ar X iv : h ep - t h / 97 05 06 6 v 1 1 1 M ay 1 99 7 On the Second Quantization of M ( atrix ) Theory

The second quantization of M(atrix) theory is considered. It provides a possible framework to the recent Susskind proposal that U (N) supersymmetic Yang Mills theories for all N might be embedded in a single dynamical system. The second quantization of M(atrix) theory can also be useful for the study of the Lorentz symmetry of the theory and for the consideration of processess with creation and annihilation of D-branes. Recently Susskind [1] has suggested that there is the connection between M-theory and U(N) supersymmetric Yang-Mills theory not only in the large N limit but even at finite N. He also conjectured that there is an embedding the super Yang-Mills theories for all N in a single dynamical system. In this note we attempt to pursue this idea by using the second quantization of M(atrix) theory. The second quantization would also be useful for the consideration of processess with creation and annihilation of D-branes [3]. Another problem which requires the consideration of processess which change the size of matrices is the problem of the Lorentz symmetry because the moment exchange in the eleventh dimension means the exchange of zero-brane charge [4]. The bosonic part of M(atrix) theory [2] is described by the following Lagrangian