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The unitary irreducible representations of a Lie group defines the Hilbert space on which the representations act. If this Lie group is a physical quantum dynamical symmetry group, this Hilbert space is identified with the physical quantum…
We introduce a new symmetry, Light-Cone Reflection (LCR), which interchanges timelike and spacelike intervals. Our motivation is to provide a reason, based on symmetry, why tachyons might exist, with emphasis on application to neutrinos. We…
We review how antiparticles may be introduced in classical relativistic mechanics, and emphasize that many of their paradoxical properties can be more transparently understood in the classical than in the quantum domain.
It is known that every irreducible unitary representation of positive energy of the Poincar\'e group can be realized as a subspace of tensor fields on Minkowski spacetime subjected to suitable partial differential equations. We first…
The Heisenberg position-momentum uncertainty principle shares with the equivalence principle the role of main pillar of our current description of nature. However, in its original formulation it is inconsistent with special relativity, and…
In the context of asymptotically flat space-times, it has been suggested to label elementary particles as unitary irreducible representations of the BMS group. We analyse this idea in the spirit of the holographic principle advocating the…
For finite-dimensional linear semigroups which leave a proper cone invariant it is shown that irreducibility with respect to the cone implies the existence of an extremal norm. In case the cone is simplicial a similar statement applies to…
Superluminal particles are not excluded by particle physics. The apparent Lorentz invariance of the laws of physics does not imply that space-time is indeed minkowskian. Matter made of solutions of Lorentz-invariant equations would feel a…
Newtonian mechanics has the concept of an absolute inertial rest frame. Special relativity eliminates the absolute rest frame but continues to require the absolute inertial frame. General relativity solves this for gravity by requiring…
In recent experiments conducted by the OPERA collaboration, researchers claimed the observation of neutrinos propagating faster than the light speed in vacuum. If correct, their results raise several issues concerning the special theory of…
We adopt in this work the idea that the building blocks of the visible Universe belong to a class of the irreducible representations of the Poincare group of transformations (the "things") endowed with classificatory quantum numbers ("the…
Bound and scattering state Schr\"odinger functions of nonrelativistic quantum mechanics as representation matrix elements of space and time are embedded into residual representations of spacetime as generalizations of Feynman propagators.…
As 2011 ended, two results stood out which seemed to go against twentieth century ideas. The first was the OPERA superluminal neutrino observation contradicting Special Relativity. The second was lack of a definitive appearance of the Higgs…
The OPERA collaboration has claimed the discovery of supeluminal neutrino propagation. However the superluminal interpretation of the OPERA result was refuted by Cohen and Glashow because it was shown that such superluminal neutrinos would…
We show that Calogero-Sutherland models for interacting particles have a natural supersymmetric extension. For the construction, we use Jacobians which appear in certain superspaces. Some of the resulting Hamiltonians have a direct physics…
This paper proposes that the elusive neutrino is a space-like unitary irreducible representation of the Poincare Group. Although its imaginary mass is not a physical observable, its square is. This amount is found experimentally to be…
We present a quantum model for the motion of N point particles, implying nonlocal (i.e., superluminal) influences of external fields on the trajectories, that is nonetheless fully relativistic. In contrast to other models that have been…
We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…
Current quantum theories of an elementary free particle assume unitary space inversion and anti-unitary time reversal operators. In so doing robust classes of possible theories are discarded. The present work shows that consistent theories…
Born proposed a unification of special relativity and quantum mechanics that placed position, time, energy and momentum on equal footing through a reciprocity principle and extended the usual position-time and energy-momentum line elements…