Improvement of stress-energy tensor using space-time symmetries

In 1970 Callan, Coleman, and Jackiw found that it is always possible to improve the symmetric stress-energy tensor of a renormalizable relativistic field theory over (3+1)-dimensional flat space-time manifold. The improved stress-energy tensor defines the same field energy-momentum and angular momentum as the conventional tensor, and it is traceless for a non-interacting field theory when all coupling constants are physically dimensionless. The question for existence of an improved stress-energy tensor for a scale invariant relativistic field theory on a (1+1)-dimensional flat space-time manifold has been a long standing open problem for almost 30 years. In this thesis, I develop the weakest set of necessary and sufficient conditions for existence of a conserved symmetric traceless stress-energy tensor for a scale invariant relativistic field theory over a d-dimensional flat space-time manifold. This improved tensor, which defines the same conserved charges as the canonical tensor, has been explicitly constructed for arbitrary space-time dimensions including d = 2 intrinsically from the flat space-time field theory without coupling it with gravity. As an example, I derive the improved tensor of (1+1)-dimensional Liouville field theory. We discuss two remarkable results: (1) full conformal symmetry over the flat space-time is sufficient but not necessary for the existence of an improved tensor; (2) quite surprisingly, the improved stress-energy tensor exists in all space-time dimensions for a free massless Abelian U(1) gauge theory provided the gauge symmetry has been broken in favor of Lorentz gauge for d ≠ 2,4.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2012

Author dc:creator

• Bandyopadhyay, Akash

Contributors dc:contributor

• Oono, Yoshitsugu

• stress-energy tensor

Statement dc:rights

• ©2001 Akash Bandyopadhyay

Language dc:language

en

Identifier

4377422

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/31307