Description of a domain using a squeezed state in a scalar field theory
- PDF / 428,035 Bytes
- 8 Pages / 595.276 x 790.866 pts Page_size
- 72 Downloads / 185 Views
Regular Article - Theoretical Physics
Description of a domain using a squeezed state in a scalar field theory Masamichi Ishiharaa Department of Human Life Studies, Koriyama Women’s University, Koriyama, 963-8503, Japan
Received: 8 January 2013 / Revised: 5 April 2013 / Published online: 8 May 2013 © Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013
Abstract We attempt to describe a domain using a squeezed state within quantum field theory. An extended squeeze operator is used to construct the state. Using a scalar field theory, we describe a domain in which the distributions of the condensate and of the fluctuation are both Gaussian. The momentum distribution, chaoticity, and correlation length are calculated. It is found that the typical value for the momentum is approximately the inverse of the domain size. It is also found that the chaoticity reflects the ratio of the size of the squeezed region to that of the coherent region. The results indicate that the quantum state of a domain is defined by these quantities under the assumption that the distributions are Gaussian. As an example, this method is applied to a pion field, and the momentum distribution and chaoticity are shown.
1 Introduction Squeezing is a basic concept in various branches of physics and is applicable to many subjects. This concept is used in quantum optics [1–4], quantum field theory, etc. The squeezed state is a good base for studying non-perturbative behavior in quantum mechanics and quantum field theory. For example, this state appears in particle creation [5, 6] and is used to calculate the effective potential [7–10]. The important property is the relationship between fluctuations of conjugate variables. The uncertainty relation is minimized by not only a coherent state but also by a squeezed state. A coherent state is expected to be formed generally. The expectation value of a scalar field φ is nonzero in a broken phase of the symmetry, even when a theory is symmetric under the interchange of φ and −φ. This nonzero expectation value can be represented using a coherent state. Therefore, a coherent state is a candidate for describing a condensate when a nonzero expectation value exists. a e-mail:
[email protected]
Domains will be formed in some processes. For instance, it is expected that a domain will be formed in a chiral phase transition. The chiral symmetry is restored, and this symmetry is broken again afterwards. The order parameter φ rolls down from the top of the potential hill, and it reaches the minimum of the potential. The condensate is spatially dependent on such a phenomenon, and the spatial dependence indicates a domain formation. The condensate is described by a coherent state that is constructed by a displacement operator [11]. A domain will be formed even when the symmetry restoration does not occur. The system is in a local thermal equilibrium during high-energy heavy ion collisions. The equilibration occurs locally even when the distribution is described by Tsallis statistics [12]. T
Data Loading...
