Renormalization of self-interacting scalar field theories in a nonsimply connected spacetime

Massive scalar field in multiply connected flat spacetimes

“…The calculation of 0 |T µν | 0 for a self-interacting field is much more complicated than that for a free field since it requires renormalization of quantities such as the field mass, which will be dependent on the field φ, the curvature coupling constant ξ, and the field coupling constant λ. In spacetimes with relatively simple topology, such as R 3 × T 1 and Casimir-type spacetime, 0 |T µν | 0 has been calculated by Birrell and Ford, Ford, Ford and Yoshimura, Kay, and Toms [18][19][20][21][22][23]. In a spacetime with CTC's self-interaction is known to cause failure of unitarity [24][25][26][27][28].…”

Finite size effects in the anisotropic (λ/4!)(φ14+φ24)d model

“…Hanson between two parallel plates and the photon field is unconfined. In flat spacetime, for systems where some dimensions are compactified but translational invariance is maintained, Toms [14] and also Birrel and Ford [15] have shown that all the counterterms are independent on the compactified spatial size. A more general discussion has been given by Banach [16].…”

Finite-size effects on the phase transition in a four- and six-fermion interaction model

“…Since correlation functions should satisfy periodicity conditions on the time coordinate, known as Kubo-Martin-Schwinger (KMS) conditions, the finite-temperature theory is defined on the compactified manifold Γ 1 4 = S 1 ×R 3 , where S 1 is a circumference with length proportional to the inverse of the temperature and R 3 is the Euclidean 3-dimensional space. Compactification of spatial dimensions [5,6] is considered in a similar way. An unified treatment, generalizing various approaches dealing with finite-temperature and spatialcompactification concurrently, has been constructed [7,8,9] These methods have been employed to investigate spontaneous symmetrybreaking induced by temperature and/or spatial constraints in some bosonic and fermionic models describing phase transitions in condensed-matter, statistical and particle physics; for instance, for describing the size-dependence of the transition temperature of superconducting films, wires and grains [10,11]; for investigating size-effects in first-and second-order transitions [12,13,14,15]; and for analyzing size and magnetic-field effects on the Gross-Neveu (GN) [16] and the Nambu-Jona-Lasinio (NJL) [17] models, taken as effective theories [18] for hadronic physics [19,20,21].…”