Related papers: Free massless particles and extended space-time al…
It is proven that the Poincare symmetry determines equations of motion, which are for massless particles of any spin in d-dimensional spaces linear in the momentum. The proof is made only for even d and for fields with no gauge symmetry. We…
The new 4D geometry whose Killing vectors span the Poincar\'e algebra is presented and its structure is analyzed. The new geometry can be regarded as the Poincar\'e-invariant solution of the degenerate extension of the vacuum Einstein field…
In this note we shall construct, in the framework of relativistic quantum mechanics, the Poincare-invariant motion equations with realistic mass spectra. These equations describe a system with mass spectra of the form $m^2=a^2+b^2 s(s+1)$,…
We analyze the decomposition of the enveloping algebra of the conformal algebra in arbitrary dimension with respect to the mass-squared operator. It emerges that the subalgebra that commutes with the mass-squared is generated by its…
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…
We study actions for massive bosonic particles of higher spins by dimensionally reducing an action for massless particles. For the latter we take a model with a SO(N) extended local supersymmetry on the worldline, that is known to describe…
The properties of the equation of Dirac type in three-dimensional and five-dimensional Minkowski space-time with respect to time reflection (in sense of Pauli and Wigner) as well as to the operation of charge conjugation are investigated.…
We analyze possible local extensions of the Poincar\'e symmetry in light-cone gravity in four dimensions. We use a formalism where we represent the algebra on the two physical degrees of freedom, one with helicity $2$ and the other with…
In the present paper we review in a fibre bundle context the covariant and massless canonical representations of the Poincare' group as well as certain unitary representations of the conformal group (in 4 dimensions). We give a simplified…
It is noted that the internal space-time symmetries of relativistic particles are dictated by Wigner's little groups. The symmetry of massive particles is like the three-dimensional rotation group, while the symmetry of massless particles…
We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general 2-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension $D>4$, these conformal…
We present an approach for construction of functional bases of differential invariants for some infinite-dimensional algebras with coefficients of generating operators depending on arbitrary functions. An example for the…
For the rigid, nonrotating motion of an extended charge in an arbitrary electromagnetic field, an equation of motion is derived by Lorentz-invariantly calculating the 4-Lorentz force = external 4-force + 4-self-force, acting upon the…
Current theories of massless free particle assume {\sl unitary} space inversion and {\sl anti-unitary} time reversal operators. In so doing robust classes of possible theories are discarded. In the present work theories of massless systems…
In this letter we study an infinite extension of the Galilei symmetry group in any dimension that can be thought of as a non-relativistic or post-Galilean expansion of the Poincare symmetry. We find an infinite-dimensional vector space on…
The most general 2+1 dimensional spinning particle model is considered. The action functional may involve all the possible first order Poincare invariants of world lines, and the particular class of actions is specified thus the…
The relativistic two-component equation describing the free motion of particles with zero mass and spin 1/2, which is P- and T-non-invariant but C-invariant, is found. The representation of the Poincare group for zero mass and discrete spin…
We construct two possible candidates for the non-relativistic $\mathfrak{bms}_4$ algebra in 4 space-time dimensions by contracting the original relativistic $\mathfrak{bms}_4$ algebra. The $\mathfrak{bms}_4$ algebra is infinite-dimensional,…
Free field equations, with various spins, for space-time algebras with second-rank tensor (instead of usual vector) momentum are constructed. Similar algebras are appearing in superstring/M theories. The most attention is payed to the gauge…
Extending the commutator algebra of quantum $\kappa$-Poincar\'e symmetry to the whole of the phase space, and assuming that this algebra is to be covariant under action of deformed Lorentz generators, we derive the transformation properties…