scholarly journals Poincaré Algebra and Space-Time Critical Dimensions for Paraspinnings Strings

2004 ◽  
Vol 54 (6) ◽  
pp. 621-632 ◽  
Author(s):  
N. Belaloui ◽  
H. Bennacer
Keyword(s):  
Space Time ◽  
Critical Dimensions ◽  
Poincaré Algebra ◽  
Time Critical

scholarly journals Fractional superstrings with space-time critical dimensions four and six

1991 ◽  
Vol 67 (24) ◽  
pp. 3339-3342 ◽  
Author(s):  
Philip C. Argyres ◽  
S.-H. Henry Tye
Keyword(s):  
Space Time ◽  
Critical Dimensions ◽  
Time Critical

scholarly journals A Parafermion Generalization of Poincaré Supersymmetry

1978 ◽  
Vol 31 (6) ◽  
pp. 461 ◽  
Author(s):  
PD Jarvis
Keyword(s):  
Arbitrary Order ◽  
Space Time ◽  
Supersymmetry Algebra ◽  
Commutation Relations ◽  
Poincaré Algebra ◽  
Special Case

The space-time Poincare algebra is extended by introducing a four-spinor generator whose components satisfy certain trilinear parafermi commutation relations. The spin content of the irreducible multiplets is analysed in the massive and massless cases, and weight diagrams constructed, for arbitrary order p of the parastatistics. The supersymmetry algebra of Wess and Zumino, and of Salam and Strathdee, is exhibited as the special case of order p = 1 in this formulation.

scholarly journals DUAL KAPPA POINCAŔE ALGEBRA

2010 ◽  
Vol 25 (09) ◽  
pp. 1881-1890 ◽  
Author(s):  
JOSE A. MAGPANTAY
Keyword(s):  
Phase Space ◽  
Space Time ◽  
Lorentz Algebra ◽  
Poincaré Algebra ◽  
New Space ◽  
Heisenberg Double

We show a different modification of Poincaré algebra that also preserves Lorentz algebra. The change begins with how boosts affect space–time in a way similar to how they affect the momenta in kappa Poincaré algebra; hence the term "dual kappa Poincaré algebra." Since by construction the new space–time commutes, it follows that the momenta cocommute. Proposing a space–time coalgebra that is similar to the momentum coproduct in the bicrossproduct basis of kappa Poincaré algebra, we derive the phase space algebra using the Heisenberg double construction. The phase space variables of the dual kappa Poincaré algebra are then related to SR phase space variables. From these relations, we complete the dual kappa Poincaré algebra by deriving the action of rotations and boosts on the momenta.

scholarly journals FIELD THEORETIC REALIZATIONS FOR CUBIC SUPERSYMMETRY

2004 ◽  
Vol 19 (32) ◽  
pp. 5585-5608 ◽  
Author(s):  
N. MOHAMMEDI ◽  
G. MOULTAKA ◽  
M. RAUSCH DE TRAUBENBERG
Keyword(s):  
Gauge Symmetry ◽  
Dimensional Space ◽  
A Priori ◽  
Space Time ◽  
Time Symmetry ◽  
Poincaré Algebra ◽  
Dimensional Space Time

We consider a four-dimensional space–time symmetry which is a nontrivial extension of the Poincaré algebra, different from supersymmetry and not contradicting a priori the well-known no-go theorems. We investigate some field theoretical aspects of this new symmetry and construct invariant actions for noninteracting fermion and noninteracting boson multiplets. In the case of the bosonic multiplet, where two-form fields appear naturally, we find that this symmetry is compatible with a local U(1) gauge symmetry, only when the latter is gauge fixed by a 't Hooft–Feynman term.

EXTENDED POINCARÉ SUPERSYMMETRY

1987 ◽  
Vol 02 (01) ◽  
pp. 273-300 ◽  
Author(s):  
J. STRATHDEE
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Poincaré Algebra ◽  
Dimensional Space Time

Supersymmetric extensions of the Poincaré algebra in D-dimensional space-time are reviewed and a catalogue of their representations is developed. This catalogue includes all supermultiplets whose states carry helicity ≤ 2 in the massless cases and ≤ 1 in the massive cases.

scholarly journals Space-Time Defects and Group Momentum Space

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Michele Arzano ◽  
Tomasz Trześniewski
Keyword(s):  
Minkowski Space ◽  
Lorentz Group ◽  
Momentum Space ◽  
Abelian Subgroup ◽  
Space Time ◽  
Noncommutative Space ◽  
De Sitter ◽  
Maximal Abelian Subgroup ◽  
Dimensional Minkowski Space ◽  
Poincaré Algebra

We study massive and massless conical defects in Minkowski and de Sitter spaces in various space-time dimensions. The energy momentum of a defect, considered as an (extended) relativistic object, is completely characterized by the holonomy of the connection associated with its space-time metric. The possible holonomies are given by Lorentz group elements, which are rotations and null rotations for massive and massless defects, respectively. In particular, if we fix the direction of propagation of a massless defect in n+1-dimensional Minkowski space, then its space of holonomies is a maximal Abelian subgroup of the AN(n-1) group, which corresponds to the well known momentum space associated with the n-dimensional κ-Minkowski noncommutative space-time and κ-deformed Poincaré algebra. We also conjecture that massless defects in n-dimensional de Sitter space can be analogously characterized by holonomies belonging to the same subgroup. This shows how group-valued momenta related to four-dimensional deformations of relativistic symmetries can arise in the description of motion of space-time defects.

scholarly journals A free Lie algebra approach to curvature corrections to flat space-time

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Joaquim Gomis ◽  
Axel Kleinschmidt ◽  
Diederik Roest ◽  
Patricio Salgado-Rebolledo
Keyword(s):  
Lie Algebra ◽  
Flat Space ◽  
Geodesic Equation ◽  
Space Time ◽  
Free Lie Algebra ◽  
Dimensional Algebra ◽  
Infinite Dimensional ◽  
Algebra Approach ◽  
Poincaré Algebra ◽  
Particle Action

Abstract We investigate a systematic approach to include curvature corrections to the isometry algebra of flat space-time order-by-order in the curvature scale. The Poincaré algebra is extended to a free Lie algebra, with generalised boosts and translations that no longer commute. The additional generators satisfy a level-ordering and encode the curvature corrections at that order. This eventually results in an infinite-dimensional algebra that we refer to as Poincaré∞, and we show that it contains among others an (A)dS quotient. We discuss a non-linear realisation of this infinite-dimensional algebra, and construct a particle action based on it. The latter yields a geodesic equation that includes (A)dS curvature corrections at every order.

scholarly journals Quaternion generalization of super-Poincaré group

2019 ◽  
Vol 34 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Bhupendra C. S. Chauhan ◽  
Pawan Kumar Joshi ◽  
O. P. S. Negi
Keyword(s):  
Lorentz Group ◽  
Space Time ◽  
Poincaré Group ◽  
Poincare Group ◽  
Poincaré Algebra

Super-Poincaré algebra in [Formula: see text] space–time dimensions has been studied in terms of quaternionic representation of Lorentz group. Starting the connection of quaternion Lorentz group with [Formula: see text] group, the [Formula: see text] spinors for Dirac and Weyl representations of Poincaré group are described consistently to extend the Poincaré algebra to super-Poincaré algebra for [Formula: see text] space–time.

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