Modern Physics Letters A

We consider the possibility of detecting in a hypothetical 1 km³ neutrino telescope high energy neutrinos resulting from the annihilation of very heavy neutrinos of fourth generation in the galactic halo. It is shown that such a large telescope could in principle detect this negligible component which, if it does exist, gives a contribution of order 10^–2 to the dark matter of the universe.

We establish the exactness of the complete quantum action of arbitrary dimensional BF theories with respect to an off-shell nilpotent and metric independent BRST operator. This is realized by enlarging the system of fields in such theories by extra ghosts playing the role of auxiliary fields.

We have found that the functional integral for quantum gravity can be represented as a superposition of less complicated theory of random surfaces with Euler character as an action. We propose an alternative linear action A(M₄) for quantum gravity. On the lattice we constructed spin system with local interaction, which has the equivalent partition function. The scaling limit is discussed.

We present a simple physical representation for states of two-dimensional string theory. In order to incorporate a fundamental cutoff of the order 1/g_st we use a picture consisting of q oscillators at the first quantized level. In this framework we also find a representation for the (singular) negatively dressed states representing nontrivial string backgrounds.

By taking into account both quantum mechanical and general relativistic effects, we derive an equation that describes limitations on the measurability of spacetime distances as defined by a material reference system.

Starting from a polynomial (higher-order derivative) quantum mechanical SUSY algebra we study its contraction to the standard SUSYQM in the limit of large energy shifts between the lowest states of the super-Hamiltonian (of Schrödinger type). By a quasi-linearization method we obtain the charges of the higher derivative SUSY algebra in the (singular) limit of infinite energy gap, and find the resulting Hamiltonian. The singular behavior of the potential generated by this construction reflects the existence of the very deep level. Our results can suggest constructions of toy models where large energy splittings between fermionic and bosonic partners do not affect SUSY for other states.

Starting from the general covariant Dirac equation with minimal coupling of an electromagnetic field the corrections to the energy levels of the electron in a Penning trap caused by the gravitational field of the Earth are computed. Our discussion shows that the resulting effect is detectable only at the specific eigenfrequencies of the electron. The relative shift of these frequencies due to the gravitational field is found to be 2.1×10^–9. It is briefly indicated how this effect in principle could be observed in suitable experiments performed with higher precision.