Aspects of polymer quantization of scalar matter field

Sardar, Gopal Chandra (2018) Aspects of polymer quantization of scalar matter field. PhD thesis, Indian Institute of Science Education and Research Kolkata.

PDF (PhD thesis of Gopal Chandra Sardar (11RS009)) 11RS009.pdf - Submitted Version Restricted to Repository staff only Download (826kB)

Abstract

Using a combination of analytical and numerical methods, in this thesis, we have shown that the Wightman function i.e. vacuum two-point function for the massless free scalar field is bounded from above in polymer quantization or loop quantization which is used in Loop Quantum Gravity. The bounded value of the Wightman function is governed by the polymer scale and its bounded nature can be viewed as if the spacetime has a zero-point length. This emergence of effective discreteness in spacetime appears from polymer quantization of matter field alone as the geometry is treated classically. Further, we have shown that the two-point function including leading order perturbative corrections due to polymer quantization, violates Kubo-Martin-Schwinger (KMS) condition in low-energy regime. This violation is caused by correction terms which are not Lorentz invariants. Consequently, polymer corrected two-point function along Rindler trajectory loses its thermal interpretation. In addition, we have employed the method which is analogous to the Bogoliubov transformation method for the computation of vacuum expectation value of number density operator. In particular, we have defined the number density operator in a new way as the notion of creation and annihilation operators are not readily available in polymer quantization. Subsequently, we have shown that the expectation value of number density operator in polymer vacuum state remains zero even for the accelerating observer. It provides additional support to the result that follows from the violation of KMS condition.

Actions (login required)

View Item