Volume 110, Number 4, May 2015
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||11 June 2015|
Entropy from scaling symmetry breaking
1 Instituto de Física, Universidade de Brasília - Caixa Postal 04455, 70919-970, Brasília, DF, Brazil
2 Instituto de Física - Universidade Federal do Rio de Janeiro - Caixa Postal 68528, 21945-970 Rio de Janeiro, RJ, Brazil
3 Theory Division, Saha Institute of Nuclear Physics - 1/AF Bidhannagar, Kolkata 700064, India
4 Departamento de Fíisica Teórica, Facultad de Ciencias, Universidad de Zaragoza - 50009 Zaragoza, Spain
Received: 21 December 2014
Accepted: 21 May 2015
The scaling symmetry in conformal quantum mechanics (CQM) can be broken due to the boundary conditions that follow from the requirement of a unitary time evolution of the Hamiltonian. We show that the scaling symmetry of CQM can be restored by introducing a suitable mixed state, which is associated with a nonvanishing von Neumann entropy. We give an explicit formula for the entropy arising from the mixed state in CQM. Our work provides a direct link between the restoration of a broken symmetry and the von Neumann entropy.
PACS: 89.70.Cf – Entropy and other measures of information / 11.10.-z – Field theory
© EPLA, 2015
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