2,046 research outputs found
Higher dimensional Loop Quantum Cosmology
Loop quantum cosmology(LQC) is the symmetric model of loop quantum gravity.
In this paper, we generalize the structure of loop quantum cosmology to the
theories with arbitrary spacetime dimensions. The isotropic and homogenous
cosmological model in n+1 dimensions is quantized by the loop quantization
method. Interestingly, we find that the underlying quantum theories are divided
into two qualitatively different sectors according to spacetime dimensions. The
effective Hamiltonian and modified dynamical equations of n+1 dimensional LQC
are obtained. Moreover, our results indicate that the classical big bang
singularity is resolved in arbitrary spacetime dimensions by a quantum bounce.
We also briefly discuss the similarities and differences between the n+1
dimensional model and the 3+1 dimensional one. Our model serves as a first
example of higher dimensional loop quantum cosmology and offers possibility to
investigate quantum gravity effects in higher dimensional cosmology.Comment: 14 pages. Minor revision and references added, presentation improve
On the renormalization of quasi parton distribution
Recent developments showed that light-cone parton distributions can be
studied by investigating the large momentum limit of the hadronic matrix
elements of spacelike correlators, which are known as quasi parton
distributions. Like a light-cone parton distribution, a quasi parton
distribution also contains ultraviolet divergences and therefore needs
renormalization. The renormalization of non-local operators in general is not
well understood. However, in the case of quasi quark distribution, the bilinear
quark operator with a straight-line gauge link appears to be multiplicatively
renormalizable by the quark wave function renormalization in the axial gauge.
We first show that the renormalization of the self energy correction to the
quasi quark distribution is equivalent to that of the heavy-light quark vector
current in heavy quark effective theory at one-loop order. Assuming this
equivalence at two-loop order, we then show that the multiplicative
renormalizability of the quasi quark distribution is true at two-loop order.Comment: 14 pages, 4 figure
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