Quantization And Spectrum Of P-brane

In this thesis, we review the construction of actions bosonic p-brane firstly. We canfind easily the internal relations between Nambu-Goto action and Polyakov action byintroducing interpolating action.Secondly, starting from Polyakov action, we obtain the explicit forms of solutionsto the Euler-Lagrange equation of p-brane. By requiring the natural quantization be-tween canonical variables, we obtain the commutative relations between normal modes,with which we can construct the raising and lowering operators. After defining the vac-uum states, we can get the general basis by acting the raising operators on the vacuumstates. In the bosonic string theory, the critical dimensionality of spacetime is 26, andwe suppose it still holds in our bosonic p-brane models. Using the vanishing Hamil-tonian , we calculate the spectrum of high dimensional branes. In the open 2-branemodel, we obtain a kind of vectorial tachyon states which are di?erent from stringtheory. Besides, the photon states produced in open string theory, and graviton states,Kalb-Ramond field and dilaton which are produced in closed string theory, are all ap-peared in the same level in the open 2-brane model. Because there are two sets ofindependent normal modes in the compacted direction, we generalize the definitionof the raising and lowering operators by introducing compensatory identity operator.Accordingly, the vacuum state must be defined accompanying the raising and loweringoperators. Then we achieve the spectrum of the cylindrical 2-brane at di?erent levels.Interestingly, there are some kinds of tachyon states appeared as tensor states withdi?erent orders, respectively. Later, we give the solution of Euler-Lagrange equation oftorus brane and discuss the quantization between the normal modes. When we considerhigher dimensional branes, all the energy levels will be suppressed greatly, and higherrank tensor states will be produced at lower levels due to more and more spacial direc-tions considered. What attract us is still the tachyon states which will contribute tothe instability of the D-brane with p-brane attached. While the appearance of higherrank tachyon states will make the tachyon potential more and more complicated.Finally, we give the scheme of Dirac quantization of open p-brane in the D-branebackground. Treating the mixed boundary conditions as primary constraints, we get aset of secondary constraints, then the constraints conditions are shown to be equivalentto orbifold conditions imposed on normal p-brane modes.