| General relativity and quantum field theory, the two revolutionary theories in mod-ern physics, have achieved great successes. However, there exists obvious incompatible contradictions between them. When people attempt to bring general relativity into the framework of quantum field theory to construct quantum gravity theory, their careful-ly deliberated theories fail without exception because they can not be renormalization, which indicates gravity’s individual property differentiating itself from other three fun-damental interactions. In order to gain the self-consistent quantum gravity theory, peo-ple have proposed several schemes such as string theory, loop quantum gravity, and so forth. As a kind of attempts to investigate the self-consistent quantum gravity theory, spacetime noncommutativity has developed rapidly. Now noncommutativity exists as a fundamental theory rather than an effective one of the string theory in low energy regime because people guess at very small scale or very high energy scale noncom-mutativity is the essential property of the spacetime, which means that near the Planck scale the concepts of point and position become ambiguity. Moreover, theories de-scribing strong gravity systems such as black holes in commutative spacetime confront dilemmas:the singularity, the black hole information paradox, etc.. So it is natural to construct theories in noncommutative spacetime, which highlights the road to the final theory of quantum gravity.This thesis mainly deals with two different approaches to noncommutativity, and also pays attention to Dirac quantization of constrained systems. In chapter2we intro-duce two different approaches to construct noncommutative theories including general uncertainty principle(GUP) and noncommutative geometry(NCG), and in chapter3we introduce a variety of black holes and their thermodynamic properties along with the Parikh-Wilczek method to interpret the black hole information paradox, which prepare for our main work as follows:●In chapter4we propose an improved exponential GUP, derive its algebraic struc-ture, and generalize its algebraic structure to D-dimensional spacetime. We prove that the weighted phase space volume remains invariance under time evolution in the classical limit and provide the formula to caculate the cosmological con-stant in the framework of improved exponential GUP. By choosing the value of the suppressing index suitably and considering UV/IR mixing effect, we work out the cosmological constant that is consistent with the experimentally observed value. This result is smaller than the commutative QFT result by121order of magnitude.●In chapter5we construct the expression of the improved exponential GUP in the Hilbert space, calculate the maximally localized states and obtain the generalized Fourier transformation. We investigate how the thermodynamic quantities are modified and how the Schwardzschild black hole evaporates under our new GUP and the corrected outcomes are different from that under other GUPs. We have two significant consequences:One is that the evaporation rate is extremely small, in other words, the evaporation process of black holes is remarkably prolonged, when the UV/IR mixing effect is particularly considered, and the other is that the larger the suppressing index is the less radiation the Schwardzschild black hole emits, and the extreme case is that the black hole stops emitting when suppressing index goes to infinity.●In chapter6we deal with three interacting models of chiral bosons and gauge fields by following the new proposal of noncommutative extended Minkowski spacetime, i.e., the connection between noncommutative κ-Minkowski spacetime and a well-defined extended Minkowski spacetime. We quantize the three models in the extended Minkowski spacetime by the use of Dirac’s method, derive the Hamilton canonical equations, find out the spectra of the models, and investigate their duality symmetries. We prove that even in noncommutative spacetime their self-dualities still remain. |
PDF Full Text Request