scholarly journals p-form surface charges on AdS: renormalization and conservation

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Erfan Esmaeili ◽  
Vahid Hosseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Infinite Number ◽  
Symplectic Form ◽  
Zero Mode ◽  
Surface Charges ◽  
Abelian Algebra ◽  
Form Theory

Abstract Surface charges of a p-form theory on the boundary of an AdSd+1 spacetime are computed. Counter-terms on the boundary produce divergent corner-terms which holographically renormalize the symplectic form. Different choices of boundary conditions lead to various expressions for the charges and the associated fluxes. With the usual standard AdS boundary conditions, there are conserved zero-mode charges. Moreover, we explore two leaky boundary conditions which admit an infinite number of charges forming an Abelian algebra and non-vanishing flux. Finally, we discuss magnetic p-form charges and electric/magnetic duality.

scholarly journals Boundary states for chiral symmetries in two dimensions

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Philip Boyle Smith ◽  
David Tong
Keyword(s):  
Boundary Conditions ◽  
Ground State ◽  
Zero Mode ◽  
Central Charge ◽  
Two Dimensions ◽  
Dirac Fermions ◽  
Chiral Symmetries ◽  
Boundary States ◽  
Ground State Degeneracy ◽  
Left And Right

Abstract We study boundary states for Dirac fermions in d = 1 + 1 dimensions that preserve Abelian chiral symmetries, meaning that the left- and right-moving fermions carry different charges. We derive simple expressions, in terms of the fermion charge assignments, for the boundary central charge and for the ground state degeneracy of the system when two different boundary conditions are imposed at either end of an interval. We show that all such boundary states fall into one of two classes, related to SPT phases supported by (−1)F , which are characterised by the existence of an unpaired Majorana zero mode.

scholarly journals Parameters characterizing the charge state of dielectrics

2017 ◽  
Vol 35 (3) ◽  
pp. 601-605 ◽  
Author(s):  
Bożena Łowkis
Keyword(s):  
Free Surface ◽  
Electric Field ◽  
Charge State ◽  
Free Volume ◽  
Infinite Number ◽  
Polarization State ◽  
Surface Charges ◽  
Volume Conductivity ◽  
Total Lifetime ◽  
Relaxation Decay

AbstractThis paper presents three physical sources of the electric field in dielectrics: excess free volume charges with the distribution qv(x,y,z), free surface charges with the distribution qs(x,y,z) and frozen polarization state in the dielectric. They have a deciding influence on the parameters of the electret, in particular they determine the total lifetime of the electret and technical components made of it. The indeterminacy related to the mutual proportions of the spatial and surface charges was discussed: one can find an infinite number of distributions of surface qse(x,y,z) and spatial qve(x,y,z) charges leading to the same distribution of the electric field E(x,y,z). A general case of electret was considered, where a coexistence of relaxation decay of frozen polarization and Maxwellian relaxation dependent on volume conductivity of the dielectric is assumed. An attempt to interpret the charge lifetime in real electrets was made.

scholarly journals Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: Theory and boundary conditions

2013 ◽  
Vol 234 ◽  
pp. 353-375 ◽  
Author(s):  
Travis C. Fisher ◽  
Mark H. Carpenter ◽  
Jan Nordström ◽  
Nail K. Yamaleev ◽  
Charles Swanson
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Conservation Laws ◽  
Nonlinear Conservation Laws ◽  
Form Theory ◽  
Split Form

scholarly journals INFINITE RESONANT SOLUTIONS AND TURNING POINTS IN A PROBLEM WITH UNBOUNDED BIFURCATION

2010 ◽  
Vol 20 (09) ◽  
pp. 2885-2896 ◽  
Author(s):  
J. M. ARRIETA ◽  
R. PARDO ◽  
A. RODRÍGUEZ-BERNAL
Keyword(s):  
Elliptic Equation ◽  
Boundary Conditions ◽  
Infinite Number ◽  
Nonlinear Boundary ◽  
Turning Points ◽  
Nonlinear Boundary Conditions ◽  
Steklov Eigenvalue

We consider an elliptic equation -Δu + u = 0 with nonlinear boundary conditions ∂u/∂n = λu + g(λ, x, u), where (g(λ, x, s))/s → 0, as |s| → ∞. In [Arrieta et al., 2007, 2009] the authors proved the existence of unbounded branches of solutions near a Steklov eigenvalue of odd multiplicity and, among other things, provided tools to decide whether the branch is subcritical or supercritical. In this work, we give conditions on the nonlinearity, guaranteeing the existence of a bifurcating branch which is neither subcritical nor supercritical, having an infinite number of turning points and an infinite number of resonant solutions.

