A special fermionic generalization of lineal gravity

The central extension of the (1+1)-dimensional Poincaré algebra by including fermionic charges which obey not supersymmetric algebra, but a special graded algebra containing in the right hand side a central element only is obtained. The corresponding theory being the fermionic extension of the lineal gravity is proposed. We considered the algebra of generators, the field transformations and found Lagrangian and equation of motion, then we derived the Casimir operator and obtained the con- stant black hole mass.

THE PLANCHEREL FORMULA FOR THE LINE BUNDLES ON SL(n + 1, R)/S(GL(1, R) × GL(n, R))

In this paper we obtain the Plancherel formula for the spaces of L2-sections of the line bundles over the pseudo-Riemannian symmetric space G/H where G=SL（n ＋ 1, R） and H=S（GL（1, R）×GL（n, R））. The Plancherel formula is given in an explicit form by means of spherical distributions associated with the character χλ of the subgroup H. We follow the method of Faraut, Kosters and van Dijk.

Origin of Particle Spins, Bosons and Fermions, Compounds of Zero Spin Particles, in Complex Spin Region

This paper shows： Bosons and Fermions maybe the compounds П of two zero spin particles which are spin-conjugates each other in complex region. There are two kinds of spin-conjugates of zero spin particle： real spin-conjugate （πReal,π） and imaginary spin-conjugate （πImaginary,π）. Using （πReal, π）, Bosons and Fermions of Antimatter ПR could be formed, and using （πImaginary,π）, Bosons and Fermions of Matter П1 could be formed.

There Is a Way to Comprise Half-Integer Eigenvalues for Photon Spin

In this article, an attempt based on Spin Topological Space, STS, to give areasonable detailed account of the cause of photonic fermionization phenomena of light photon is made. STS is an unconventional spin space in quantum mechanics, which can be used to account for where the unconventional half-integer spin eigenvalues phenomenon of light photon comes from. We suggest to dectect the possible existence of photonic one-third-spinization phenomenon of light photon, by using three beams of light photon in interference experiment.

What Will Happen, If Zero SpinParticle Possesses Spin Rotational Construction, With Non-Zero Eigenvalues Of Spin Angular Momentum?

There is no any spin rotational construction for zero spin particle, Casimir operator and the thired component of zero spin particle areandrespectively. Further, there are no spin interactions between zero spin particle and other spin particles. This paper shows: in Spin Topological Space, STS [1], the third component of zero spin particle possesses non-zero eigenvalues besides original zero value, this leads to a miraculous spin interaction phenomenon between zero spin particle and other spin particles. In STS, zero spin particle could "dissolve other spin particles", degrade the values of their Casimir operator, and decay these spin particles into other forms of spin particle.

Spin Forms and Spin Interactions among Higgs Bosons, between Higgs Boson and Graviton

This paper offers concrete spin matrix forms of 0h spin zero particle, and shows the existent of the spin interactions among 0h spin zero particles. It is obviously hoping to approach, on the most comprehensive level, to understand what really Higgs Boson is and what role-play Higgs Boson is acting in particle physics. As a "particle" of gravitational force, the spin interaction between 0h spin zero particle (Higgs Boson) and 2h spin particle (Graviton) is given, which maybea way that people would find Graviton in future.

A Kind of Invariant Hankel Operators

For two kinds of the Moebius invariant subspace A_l^(a,2)(D) and A_l^(-a,2)(D) of L^(a,2)(D), we define big and small Hankel operators H_b^(ll') and h_b^(ll') for the analytic symbol function b(z), and study their boundedness, compactness and Schatten-von Neumanu classes S_p-estimates, and hence develope Schatten -von Neumann properties of these op- erators.

Note on Co-split Lie Algebras

It is proved that, any finite dimensional complex Lie algebra/~ = [Z：, ~：], hence, over a field of characteristic zero, any finite dimensional Lie algebra l： = [/2, ~：] possessing a basis with complex structure constants, should be a weak co-split Lie algebra. A class of non-semi-simple co-split Lie algebras is given.