Related papers: Linking electroweak and gravitational generators
World spinors are objects that transform w.r.t. double covering group $\bar{Diff}(4,R)$ of the Group of General Coordinate Transformations. The basic mathematical results and the corresponding physical interpretation concerning these,…
We construct a class of negative spin irreducible representations of the su(2) Lie algebra. These representations are infinite-dimensional and have an indefinite inner product. We analyze the decomposition of arbitrary products of positive…
The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the…
The algebra of the generators for infinitesimal transformations of the $\Gamma={1 \over 2}$ representation of causal spinor fields (Dirac fields) \emph{explicitly} constructs the Minkowski metric \emph{within} the internal group space as a…
We construct the Lagrangeans of N=3 and N=4 two-form supergravities. The two-form gravity theories are classically equivalent to the Einstein gravity theories and can be formulated as gauge theories. The gauge algebras used here can be…
W_k structure underlying the tensverse realization of SU(2) at level k is analyzed. Extension of the equivalence existing between covariant and light-cone gauge realization of affine Kac-Moody algebra to W_k algebras is given. Higher spin…
A spinor current-source is found in the Weyl non-Abelian gauge theory which does not contain the abstract gauge space. It is shown that the searched spinor representation can be constructed in the space of external differential forms and it…
Einstein- Schroedinger (ES) non-symmetric theory has been extended to accommodate the Abelian and non-Abelian gauge theories of dyons in terms of the quaternion-octonion metric realization. Corresponding covariant derivatives for complex,…
We have systematically computed the generators of the symmetries arising in Poincare gauge theory formulation of gravity, both in 2+1 and 3+1 dimensions. This was done using a completely Lagrangian approach. The results are expected to be…
What symmetry breaking would be required for gauginos from a supersymmetric theory to behave like left-handed quarks of the Standard Model? Starting with a supersymmetric SU(3)xSU(3)xU(1)xU(1) gauge theory, the 18 adjoint-representation…
The local $SL(2N,C)$ symmetry is shown to provide, when appropriately constrained, a viable framework for a consistent unification of the known elementary forces, including gravity. Such a covariant constraint implies that an actual gauge…
We study N=1,2,4 higher spin superalgebras in four dimensions and higher spin gauge theories based on them. We extend the existing minimal N=2,4 theories and find a minimal N=1 theory. Utilizing the basic structure of the minimal N=8…
The representation theory of the symmetric groups is intimately related to geometry, algebraic combinatorics, and Lie theory. The spin representation theory of the symmetric groups was originally developed by Schur. In these lecture notes,…
Effective Lagrangian for pure Yang-Mills gauge fields invariant under the standard space-time and local gauge SU(3) transformations is considered. It is demonstrated that a set of twelve degenerated minima exists as soon as a nonzero gluon…
A universal description of particles with spins j greater or equal one , transforming in (j,0)+(0,j), is developed by means of representation specific second order differential wave equations without auxiliary conditions and in covariant…
We investigate the structure of Spin-$G$ bordism groups, focusing on the interplay between Spin and additional twisting symmetries such as $Sp(4)$, $SU(8)$ and $Spin(16)$. Using techniques from spectral sequences, obstruction theory, and…
We initiate the geometric engineering of 2d $\mathcal{N}=(0,1)$ gauge theories on D1-branes probing singularities. To do so, we introduce a new class of backgrounds obtained as quotients of Calabi-Yau 4-folds by a combination of an…
The use of complexified quaternions and $i$-complex geometry in formulating the Dirac equation allows us to give interesting geometric interpretations hidden in the conventional matrix-based approach.
In the representation theory of Lorentzian orthogonal groups, there are well known arguments as to why the parity inversion operator $\mathcal{P}$ and the time reversal operator $\mathcal{T}$, should be realized as linear and anti-linear…
Within the 4-dimensional conformal algebra, the presence of two translation operators implies the existence of 3 distinct metrics of definite Weyl weight constructible from the translational gauge fields. If we demand that each of these…