TY - JOUR

T1 - On geometric entropy

AU - Callan, Curtis

AU - Wilczek, Frank

N1 - Funding Information:
The microscopic definition S = -trplnp of entropy, where p is the density matrix of a quantum-mechanical system, has an appealing information-theoretic meaning apart from any thermodynamic interpretation. In quantum field theory, one can define the "geometric entropy" associated with a pure state and a geometrical region by forming the pure state density matrix, tracing over the field variables inside the region to create an "impure" density matrix and then evaluating S. In recent years, 't Hooft \[1\] and several other authors \[2-4\] have suggested that quantum-mechanical geometric entropy might be related to the mysterious Bekenstein-Hawking thermodynamic entropy of a black hole. In this Letter we will show that geometric entropy is the first quantum correction to a thermodynamic entropy which reduces i On leave from Princeton University. Research supported in part by DOE grant DE-FG02-90ER40542 and by the Monell Foundation. 2 Research supported in part by DOE grant DE-FG02-90ER40542.

PY - 1994/7/28

Y1 - 1994/7/28

N2 - We show that a geometrical notion of entropy, definable in flat space, governs the first quantum correction to the Bekenstein-Hawking black hole entropy. We describe two methods for calculating this entropy - a straightforward Hamiltonian approach, and a less direct but more powerful Euclidean (heat kernel) method. The entropy diverges in quantum field theory in the absence of an ultraviolet cutoff. Various related finite quantities can be extracted with further work. We briefly discuss the corresponding question in string theory.

AB - We show that a geometrical notion of entropy, definable in flat space, governs the first quantum correction to the Bekenstein-Hawking black hole entropy. We describe two methods for calculating this entropy - a straightforward Hamiltonian approach, and a less direct but more powerful Euclidean (heat kernel) method. The entropy diverges in quantum field theory in the absence of an ultraviolet cutoff. Various related finite quantities can be extracted with further work. We briefly discuss the corresponding question in string theory.

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U2 - 10.1016/0370-2693(94)91007-3

DO - 10.1016/0370-2693(94)91007-3

M3 - Article

AN - SCOPUS:4243671652

VL - 333

SP - 55

EP - 61

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 1-2

ER -