Phase transition and the Casimir effect are studied in the complex scalar field with one spatial dimension to be compactified. It is shown that the phase transition is of the second order and the Casimir effect behaves quite differently depending on whether it’s under periodic or anti-periodic boundary conditions. | JOURNAL OF SCIENCE OF HNUE Mathematical and Physical Sci. 2013 Vol. 58 No. 7 pp. 138-146 This paper is available online at http PHASE TRANSITION AND THE CASIMIR EFFECT IN A COMPLEX SCALAR FIELD WITH ONE COMPACTIFIED SPATIAL DIMENSION Tran Huu Phat1 and Nguyen Thi Tham2 1 Vietnam Atomic Energy Institute 2 Faculty of Physics Hanoi University of Education No. 2 Xuan Hoa Vinh Phuc Abstract. Phase transition and the Casimir effect are studied in the complex scalar field with one spatial dimension to be compactified. It is shown that the phase transition is of the second order and the Casimir effect behaves quite differently depending on whether it s under periodic or anti-periodic boundary conditions. Keywords Phase transition Casimir effect complex scalar field compactified spatial. 1. Introduction It is well known that a characteristic of quantum field theory in space-time with nontrivial topology is the existence of non-equivalent types of fields with the same spin 1 2 3 . For a scalar system in space-time which is locally flat but with topolog that is a Minkowskian space with one of the spatial dimensions compactified in a circle of finite radius L the non-trivial topology is transferred into periodic sign and anti-periodic sign - boundary conditions φ t x y z φ t x y z L The seminal discovery in this direction is the so-called Casimir effect 4 5 where the Casimir force generated by the electromagnetic field that exists in the area between two parallel planar plates was found to be π 2 cS F 240L4 here S is the area of the parallel plates and L is the distance between two plates fulfilling the condition L2 S. The Casimir effect was first written about in 1948 4 but since the Received June 30 2013. Accepted August 27 2013. Contact Nguyen Thi Tham e-mail address nguyenthamhn@ 138 Phase transition and the casimir effect in a complex scalar field. 1970s this effect has received increasing attention of scientists. Newer and more precise .
