FERMIONIC CONDENSATE AND INDUCED CURRENT IN A CONICAL SPACE WITH A CIRCULAR BOUNDARY AND MAGNETIC FLUX

2012 ◽  
Vol 14 ◽  
pp. 496-500
Author(s):  
A. A. SAHARIAN
Keyword(s):  
Boundary Condition ◽  
Magnetic Flux ◽  
Charge Density ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Opening Angle ◽  
Finite Radius ◽  
Current Decay ◽  
Circular Boundary ◽  
Cone Apex

The fermionic condensate and current density are investigated in a (2 + 1)-dimensional conical spacetime in the presence of a circular boundary and a magnetic flux. On the boundary the fermionic field obeys the MIT bag boundary condition. For irregular modes, we consider a special case of boundary conditions at the cone apex, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The condensate and current are periodic functions of the magnetic flux with the period equal to the flux quantum. For both exterior and interior regions, the expectation values are decomposed into boundary-free and boundary-induced parts. In the case of a massless field the boundary-free part in the vacuum expectation value of the charge density vanishes, whereas the presence of the boundary induces nonzero charge density. At distances from the boundary larger than the Compton wavelength of the fermion particle, the condensate and current decay exponentially, with the decay rate depending on the opening angle of the cone.

scholarly journals Fermionic Condensate on Finite Radius Cones

2021 ◽  
pp. 1-7
Author(s):  
A. A. Hovhannisyan
Keyword(s):  
Boundary Condition ◽  
Magnetic Flux ◽  
Flux Quantum ◽  
Periodic Functions ◽  
Finite Radius ◽  
Dimensional Cone ◽  
Cone Apex

The fermionic condensate is investigated for a field localized on a finite radius 2- dimensional cone in the presence of a magnetic flux threading the cone apex. On the edge of the cone a boundary condition is imposed that differs from the MIT bag boundary condition, most frequently used for the confinement of fermions. The fermionic condensate is decomposed into the boundary-free and edge-induced contributions. Both these parts are periodic functions of the magnetic flux with the period equal to the flux quantum.

CHARGE-DENSITY-WAVES IN THE PRESENCE OF IMPURITY POTENTIAL IN ONE-DIMENSIONAL SYSTEMS: A FIELD THEORY APPROACH

2004 ◽  
Vol 18 (06) ◽  
pp. 883-898 ◽  
Author(s):  
L. V. BELVEDERE ◽  
R. L. P. G. DO AMARAL ◽  
A. F. DE QUEIROZ
Keyword(s):  
Charge Density ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Charge Density Waves ◽  
Lagrangian Model ◽  
Theory Approach ◽  
Density Waves ◽  
Impurity Potential ◽  
One Dimensional ◽  
Phonon Field

The effective Lagrangian model for charge-density waves interacting with an impurity potential in one-dimensional systems is considered in the dynamical phonon phase approach. Using the fermion–boson mapping we obtain the effective bosonized version of the model. The impurity potential breaks the linked electron–phonon symmetry, the phason field turns out to be in interaction with the electron–phonon condensate and the phonon field develops a non-vanishing vacuum expectation value. The effective fermionized version of the model corresponds to the chiral Gross–Neveu model with quartic self-interaction among a massless and a massive (electron) Fermi fields. The electron–phonon system exhibits a conserved topological charge which is independent of local variations of the phases of the phonon and electron fields. The equation of state of the associated statistical-mechanical system is obtained. For the dynamical phonon phase field the Kosterlitz–Thouless phase transition is suppressed.

RELATION BETWEEN THE ALGEBRA OF CURRENTS AND THEIR DEFINITION IN CHIRAL GAUGE THEORIES

1992 ◽  
Vol 07 (04) ◽  
pp. 765-776
Author(s):  
C. FOSCO ◽  
R. C. TRINCHERO
Keyword(s):  
Charge Density ◽  
Gauge Field ◽  
Gauge Theories ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Simple Relation ◽  
Expectation Value ◽  
Covariant Gauge ◽  
The Difference ◽  
Definition Of

We consider anomalous commutators between the charge density and any component of the gauge current in chiral gauge theories. This is done using the BJL definition of commutators, and without quantizing the gauge field. We study the relation between the vacuum expectation value (VEV) of these commutators for the case of consistent and covariant gauge currents. We obtain a simple relation valid for any dimension and gauge group. This relation shows that the difference between the VEV's of the commutators for the consistent and covariant gauge currents depends only on the difference between the VEV's of the corresponding currents.

scholarly journals Vacuum fermionic currents in braneworld models on AdS bulk with a cosmic string

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
S. Bellucci ◽  
W. Oliveira dos Santos ◽  
E.R. Bezerra de Mello ◽  
A.A. Saharian
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Current Density ◽  
Cosmic String ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Vacuum State ◽  
Total Current ◽  
De Sitter ◽  
Proper Distance

Abstract We investigate the effects of a brane and magnetic-flux-carrying cosmic string on the vacuum expectation value (VEV) of the current density for a charged fermionic field in the background geometry of (4+1)-dimensional anti-de Sitter (AdS) spacetime. The brane is parallel to the AdS boundary and the cosmic string is orthogonal to the brane. Two types of boundary conditions are considered on the brane that include the MIT bag boundary condition and the boundary conditions in Z2-symmetric braneworld models. The brane divides the space into two regions with different properties of the vacuum state. The only nonzero component of the current density is along the azimuthal direction and in both the regions the corresponding VEV is decomposed into the brane- free and brane-induced contributions. The latter vanishes on the string and near the string the total current is dominated by the brane-free part. At large distances from the string and in the region between the brane and AdS horizon the decay of the brane-induced current density, as a function of the proper distance, is power-law for both massless and massive fields. For a massive field this behavior is essentially different from that in the Minkowski bulk. In the region between the brane and AdS boundary the large-distance decay of the current density is exponential. Depending on the boundary condition on the brane, the brane-induced contribution is dominant or subdominant in the total current density at large distances from the string. By using the results for fields realizing two inequivalent irreducible representations of the Clifford algebra, the vacuum current density is investigated in C - and P -symmetric fermionic models. Applications are given for a cosmic string in the Randall-Sundrum-type braneworld model with a single brane.

