Improvement of stress-energy tensor using space-time symmetries
Bandyopadhyay, Akash
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https://hdl.handle.net/2142/31307
Description
Title
Improvement of stress-energy tensor using space-time symmetries
Author(s)
Bandyopadhyay, Akash
Issue Date
2001
Doctoral Committee Chair(s)
Oono, Yoshitsugu
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
stress-energy tensor
Language
en
Abstract
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.
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