matrix from the Gaussian Unitary Ensemble (GUE). Using the supersymmetry approach we derive analytical results for the statistics…
A review is given of the formulation of relativistic atomic theory, in which there is an explicit realization of the Poincare' generators, both in the inertial and in the non-inertial rest-frame instant form of dynamics in Minkowski…
We propose a new approach to construct the eigenvalue expansion in a weighted Hilbert space of the solution to the Cauchy problem associated to Gauss-Laguerre invariant Markov semigroups that we introduce. Their generators turn out to be…
Proton emission from deformed nuclei is described within the non-adiabatic weak coupling model which takes into account the coupling to $\gamma$-vibrations around the axially-symmetric shape. The coupled equations are derived within the…
Change and local spatial variation are missing in Hamiltonian General Relativity according to the most common definition of observables (0 Poisson bracket with all first-class constraints). But other definitions have been proposed. Seeking…
We develop a relativistic framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the…
We study complex eigenvalues of large $N\times N$ symmetric random matrices of the form ${\cal H}=\hat{H}-i\hat{\Gamma}$, where both $\hat{H}$ and $\hat{\Gamma}$ are real symmetric, $\hat{H}$ is random Gaussian and $\hat{\Gamma}$ is such…
We develop relativistic wave equations in the framework of the new non-hermitian ${\cal PT}$ quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of ${\cal…
We study classically the problem of two relativistic particles with an invariant Duffing-like potential which reduces to the usual Duffing form in the nonrelativistic limit. We use a special relativistic generalization (RGEM) of the…
General covariance is a crucial notion in the study of field theories in curved spacetime. A field theory defined with respect to a semi-Riemannian metric is generally covariant if two metrics which are related by a diffeomorphism produce…
We exhibit a purely quantum mechanical carrier of the imprints of gravitation by identifying for a relativistic system a property which (i) is independent of its mass and (ii) expresses the Poincare invariance of spacetime in the absence of…
We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincar\'e group, taken as…
We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner's ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with…