Search results for "Lorentz group"
showing 7 items of 7 documents
Star representations of E(2)
1990
We give a complete and explicit realization of the unitary irreducible representations of the universal covering group G of E(2), the Euclidean group in two dimensions, by deformation of the algebra of functions on the dual g* of the Lie algebra of G. We define an adapted Fourier transform for G which gives a natural description of the harmonic analysis of G.
Mass, zero mass and ... nophysics
2017
In this paper we demonstrate that massless particles cannot be considered as limiting case of massive particles. Instead, the usual symmetry structure based on semisimple groups like $U(1)$, $SU(2)$ and $SU(3)$ has to be replaced by less usual solvable groups like the minimal nonabelian group ${\rm sol}_2$. Starting from the proper orthochronous Lorentz group ${\rm Lor}_{1,3}$ we extend Wigner's little group by an additional generator, obtaining the maximal solvable or Borel subgroup ${\rm Bor}_{1,3}$ which is equivalent to the Kronecker sum of two copies of ${\rm sol}_2$, telling something about the helicity of particle and antiparticle states.
Supersymmetry and Noncommutative Geometry
1996
The purpose of this article is to apply the concept of the spectral triple, the starting point for the analysis of noncommutative spaces in the sense of A.~Connes, to the case where the algebra $\cA$ contains both bosonic and fermionic degrees of freedom. The operator $\cD$ of the spectral triple under consideration is the square root of the Dirac operator und thus the forms of the generalized differential algebra constructed out of the spectral triple are in a representation of the Lorentz group with integer spin if the form degree is even and they are in a representation with half-integer spin if the form degree is odd. However, we find that the 2-forms, obtained by squaring the connectio…
Symmetries and Covariance of the Maxwell Equations
2012
Already within a given, fixed division of four-dimensional spacetime into the space where experiments are performed, and the laboratory time variable, Maxwell’s equations show interesting transformation properties under continuous and discrete space-time transformations. However, only the action of the whole Lorentz group on them reveals their full symmetry structure. A good example that illustrates the covariance of Maxwell’s equations is provided by the electromagnetic fields of a point charge uniformly moving along a straight line.
Reflection equations and q-Minkowski space algebras
1994
We express the defining relations of the $q$-deformed Minkowski space algebra as well as that of the corresponding derivatives and differentials in the form of reflection equations. This formulation encompasses the covariance properties with respect the quantum Lorentz group action in a straightforward way.
Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models
2007
We study a model of N-component complex fermions with a kinetic term that is second order in derivatives. This symplectic fermion model has an Sp(2N) symmetry, which for any N contains an SO(3) subgroup that can be identified with rotational spin of spin-1/2 particles. Since the spin-1/2 representation is not promoted to a representation of the Lorentz group, the model is not fully Lorentz invariant, although it has a relativistic dispersion relation. The hamiltonian is pseudo-hermitian, H^\dagger = C H C, which implies it has a unitary time evolution. Renormalization-group analysis shows the model has a low-energy fixed point that is a fermionic version of the Wilson-Fisher fixed points. T…
Classifying Reported and "Missing" Resonances According to Their P and C Properties
2000
The Hilbert space ℋ3q of the three quarks with one excited quark is decomposed into Lorentz group representations. It is shown that the quantum numbers of the reported and "missing" resonances fall apart and populate distinct representations that differ by their parity or/and charge conjugation properties. In this way, reported and "missing" resonances become distinguishable. For example, resonances from the full listing reported by the Particle Data Group are accommodated by Rarita–Schwinger (RS) type representations [Formula: see text] with k=1, 3, and 5, the highest spin states being J=3/2-, 7/2+, and 11/2+, respectively. In contrast to this, most of the "missing" resonances fall into t…