^{1, 2}

^{1}

^{1}

^{2}

^{3}.

We show that the spectrum of a bosonic open 2-brane does not contain any massless states to take the role of gravitons. Moreover, the spectrum of this open 2-brane only contains half integer mass squared values.

Besides the impressive progress of string theories in the past few decades which compelled physicists to believe that a consistent theory of quantum gravity based on string philosophy would be built soon has slowed down. The early success of string theory also sparked the motivation to study higher dimensional extended objects. Indeed if one can give up 0-dimensional particles in favor of strings which are one-dimensional objects, then why not strings in favor of two-dimensional membranes? The basic idea that elementary particles could be interpreted as vibrating modes of a membrane originally came in 1962 by Dirac [

Since the task of achieving a consistent theory of quantum gravity based on string philosophy became more and more subtle, physicists tried to find alternative candidates to construct a theory of fundamental interactions; one of these candidates was supermembrane theory [

Compared to the works on string quantization, works on membrane quantization are very few, precisely because of the difficulty the Nambu action meets when one tries to generalize it to

We will analyze the mass squared values in the spectrum of the bosonic open 2-brane. The bosonic membranes could be related to the bosonic string theory via dimensional reduction [

The organization of this paper is as follows: Section

The quantization of bosonic open branes was studied in [

The energy-momentum tensor is given by the variation of the action (

Under the flat metric condition

According to the standard commutation relation

Under the tensorial assumption,

We will employ the Zeta function regularization scheme to regularize the infinite divergent summation in (

In fact, there is another scheme [

According to the above calculation and the fact that

At the lowest mass level, the number operators

At the second excited level, there are four kinds of tensor states, featured by

In this paper, firstly we review the quantization of open 2-brane, starting from the Polyakov action. We then investigate the spectrum of the open 2-brane by taking into account the contributions of both the infinite sums (

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors thank Jian-Feng Wu for suggesting to them literatures on the special zeta functions [