Energy-momentum tensor in quantum field theory

Journal Article · Fri May 15 04:00:00 EDT 1981 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.23.2262· OSTI ID:6498416

Fujikawa, K

The definition of the energy-momentum tensor as a source current coupled to the background gravitational field receives an important modification in quantum theory. In the path-integral approach, the manifest covariance of the integral measure under general coordinate transformations dictates that field variables with weight 1/2 should be used as independent integration variables. An improved energy-momentum tensor is then generated by the variational derivative, and it gives rise to well-defined gravitational conformal (Weyl) anomalies. In the flat--space-time limit, all the Ward-Takahashi identities associated with space-time transformations including the global dilatation become free from anomalies in terms of this energy-momentum tensor, reflecting the general covariance of the integral measure; the trace of this tensor is thus finite at zero momentum transfer for renormalizable theories. The Jacobian for the local conformal transformation, however, becomes nontrivial, and it gives rise to an anomaly for the conformal identity. All the familiar anomalies are thus reduced to either chiral or conformal anomalies. The consistency of the dilatation and conformal identities at vanishing momentum transfer determines the trace anomaly of this energy-momentum tensor in terms of the renormalization-group b function and other parameters. In contrast, the trace of the conventional energy-momentum tensor generally diverges even at vanishing momentum transfer depending on the regularization scheme, and it is subtractively renormalized. We also explain how the apparently different renormalization properties of the chiral and trace anomalies arise.

• Research Organization: Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo 188, Japan
• OSTI ID: 6498416
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 23:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHIRAL SYMMETRY
ENERGY-MOMENTUM TENSOR
FEYNMAN PATH INTEGRAL
FIELD THEORIES
GRAVITATIONAL FIELDS
INTEGRALS
PERTURBATION THEORY
QUANTUM FIELD THEORY
RENORMALIZATION
SPACE-TIME
SYMMETRY
TENSORS
WARD IDENTITY