相关论文: On the Representation of Intermediate States in th…
The main subject of the paper is the description of unstable states in quantum mechanics and quantum field theory. Unstable states in quantum field theory can only be introduced as the intermediate states and not as asymptotic states. The…
We present a field theoretical model of point-form dynamics which exhibits resonance scattering. In particular, we construct point-form Poincar\'e generators explicitly from field operators and show that in the vector spaces for the…
A relativistic resonance which was defined by a pole of the $S$-matrix, or by a relativistic Breit-Wigner line shape, is represented by a generalized state vector (ket) which can be obtained by analytic extension of the relativistic…
The notion that elementary systems correspond to irreducible representations of the Poincare group is the starting point for this paper, which then goes on to discuss how a semigroup for the time evolution of unstable states and resonances…
Motivated by the debate of possible definitions of mass and width of resonances for $Z$-boson and hadrons, we suggest a definition of unstable particles by ``minimally complex'' semigroup representations of the Poincar\'e group…
We construct one-particle states as unitary, irreducible representations of Poincare group in front form, characterized by a special null vector, dubbed reference vector. We demonstrate that this construction has massive-massless…
Gamow vectors are generalized eigenvectors (kets) of self-adjoint Hamiltonians with complex eigenvalues $(E_{R}\mp i\Gamma/2)$ describing quasistable states. In the relativistic domain this leads to Poincar\'e semigroup representations…
The velocity basis of the Poincare group is used in the direct product space of two irreducible unitary representations of the Poincare group. The velocity basis with total angular momentum j will be used for the definition of relativistic…
In the data-based setting, analysis and control design of dynamical systems using measured data are typically based on overlapping trajectory segments of the input and output variables. This could lead to complex designs because the system…
We consider the role of the velocity in Lorentz-violating fermionic quantum theory, especially emphasizing the nonrelativistic regime. Information about the velocity will be important for the kinematical analysis of scattering and other…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
The main notions of semiclassical scalar electrodynamics in different gauges (Hamiltonian, Couloumb, Lorentz) are discussed. These are semiclassical states, Poincare transformations, fields, observables, gauge equivalence. General…
The formulation of quantum mechanics with a complex Hilbert space is equivalent to a formulation with a real Hilbert space and particular density matrix and observables. We study the real representations of the Poincare group, motivated by…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use…
State representations summarize our knowledge about a system. When unobservable quantities are introduced the state representation is typically no longer unique. However, this non-uniqueness does not affect subsequent inferences based on…
Shift vectors play a central role in nonlinear optics and transport phenomena, where they are usually understood as charge-center shifts associated with transitions between quantum states. Here we show that the same geometric structure can…
We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. In contrast to Young's interference characterized by path lengths,…
We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…