Massive spinor fields in flat spacetimes with nontrivial topology

Ahmadi, N.

doi:10.1103/physrevd.71.104012

Cited by 12 publications

(20 citation statements)

References 20 publications

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“…For the scalar field our results on M 0 agree with those in [3]. For the spinor field on M 0 our results are twice those of [4] as expected. On M − the results for the massive fields are new.…”

Section: Discussionsupporting

confidence: 88%

Stress tensor for massive fields on flat spaces of spatial topology

Langlois

2005

Class. Quantum Grav.

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We calculate the expectation values of the energy-momentum tensor T µν for massive scalar and spinor fields, in the Minkowski-like vacuum states on the two flat spaces which are quotients of Minkowski space under the discrete isometries (t, x, y, z) → (t, x, y, z + 2a) and (t, x, y, z) → (t, −x, −y, z + a). The results on the first space confirm the literature. The results on the second space are new. We note some qualitative differences between the massless and massive fields in the limits of large a and large x 2 + y 2 . * Electronic Address: pmxppl@nottingham.ac.uk 1 The expectation values for the massless scalar field on M0 appear in a number of places in the literature [1,11,12]. Those for 2-component spinors are also found in [11,12].

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Section: Discussionsupporting

confidence: 88%

Stress tensor for massive fields on flat spaces of spatial topology

Langlois

2005

Class. Quantum Grav.

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“…This allows us to consider field theoretical models with spatial constraints, at zero or finite temperature, by using generating functionals with a path-integral formalism on the topology [29][30][31][32]. These ideas have been established recently on a firm foundation [33,34] and applied in different physical situations, for example: for spontaneous symmetry breaking in the compactified φ 4 model [37][38][39]; for second-order phase transitions in superconducting films, wires and grains [40][41][42]; for the Casimir effect for bosons and fermions [43][44][45][46][47][48]; for size effects in the NJL model [49][50][51][52][53]; and, for electrodynamics with an extra dimension [54].…”

Section: Introductionmentioning

confidence: 99%

Phase transition in the massive Gross-Neveu model in toroidal topologies

Khanna

Malbouisson

et al. 2012

Phys. Rev. D

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We use methods of quantum field theory in toroidal topologies to study the N -component D-dimensional massive Gross-Neveu model, at zero and finite temperature, with compactified spatial coordinates. We discuss the behavior of the large-N coupling constant (g), investigating its dependence on the compactification length (L) and the temperature (T ). For all values of the fixed coupling constant (λ), we find an asymptotic-freedom type of behavior, with g → 0 as L → 0 and/or T → ∞. At T = 0, and for λ ≥ λ

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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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Massive spinor fields in flat spacetimes with nontrivial topology

Cited by 12 publications

References 20 publications

Stress tensor for massive fields on flat spaces of spatial topology

Stress tensor for massive fields on flat spaces of spatial topology

Phase transition in the massive Gross-Neveu model in toroidal topologies

Quantum fields in toroidal topology

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