Vacuum energy through Krein quantization approach

In this paper, we consider a new version of indefinite metric field quantization called "Krein" quantization approach. Centering on the vacuum energy, fundamental subjects revolving around this concept will be discussed. In this approach, vacuum expectation value of the energy-momentum tensor can be defined properly and uniquely. Actually, no infinite term appears and the vacuum energy of the free field vanishes. These properties allow us to propose a discussion that creates an interesting link to the cosmological constant problem. Achieving this goal, however, necessitates consistency of the theory with conventional ones, so we have studied and made comparison with essential issues, such as unitarity of the theory, physical achievements of renormalizing process, and the trace anomaly subject.