Radiation from a Moving Mirror in Two Dimensional SpaceTime: Conformal Anomaly
Abstract
The energymomentum tensor is calculated in the two dimensional quantum theory of a massless scalar field influenced by the motion of a perfectly reflecting boundary (mirror). This simple model system evidently can provide insight into more sophisticated processes, such as particle production in cosmological models and exploding black holes. In spite of the conformally static nature of the problem, the vacuum expectation value of the tensor for an arbitrary mirror trajectory exhibits a nonvanishing radiation flux (which may be readily computed). The expectation value of the instantaneous energy flux is negative when the proper acceleration of the mirror is increasing, but the total energy radiated during a bounded mirror motion is positive. A uniformly accelerating mirror does not radiate; however, our quantization does not coincide with the treatment of that system as a 'static universe'. The calculation of the expectation value requires a regularization procedure of covariant separation of points (in products of field operators) along timelike geodesics; more naive methods do not yield the same answers. A striking example involving two mirrors clarifies the significance of the conformal anomaly.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 March 1976
 DOI:
 10.1098/rspa.1976.0045
 Bibcode:
 1976RSPSA.348..393F
 Keywords:

 Conformal Mapping;
 Field Theory (Physics);
 Mirrors;
 Quantum Theory;
 Tensor Analysis;
 Acceleration (Physics);
 Astrophysics;
 Black Holes (Astronomy);
 Coordinate Transformations;
 Cosmology;
 Covariance;
 Optical Reflection;
 Potential Fields;
 Radiant Flux Density;
 Vector Spaces;
 Astrophysics;
 CONFORMAL MAPPING;
 FIELD THEORY (PHYSICS);
 MIRRORS;
 QUANTUM THEORY;
 TENSOR ANALYSIS;
 ACCELERATION (PHYSICS);
 ASTROPHYSICS;
 BLACK HOLES (ASTRONOMY);
 COORDINATE TRANSFORMATIONS;
 COSMOLOGY;
 COVARIANCE;
 OPTICAL REFLECTION;
 POTENTIAL FIELDS;
 RADIANT FLUX DENSITY;
 VECTOR SPACES