Related papers: Quantum Mechanics in non-inertial reference frames…
In previous work we have developed a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the…
We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on the Galilean line group, the semidirect product…
We show that the Wigner-Bargmann program of grounding non-relativistic quantum mechanics in the unitary projective representations of the Galilei group can be extended to include all non-inertial reference frames. The key concept is the…
The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid…
Recently, it was shown that when reference frames are associated to quantum systems, the transformation laws between such quantum reference frames need to be modified to take into account the quantum and dynamical features of the reference…
From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this…
Closed systems in Newtonian mechanics obey the principle of Galilean relativity. However, the usual Lagrangian for Newtonian mechanics, formed from the difference of kinetic and potential energies, is not invariant under the full group of…
We propose the implementation of Galileo group symmetry operations or, in general, linear coordinate transformations, in a quantum simulator. With an appropriate encoding, unitary gates applied to our quantum system give rise to Galilean…
Quantum groups have been widely explored as a tool to encode possible nontrivial generalisations of reference frame transformations, relevant in quantum gravity. In quantum information, it was found that the reference frames can be…
We study properties of Newton-Cartan gravity under transformations into all noninertial, nonrelativistic reference frames. The set of these transformations has the structure of an infinite dimensional Lie group, called the Galilean line…
Recently there has been much effort in developing a quantum generalisation of reference frame transformations. Despite important progress, a complete understanding of their principles is still lacking. In particular, we argue that previous…
We explore the group theoretical underpinning of noncommutative quantum mechanics for a system moving on the two-dimensional plane. We show that the pertinent groups for the system are the two-fold central extension of the Galilei group in…
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…
This article shows that one can consistently incorporate nonunitary representations of at least one group into the ``ordinary'' nonrelativistic quantum mechanics. This group turns out to be Lorentz group thus giving us an alternative…
In physical experiments, reference frames are standardly modelled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical…
The Galilei group has been taken as the fundamental symmetry for 'nonrelativistic' physics, quantum or classical. Our fully group theoretical formulation approach to the quantum theory asks for some adjustments. We present a sketch of the…
Under the classical non-relativistic consideration of the space-time we propose the model of the laws of gravity and Electrodynamics, invariant under the galilean transformations and moreover, under every change of non-inertial cartesian…
Quantum communication without a shared reference frame or the construction of a relational quantum theory requires the notion of a quantum reference frame. We analyze aspects of quantum reference frames associated with non-compact groups,…
Since their first introduction, Quantum Reference Frame (QRF) transformations have been extensively discussed, generalising the covariance of physical laws to the quantum domain. Despite important progress, a formulation of QRF…
The FRT quantum group and space theory is reformulated from the standard mathematical basis to an arbitrary one. The $N$-dimensional quantum vector Cayley-Klein spaces are described in Cartesian basis and the quantum analogs of…