Related papers: Continuous Spin Representations of the Poincar\'e …
We present an explicit construction of the unitary irreducible representations of the two-dimensional Euclidean and Poincar\'e groups, together with their Spin double covers, by means of Mackey's theory of induced representations for…
Manifestly covariant formulation of discrete-spin, real-mass unitary representations of the Poincar\'e group is given. We begin with a field of spin-frames associated with 4-mometa p and use them to simplify the eigenvalue problem for the…
We show that rigid supersymmetry theories in four dimensions can be extended to give supersymmetric trace (or generalized quantum) dynamics theories, in which the supersymmetry algebra is represented by the generalized Poisson bracket of…
We discuss the Kirillov method for massless Wigner particles, usually (mis)named "continuous spin" or "infinite spin" particles. These appear in Wigner's classification of the unitary representations of the Poincar\'e group, labelled by…
We make a simple observation that the massless continuous spin representations of the Poincar\'e group are not present in perturbative string theory constructions. This represents one of the very few model-independent low-energy…
We construct the covariant, spinor sets of relativistic wave equations for a massless field on the basis of the two copies of the R-deformed Heisenberg algebra. For the finite-dimensional representations of the algebra they give a universal…
Wigner's little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take…
Following Pasterski-Shao-Strominger we construct a new basis of states in the single-particle Hilbert space of massless particles as a linear combination of standard Wigner states. Under Lorentz transformation the new basis states transform…
We construct coherent states of the massless and massive representations of the Poincar\'e group. They are parameterised by points on the classical state space of spinning particles. Their properties are explored, with special emphasis on…
We present a gauge field theory for the continuous spin tachyonic representation of the Poincar\'e group. It was obtained by a dimensional reduction of a complex gauge field theory for a continuous spin particle in a cotangent bundle over…
Extended particles are considered in terms of the fields on the Poincar\'{e} group. Dirac like wave equations for extended particles of any spin are defined on the various homogeneous spaces of the Poincar\'{e} group. Free fields of the…
We study representations of the Poincar\'e group that have a privileged transformation law along a p-dimensional hyperplane, and uncover their associated spinor helicity variables in D spacetime dimensions. Our novel representations…
The spin of particles on a non-commutative geometry is investigated within the framework of the representation theory of the q-deformed Poincare algebra. An overview of the q-Lorentz algebra is given, including its representation theory…
It is possible to construct representations of the Lorentz group using four-dimensional harmonic oscillators. This allows us to construct three-dimensional wave functions with the usual rotational symmetry for space-like coordinates and…
We propose a (3+1)D linear set of covariant vector equations, which unify the spin 0 ``new Dirac equation'' with its spin 1/2 counterpart, proposed by Staunton. Our equations describe a spin (0,1/2) supermultiplet with different numbers of…
We give a pedagogical presentation of the irreducible unitary representations of $\mathbb{C}^4\rtimes\mathbf{Spin}(4,\mathbb{C})$, that is, of the universal cover of the complexified Poincar\'e group…
We show that the Wigner equations describing the continuous spin representations can be obtained as a limit of massive higher-spin field equations. The limit involves a suitable scaling of the wave function, the mass going to zero and the…
We present the consistent approach to finding the discrete transformations in the representation spaces of the proper Poincar\'e group. To this end we use the possibility to establish a correspondence between involutory automorphisms of the…
The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group $Sp(2)$. It is shown that this oscillator system contains the…
We describe, for arbitrary dimensions the construction of a covariant and supersymmetric constraint for the massless Super Poincare' algebra and we show that the constraint fixes uniquely the representation of the algebra. For the case of…