Suraj N Gupta’s research while affiliated with Cambridge and other places

The radiation field is quantized by introducing four types of photons - two transverse, one longitudinal, and one scalar. The scalar photons are treated by using an indefinite metric, and it is found necessary to modify the usual supplementary condition slightly. The present theory offers a justification for the symmetrical treatment of the four components of the electromagnetic potential, recently applied by a number of authors, and proves to be very convenient in applications. The results of physical interest, however, are the same as obtained from the ordinary formulation.

The quantization of the complete gravitational field is carried out by extending the work of an earlier paper. The main obstacles in the quantization of Einstein's field are overcome by expressing the field quantities in the Riemannian space as expansions in the flat space, and then splitting the gravitational field into the linear and the non-linear parts. The linear part of the gravitational field is regarded as the free gravitational field, while the non-linearity is treated as a direct interaction between the gravitons. This treatment is quite general, but it suffers from the usual limitations of the perturbation method. The gravitational self-energies of the photon and the electron are also investigated by using the linear approximation of the gravitational field It is found that the photon self-energy vanishes unambiguously, while the electron self-energy is quadratically divergent.

The approximate linear form of Einstein's gravitational field is quantized by using an indefinite metric. It is shown that only two types of gravitons can be observed, though many more can exist in virtual states in the presence of interaction. The observable gravitons are shown to be particles of spin 2. Using the interaction representation, the interaction of the gravitational field with the matter field is briefly discussed.

Stueckelberg's treatment of the vector meson field is investigated, and is found to involve difficulties similar to those of Fermi's treatment of the radiation field. It is shown that these difficulties may be removed by the same procedure as has already been applied to the radiation field in an earlier paper, which involves the use of an indefinite metric and a modification of the supplementary condition.

It is shown that the divergencies in classical electrodynamics may be removed by subtracting the self-energies of isolated electrons by means of a modification of the usual expression for the force density in an electromagnetic field. The results obtained are equivalent to those of Dirac and Wentzel.

A consistent scheme of quantum electrodynamics with auxiliary fields of photons and electrons of infinitely large masses is developed. The auxiliary fields are introduced from the very beginning in the Lagrangian density, but it is ensured by means of suitable initial conditions that these fields are completely unobservable. For some of the auxiliary photon fields the usual sign of the Lagrangian density is reversed, while for some of the auxiliary electrons fields the usual statistics of the field is reversed. For such fields it is found necessary to use an indefinite metric. It is shown that the present treatment provides us with a well-defined procedure for the evaluation of divergent integrals in quantum electrodynamcs. As an application, the self-energy of the photon is evaluated and shown to vanish for a free photon.