The effect of boundary conditions on dimensionally reduced field-theoretical models at finite temperature

Abstract

Here we understand \textit{dimensional reduction} as a procedure to obtain an effective model in $D-1$ dimensions that is related to the original model in $D$ dimensions. To explore this concept we use both a self-interacting fermionic model and self-interacting bosonic model. Furthermore, in both cases, we consider different boundary conditions in space: periodic, antiperiodic, Dirichlet and Neumann. For bosonic fields, we get the so defined dimensional reduction. Taking the simple example of a quartic interaction, we obtain that the boundary condition (periodic, Dirichlet, Neumann) influence the new coupling of the reduced model. For fermionic fields, we get the curious result that the model obtained reducing from $D$ dimensions to $D-1$ dimensions is distinguishable from taking into account a fermionic field originally in $D-1$ dimensions. Moreover, when one considers antiperiodic boundary condition in space (both for bosons or fermions) it is found that the dimensional reduction is not allowed.

References in corpus (8)

• The equation of state in (2+1)-flavor QCD
• Linear Confinement and AdS/QCD
• Rare K and B Decays in a Warped Extra Dimension with Custodial Protection
• Quantum field theory on toroidal topology: algebraic structure and applications
• Electroweak Symmetry Breaking and Precision Tests with a Fifth Dimension
• First-order phase transitions in superconducting films: A Euclidean model
• Properties of size-dependent models having quasiperiodic boundary conditions
• Dimensional reduction of a finite-size scalar field model at finite temperature

Cited by in corpus (1)

• Feynman Amplitudes in Periodically Compactified Spaces -- Spin 0