Related papers: $gl(4|4)$ current algebra: free field realization …
Let g denote a Lie algebra, and let T(g) denote the tensor product of g with a ring of truncated polynomials. The Lie algebra T(g) is called a truncated current Lie algebra. The highest-weight representation theory of T(g) is developed, and…
The minimal models M(p',p) with p' > 2 have a unique (non-trivial) simple current of conformal dimension h = (p' - 2) (p - 2) / 4. The representation theory of the extended algebra defined by this simple current is investigated in detail.…
We show that Geroch decomposition leads us to Maxwell-like representation of gravity in $(3+1)$ metrics decomposition that may be perceived as Lorentz invariant version of GEM. For such decomposition we derive four-potential $V^\mu$ and…
A modified-gravity theory with a four-form field strength $F$, a variable gravitational coupling parameter $G(F)$, and a standard matter action is considered here. Maxwell and Einstein equations are now derived when including to action also…
The geometry of 4D simplicial quantum gravity with a U(1) gauge field is studied numerically. The phase diagram shows a continuous transition when gravity is coupled with a U(1) gauge field. At the critical point measurements of the…
In the context of the local gauge group $SU(3)_c\otimes SU(3)_L\otimes U(1)_X$, we look for possible four family models, where all the particles carry ordinary electric charges. Thirteen different anomaly-free fermion structures emerge, out…
Gauge invariant conserved conformal currents built from massless fields of all spins in 4d Minkowski space-time and $AdS_4$ are described within the unfolded dynamics approach. The current cohomology associated with non-zero conserved…
A representation of the quantum affine algebra $U_{q}(\widehat{sl}_3)$ of an arbitrary level $k$ is constructed in the Fock module of eight boson fields. This realization reduces the Wakimoto representation in the $q \rightarrow 1$ limit.…
General relativity in the form where gravitational perturbations together with other physical fields propagate on an auxiliary background is considered. With using the Katz-Bi{\v{c}}\'ak-Lynden-Bell technique new conserved currents,…
We study a free field realization of the elliptic quantum algebra $U_{q,p}(sl_3^)$ for arbitrary level $k$. We give the free field realization of elliptic analogue of Drinfeld current associated with $U_{q,p}(sl_3^)$ for arbitrary level…
We propose a general action describing the dynamics of lightlike (LL) p-branes in any odd (p+1) world-volume dimensions. Next, we consider self-consistent coupling of \textsl{LL}-membranes (p=2) to D=4 Einstein-Maxwell system plus a D=4…
It is well known that the field equations of teleparallel theory which is equivalent to general relativity (TEGR) completely agree with the field equation of general relativity (GR). However, TEGR has six extra degrees of freedom which…
In this paper, the power flow in electrical systems is modelled in the time domain by using Geometric Algebra and the Hilbert Transform. The use of this mathematical framework overcomes some of the limitations shown by the existing…
We give a comprehensive review of various methods to define currents and the energy-momentum tensor in classical field theory, with emphasis on a geometric point of view. The necessity of ``improving'' the expressions provided by the…
Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is…
In this note we continue to pursue the question whether gauge theories can be represented in terms of effective "scalar" degrees of freedom. We provide such a consistent representation for a free photon theory in 3+1 dimensions. Building on…
Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates QED. Here we formalize and generalize…
A new treatment of the gravitational energy on the basis of 4-index gravitational equations is reviewed. The gravitational energy for the Schwarzschild field is considered.
The physical fields (electromagnetic and electron fields) considered in the framework of Clifford algebras $\C_2$ and $\C_4$. The electron field described by the algebra $\C_4$ which in spinor representation is realized by well-known Dirac…
We determine explicit variational expressions for the free energy of mean-field spin glasses in a transversal magnetic field, whose glass interaction is given by a hierarchical Gaussian potential as in Derrida's Generalized Random Energy…