The Lie derivation of multivector fields along multivector fields has been introduced by Schouten (see cite{Sc, S}), and studdied for example in cite{M} and cite{I}. In the present paper we define the Lie derivation of differential forms along multivector fields, and we extend this concept to covariant derivation on tangent bundles and vector bundles, and find natural relations between them and...

We prove that 1-loop n-point NMHV superamplitudes in N = 4 SYM theory are dual conformal covariant for all numbers n of external particles (after regularization and subtraction of IR divergences). This property was previously established for n ≤ 9 in arXiv:0808.0491. We derive an explicit representation of these superamplitudes in terms of dual conformal cross-ratios. We also show that all the ...

The N-extended self-dual supergravity in the ultra-hyperbolic four-dimensional space-time of kleinian signature (2+2) is given in the N-extended harmonic superspace. We reformulate the on-shell N-extended self-dual supergravity constraints of Siegel to a 'zero-curvature' representation, and solve all of them but one in terms of a single superfield prepotential, by using a covariant Frobenius ga...

Given M copies of a q-deformed Weyl or Clifford algebra in the defining representation of a quantum group Gq, we determine a prescription to embed them into a unique, inclusive Gq-covariant algebra. The different copies are “coupled” to each other and are naturally ordered into a “chain”. In the case Gq = SLq(N) a modified prescription yields an inclusive algebra which is even explicitly SLq(M)...

Using the grassman-number-integral representation of the vacuum overlap formula, it is shown that the symmetry of the auxiliary quantum fermion system in the overlap formalism induces exact chiral symmetry of the action of the type given by Luscher under the chiral transformation δψn = γ5(1 − aD)ψn and δψ̄n = ψ̄nγ5. With this relation, we consider the connection between the covariant form of the ...

Recent work in time-frequency analysis proposed to switch the focus from maxima of spectrogram toward its zeros, which, for signals corrupted by Gaussian noise, form a random point pattern with very stable structure leveraged modern spatial statistics tools perform component disentanglement and signal detection. The major bottlenecks this approach are discretization Short-Time Fourier Transform...

Assuming the spin-independence for confining force, we give a covariant quark representation of general composite meson systems with definite Lorentz transformation properties. For benefit of this representation we are able to deduce automatically the transformation rules of composite mesons for general symmetry operations from those of constituent (exciton) quarks. Applying this we investigate...

The Berry phase is analyzed for Weyl and Dirac fermions in a space representation of the worldline formalism. Kinetic theories are constructed both at classical level. Whereas fermion case reduces dimension, resembling theory quantum mechanics, takes on manifestly Lorentz covariant form. To achieve kinetic non-Abelian spinor construction Barut Zanghi utilized. axial anomaly also studied It foun...