The trace anomaly and massless scalar degrees of freedom

Journal Article · Tue Jan 01 04:00:00 EST 2008 · Physical Review. D, Particles, Fields, Gravitation and Cosmology

OSTI ID:960880

Gianotti, Maurizio ^[1]; Mottola, Emil ^[1]

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1. Los Alamos National Laboratory

The trace anomaly of quantum fields in electromagnetic or gravitational backgrounds implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. Considering first the axial anomaly and using QED as an example, we compute the full one-loop triangle amplitude of the fermionic stress tensor with two current vertices, {open_square}T{sup {mu}{nu}}J{sup {alpha}}J{sup {beta}}, and exhibit the scalar pole in this amplitude associated with the trace anomaly, in the limit of zero electron mass m{yields}0. To emphasize the infrared aspect of the anomaly, we use a dispersive approach and show that this amplitude and the existence of the massless scalar pole is determined completely by its ultraviolet finite terms, together with the requirements of Poincare invariance of the vacuum, Bose symmetry under interchange of J{sup {alpha}} and J{sup {beta}}, and vector current and stress-tensor conservation. We derive a sum rule for the appropriate positive spectral function corresponding to the discontinuity of the triangle amplitude, showing that it becomes proportional to {delta}(k{sup 2}) and therefore contains a massless scalar intermediate state in the conformal limit of zero electron mass. The effective action corresponding to the trace of the triangle amplitude can be expressed in local form by the introduction of two scalar auxiliary fields which satisfy massless wave equations. These massless scalar degrees of freedom couple to classical sources, contribute to gravitational scattering processes, and can have long range gravitational effects.

• Research Organization: Los Alamos National Laboratory (LANL)
• Sponsoring Organization: DOE
• DOE Contract Number: AC52-06NA25396
• OSTI ID: 960880
• Report Number(s): LA-UR-08-06329; LA-UR-08-6329
• Journal Information: Physical Review. D, Particles, Fields, Gravitation and Cosmology, Journal Name: Physical Review. D, Particles, Fields, Gravitation and Cosmology; ISSN PRVDAQ; ISSN 1550-7998
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
DEGREES OF FREEDOM
ELECTRONS
INTERMEDIATE STATE
MASS
QUANTUM ELECTRODYNAMICS
RANGE
SCALARS
SCATTERING
SPECTRAL FUNCTIONS
SUM RULES
SYMMETRY
TENSORS
USES
VECTOR CURRENTS
WAVE EQUATIONS