Quantum fluctuations of the stress tensor

Quantum fluctuations of the stress tensor are important in many branches of physics, including the study of the validity of semiclassical gravity and the backreaction problem in stochastic semiclassical gravity. The geometry fluctuations induced by stress tensor fluctuations are important to understand quantum gravity and the problem of lightcone fluctuations. Stress tensor fluctuations also hold the key to understand fundamental physical effects like quantum fluctuations of radiation pressure, and that is crucial to the sensitivity of interferometers and the limitations on the detection of gravitational waves. Even the wave-particle duality of light can be better understood by the study of quantum fluctuations of thermal radiation.; It is well known in quantum field theory that the expectation value of the energy density, which contains quadratic field operators (e.g. E2 and B2 in the electromagnatic field case), is divergent and can be renormalized simply by normal ordering, which is subtracting out the vacuum divergence. In addition to the mean value, fluctuations around the mean are also important in quantum theory. However, the density fluctuations are defined by the expectation value of the squared energy density minus the square of the expectation value of the energy density, and the expectation value of the squared energy density involves the field operators in fourth order. The renormalization is now far more complicated. Ambiguous state-dependent divergences show up when the squared stress tensor is expanded using Wick's theorem. We resolve this ambiguity by studying an averaged quantity instead of the local quantity. With careful regularization in the integrals, we show that this ambiguous term can be understood as containing nontrivial physics, such as the radiation pressure fluctuation of a quantized radiation field.; Models involving particle creation were also investigated, including the model of radiation created by moving mirrors and the model of particle creation due to space-time change in a collapsing black hole (Hawking radiation). Hawking radiation is (filtered) thermal radiation. We also compare them to Einstein's fluctuation formula for thermal radiation of 1909. This formula contains a “wave” term and a “particle” term. It is believed to be the first formula indicating that light can display the properties of waves and particles at the same time. We find that the “wave” term corresponds to the contribution of a fully normal-ordered term of the stress tensor fluctuation and the “particle” term corresponds to a cross term. We also calculated velocity fluctuations of a test particle due to the fluctuating Van der Waals force. We find a negative mean squared velocity fluctuation in this case. It is actually not so surprising to see this negative result, since it is a difference between a mean squared velocity with the plate and one without it. The negative factor is totally due to the cross term. This can be interpreted as a reduction of the velocity spread of a wavepacket. The metric fluctuation two point function induced by the electromagnatic stress tensor fluctuations in Minkowski vacuum is also calculated. Finally, we discuss the validity of semi-classical gravity.