scholarly journals Induced fermionic current in AdS spacetime in the presence of a cosmic string and a compactified dimension

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
S. Bellucci ◽  
W. Oliveira dos Santos ◽  
E. R. Bezerra de Mello
Keyword(s):  
Magnetic Flux ◽  
Cosmic String ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Axial Current ◽  
De Sitter ◽  
Twisted Field ◽  
Compact Dimension ◽  
Ads Spacetime ◽  
Current Densities

AbstractIn this paper, we consider a massive charged fermionic quantum field and investigate the current densities induced by a magnetic flux running along the core of an idealized cosmic string in the background geometry of a 5-dimensional anti-de Sitter spacetime, assuming that an extra dimension is compactified. Along the compact dimension quasi-periodicity condition is imposed on the field with a general phase. Moreover, we admit the presence of a magnetic flux enclosed by the compactified axis. The latter gives rise to Ahanorov–Bohm-like effect on the vacuum expectation value of the currents. In this setup, only azimuthal and axial current densities take place. The former presents two contributions, with the first one due to the cosmic string in a 5-dimensional AdS spacetime without compact dimension, and the second one being induced by the compactification itself. The latter is an odd function of the magnetic flux along the cosmic string and an even function of the magnetic flux enclosed by the compactified axis with period equal to the quantum flux. As to the induced axial current, it is an even function of the magnetic flux along the string’s core and an odd function of the magnetic flux enclosed by the compactification perimeter. For untwisted and twisted field along compact dimension, the axial current vanishes. The massless field case is presented as well some asymptotic limits for the parameters of the model.

Electromagnetic Casimir densities for planar boundaries in AdS spacetime

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040029 ◽  
Author(s):  
A. A. Saharian ◽  
A. S. Kotanjyan ◽  
A. A. Saharyan ◽  
H. G. Sargsyan
Keyword(s):  
Boundary Condition ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Curvature Radius ◽  
Perfect Conductor ◽  
Parallel Plates ◽  
Casimir Forces ◽  
Spatial Dimensions ◽  
Ads Spacetime

We investigate the vacuum expectation value of the energy-momentum tensor and the Casimir forces for the electromagnetic field in AdS spacetime for the geometry of two parallel plates. On the plates the field obeys the boundary condition that generalizes the perfect conductor boundary condition for an arbitrary number of spatial dimensions. The interaction forces between the plates are attractive. At separations larger than the curvature radius of the spacetime they decay exponentially.

scholarly journals VACUUM POLARIZATION BY FERMIONIC FIELDS IN HIGHER DIMENSIONAL COSMIC STRING SPACE-TIME

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1481-1488 ◽  
Author(s):  
J. SPINELLY ◽  
E. R. BEZERRA DE MELLO
Keyword(s):  
Magnetic Flux ◽  
Cosmic String ◽  
Vacuum Polarization ◽  
Fractional Part ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Closed Expression ◽  
Fermionic Fields ◽  
Tensor Formula

In this paper we investigate vacuum polarization effects associated with charged massive quantum fermionic fields in a six-dimensional cosmic string space-times considering the presence of a magnetic flux running along its core. We have shown that for specific values of the parameters which codify the presence of the cosmic string, and the fractional part of the ratio of the magnetic flux by the quantum one, a closed expression for the respective Green function is obtained. Adopting this result, we explicitly calculate the renormalized vacuum expectation value of the energy-momentum tensor, [Formula: see text], and analyse this result in some limiting cases.

Global symmetries and Noether’s theorem

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Global Symmetries ◽  
Symmetry Transformation ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Quantum Field ◽  
Expectation Value ◽  
Minkowski Space Time ◽  
Integral Measure ◽  
Colour Charge ◽  
Internal Symmetries

Noethers theorem shows that continuous global symmetries lead classically to conservation laws. Such symmetries can be divided into spacetime and internal symmetries. The invariance of Minkowski space-time under global Poincaré transformations leads to the conservation of the four-momentum and the total angular momentum. Examples for conserved charges due to internal symmetries are electric and colour charge. The vacuum expectation value of a Noether current is shown to beconserved in a quantum field theory if the symmetry transformation keeps the path-integral measure invariant.

scholarly journals Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra II: Tensorial Data

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 795
Author(s):  
Vincent Lahoche ◽  
Mohamed Ouerfelli ◽  
Dine Ousmane Samary ◽  
Mohamed Tamaazousti
Keyword(s):  
Principal Component Analysis ◽  
Renormalization Group ◽  
Signal Detection ◽  
Detection Threshold ◽  
Principal Component ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Component Analysis ◽  
Slight Generalization ◽  
Nearly Continuous

The tensorial principal component analysis is a generalization of ordinary principal component analysis focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative renormalization group formalism, based on a slight generalization of the covariance matrix, to investigate signal detection for the difficult issue of nearly continuous spectra. Renormalization group allows constructing an effective description keeping only relevant features in the low “energy” (i.e., large eigenvalues) limit and thus providing universal descriptions allowing to associate the presence of the signal with objectives and computable quantities. Among them, in this paper, we focus on the vacuum expectation value. We exhibit experimental evidence in favor of a connection between symmetry breaking and the existence of an intrinsic detection threshold, in agreement with our conclusions for matrices, providing a new step in the direction of a universal statement.

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