M ar 1 99 8 QUANTIZATION OF GRAVITY IN THE THEORY WITH THE MASSIVE VECTOR FIELD

The quantum theory of gravity is considered based on the assumption that gravitational interaction occurs by means of the vector field of the Planck mass. Gravitational emission is considered as a process of the decay of proton into some matter fields at the Planck scale. Within the framework of grand unification vector field of the Planck mass may be thought of as those which realize the interaction between leptons and quarks. In the Einstein theory of gravity [1] with the Lagrangian L = − 1 16πG √ gR, (1) gravitational field is defined by the components of the metric tensor g µν. If to take g µν in the form g µν = η µν + h µν , (2) where η µν is the background metric and h µν is the small perturbations of the background metric, one comes to the theory of the fields h µν in the background metric. Quantization of gravity reduces to quantization of the field h µν. As follows from the theory [1], the field h µν is a massless one of the spin 2. Quantum theory of gravity based on the above approach is nonrenormalizable. According to the dimensions analysis, the nonrenormalizable theories have the negative mass dimensions. The Newton constant G has the dimensions [m] −2 (¯ h = c = 1). In the theory of the weak interaction, the Fermi constant G F also has the dimensions [m] −2. Renormalization of the weak interaction is effected within the framework of the theory with the massive vector boson [2]. From this, it is natural to consider gravity within the framework of the theory with the massive vector boson. Let us assume that gravitational interaction occurs by means of the vector field, denote it P l. Let us define the coupling of the theory as g = (¯ hc) 1/2. Then the Newton constant is given by G = g 2 m 2 P l , (4) where m P l = (¯ hc/G) 1/2 is the Planck mass. This makes natural to assume that the field P l has the mass equal to the Planck mass. One can develop the theory of gravity with the use of the theory with the massive vector field [2]. To obtain the renormalizable theory, the original field P l is taken to be massless and acquires mass due to the Higgs mechanism.