Topology, mass and Casimir energy

Ahmadi, N.

doi:10.1016/j.nuclphysb.2006.01.010

Cited by 3 publications

(2 citation statements)

References 36 publications

(33 reference statements)

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“…There are numerous applications of such a formalism, including the Casimir effect for the electromagnetic and fermion fields within a box [20,21], the λφ 4 model describing the order parameter for the Ginsburg-Landau theory for superconductors [22], and the Gross-Neveu model as an effective approach for QCD [23,24]. The extension of this method to the Fourier integral representation is important to address many other problems in a topology Γ d D that are of interest in different areas, such as cosmology, condensed matter and particle physics [25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]. In order to proceed with such a generalization, we rely on algebraic bases, using the modular representation of the c * -algebra.…”

Section: Introductionmentioning

confidence: 99%

Quantum fields in toroidal topology

Khanna

Malbouisson

et al. 2011

Annals of Physics

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The standard representation of c*-algebra is used to describe fields in compactified space-time dimensions characterized by topologies of the type $ \Gamma_{D}^{d}=(\mathbb{S}^{1})^{d}\times \mathbb{M}^{D-d}$. The modular operator is generalized to introduce representations of isometry groups. The Poincar\'{e} symmetry is analyzed and then we construct the modular representation by using linear transformations in the field modes, similar to the Bogoliubov transformation. This provides a mechanism for compactification of the Minkowski space-time, that follows as a generalization of the Fourier-integral representation of the propagator at finite temperature. An important result is that the $2\times2$ representation of the real time formalism is not needed. The end result on calculating observables is described as a condensate in the ground state. We analyze initially the free Klein-Gordon and Dirac fields, and then formulate non-abelian gauge theories in $\Gamma_{D}^{d}$. Using the S-matrix, the decay of particles is calculated in order to show the effect of the compactification.Comment: 34 pages, LATEX, no figure

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Section: Introductionmentioning

confidence: 99%

Quantum fields in toroidal topology

Khanna

Malbouisson

et al. 2011

Annals of Physics

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“…There are numerous applications of such a generalized formalism, including the λφ 4 model describing the order parameter for the Ginzburg-Landau theory for superconductors [10][11][12][13] and the Gross-Neveu and Nambu-Jona-Lasinio models as effective approaches for quantum chromodynamics [14][15][16][17][18][19][20][21]. The extension of this method to the real-time formalism is important to address many other problems in a topology Γ d D that are of interest in different areas, such as cosmology, condensed matter and particle physics [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. In this note we will restrict ourselves to the Matsubara imaginary-time formalism.…”

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confidence: 99%

First-order phase transition for a field theory at finite chemical potential in a toroidal topology

Linhares

Malbouisson

Roditi

2012

EPL

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We study the critical behaviour of the −λϕ 4 + ηϕ 6 theory at finite chemical potential defined in a toroidal topology, with compactification of imaginary time (finite temperature) and compactification of a spatial coordinate. This is performed as an application of recently published methods for dealing with field theories defined on toroidal spaces. We study finite-size (described by the spatial compactification length L) and finite-chemical-potential (µ) effects, by carrying out an investigation of the critical temperature as a function of both L and µ. We find that there is a minimal size for the system that sustains the transition, and that this size is the same for all values of the chemical potential.

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Pre-inflationary spacetime in string cosmology

McInnes

2006

Nuclear Physics B

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Seiberg and Witten have shown that the non-perturbative stability of string physics on conformally compactified spacetimes is related to the behaviour of the areas and volumes of certain branes as the brane is moved towards infinity. If, as is particularly natural in quantum cosmology, the spatial sections of an accelerating cosmological model are flat and compact, then the spacetime is on the brink of disaster: it turns out that the version of inflationary spacetime geometry with toral spatial sections is marginally stable in the Seiberg-Witten sense. The question is whether the system remains stable before and after Inflation, when the spacetime geometry is distorted away from the inflationary form but still has flat spatial sections. We show that it is indeed possible to avoid disaster, but that requiring stability at all times imposes non-trivial conditions on the spacetime geometry of the early Universe in string cosmology. This in turn allows us to suggest a candidate for the structure which, in the earliest Universe, forbids cosmological singularities.

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Topology, mass and Casimir energy

Cited by 3 publications

References 36 publications

Quantum fields in toroidal topology

Quantum fields in toroidal topology

First-order phase transition for a field theory at finite chemical potential in a toroidal topology

Pre-inflationary spacetime in string cosmology

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