Related papers: Spin dependent masses and Sim(2) symmetry
In the literature on quantum reference frames, the internal (relative) properties of a system are defined as those which are preserved under an arbitrary change of reference frame. For a system of quantum spins, these are all properties…
We identify an extended Poincare symmetry $ISO(2) \times ISO(3,1)$ for on-shell massive scattering amplitudes, transforming under the $U(2)$ Little group symmetry. Thus the one-particle state involves in both spin and transversality $t$…
We study translationally invariant spin chains where each unit cell contains an $n$-state projective representation of a $\mathbb{Z}_n\times\mathbb{Z}_n$ internal symmetry, generalizing the spin-1/2 XYZ chain. Such spin chains possess a…
The relativistic spinning particle model, proposed in [3,4], is analyzed in a Hamiltonian framework. The spin is simulated by extending the configuration space by introducing a light-like four vector degree of freedom. The model is heavily…
The universal covering of SO(3) is modelled as a reflection group G_R in a representation independent fashion. For relativistic quantum fields, the Unruh effect of vacuum states is known to imply an intrinsic form of reflection symmetry,…
The space-time symmetry group of a model of a relativistic spin 1/2 elementary particle, which satisfies Dirac's equation when quantized, is analyzed. It is shown that this group, larger than the Poincare group, also contains space-time…
Starting with the Chern-Simons formulation of (2+1)-dimensional gravity we show that the gravitational interactions deform the Poincare symmetry of flat space-time to a quantum group symmetry. The relevant quantum group is the quantum…
We discuss relations between several relativistic spin observables and derive a Lorentz-invariant characteristic of a reduced spin density matrix.A relativistic position operator that satisfies all the properties of its nonrelativistic…
The current status of Mach's principle is discussed within the context of general relativity. The inertial properties of a particle are determined by its mass and spin, since these characterize the irreducible unitary representations of the…
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
The notion of Wigner particles is attached to irreducible unitary representations of the Poincare group, characterized by parameters m and s of mass and spin, respectively. However, the Lorentz symmetry is broken in theories with long-range…
We study the semiclassical limit of a class of invariant tensors for infinite-dimensional unitary representations of $\mathrm{SL}(2,\mathbb{C})$ of the principal series, corresponding to generalized Clebsch-Gordan coefficients with $n\geq3$…
The internal space-time symmetries of relativistic particles are dictated by Wigner's little groups. The $O(3)$-like little group for a massive particle at rest and the $E(2)$-like little group of a massless particle are two different…
The possibility of a modification of special relativity with an invariant energy scale playing the role of a minimum energy is explored. Consistency with the equivalence of different inertial frames is obtained by an appropriate choice of a…
R. P. Feynman was quite fond of inventing new physics. It is shown that some of his physical ideas can be supported by the mathematical instruments available from the Lorentz group. As a consequence, it is possible to construct a…
We develop a symmetry classification scheme to find ground states of pseudo spin-1/2, spin-1, and spin-2 spin-orbit coupled spinor Bose-Einstein condensates, and show that as the SO(2) symmetry of simultaneous spin and space rotations is…
In this work we analyse the constraints imposed by Poincar\'e symmetry on the gravitational form factors appearing in the Lorentz decomposition of the energy-momentum tensor matrix elements for massive states with arbitrary spin. By…
In this paper, we develop the quantum theory of particles that has discrete Poincar\'{e} symmetry on the one-dimensional Bravais lattice. We review the recently discovered discrete Lorentz symmetry, which is the unique Lorentz symmetry that…
Wigner's method of induced representations is applied to the N=1 super-Poincare group, and by using a state corresponding to the basic vector of the little group as a Clifford vacuum we show that the spin operator of a supersymmetric point…