On the Performance of Journal Bearings Under Conditions of Film Rupture, Part II

1975 ◽  
Vol 97 (4) ◽  
pp. 591-598
Author(s):  
W. A. Crosby ◽  
E. M. Badawy
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Finite Length ◽  
Infinite Number ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Operating Characteristics ◽  
Film Rupture ◽  
Rupture Part

An analytical analysis of journal bearing performance under conditions of film rupture by separation and by cavitation is performed. The ruptured region is considered to have an infinite number of cavities. The boundary condition of Reynolds’ equation at the trailing edge is influenced by the bearing’s operating characteristics and the method of oil admission. A variational solution is given in order to extend the applicability of the boundary conditions to bearings of finite length.

scholarly journals High-order perturbative expansions in massless gauge theories with NSPT

2018 ◽  
Vol 175 ◽  
pp. 11023
Author(s):  
Luigi Del Debbio ◽  
Francesco Di Renzo ◽  
Gianluca Filaci
Keyword(s):  
Boundary Conditions ◽  
Gauge Theories ◽  
Zero Mode ◽  
Stochastic Perturbation ◽  
High Order ◽  
Fundamental Representation ◽  
Lattice Gauge ◽  
Lattice Gauge Theories ◽  
Twisted Boundary Conditions ◽  
Wilson Fermions

We investigate the possibility of using numerical stochastic perturbation theory (NSPT) to probe high orders in the perturbative expansion of lattice gauge theories with massless Wilson fermions. Twisted boundary conditions are used to regularise the gauge zero-mode; the extension of these boundary conditions to include fermions in the fundamental representation requires to introduce a smell degree of freedom. Moreover, the mass of Wilson fermions is affected by an additive renormalisation: we study how to determine the mass counterterms consistently in finite volume. The knowledge of the critical masses will enable high-order perturbative computations in massless QCD, e.g. (as a first application) for the plaquette.

scholarly journals 4-d Chern-Simons theory: higher gauge symmetry and holographic aspects

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Roberto Zucchini
Keyword(s):  
Gauge Symmetry ◽  
Boundary Conditions ◽  
Simons Theory ◽  
Crossed Module ◽  
Surface Charges ◽  
Gauge Transformations ◽  
Invariance Properties ◽  
Edge Field ◽  
Set Up ◽  
Chern Simons

Abstract We present and study a 4-d Chern-Simons (CS) model whose gauge symmetry is encoded in a balanced Lie group crossed module. Using the derived formal set-up recently found, the model can be formulated in a way that in many respects closely parallels that of the familiar 3-d CS one. In spite of these formal resemblance, the gauge invariance properties of the 4-d CS model differ considerably. The 4-d CS action is fully gauge invariant if the underlying base 4-fold has no boundary. When it does, the action is gauge variant, the gauge variation being a boundary term. If certain boundary conditions are imposed on the gauge fields and gauge transformations, level quantization can then occur. In the canonical formulation of the theory, it is found that, depending again on boundary conditions, the 4-d CS model is characterized by surface charges obeying a non trivial Poisson bracket algebra. This is a higher counterpart of the familiar WZNW current algebra arising in the 3-d model. 4-d CS theory thus exhibits rich holographic properties. The covariant Schroedinger quantization of the 4-d CS model is performed. A preliminary analysis of 4-d CS edge field theory is also provided. The toric and Abelian projected models are described in some detail.

scholarly journals Adjoint differential equations

1927 ◽  
Vol 117 (776) ◽  
pp. 201-208
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Infinite Number ◽  
Adjoint Equation ◽  
Linear Equations ◽  
Point Of View ◽  
General Interest ◽  
Linear Difference Equations ◽  
Linear Differential

1. That adjoint differential equations have an analogue in the theory of linear difference equations seems to have been first observed by Bortolotti. The relation is essentially that of a matrix ǁ a rs ǁ to its transposed matrix ǁ a sr ǁ. It seems desirable, from this point of view, to carry out the transition from difference to differential equations, and thus prove that the analogy is a real one. This is done in Art. 2. There are further consequences of general interest. A set of linear equations corresponds to a differential equation and its boundary conditions, and thus we can find an interpretation of the adjoint boundary conditions introduced by Birkhoff into the theory of linear differential equations (Arts. 3-6). The relation between the two Green’s functions, implicit in Birkhoff’s work, then becomes evident (Art. 7). 2. We first prove that if the equations a r 1 y 1 + a r 2 y 2 + ... + a rn y n = fr ( r = 1 to n ) (1) are so constituted that they merge into the differential equation L ( y ) Ξ a m d m y / dx m . . . + a 1 dy / dx + a o y = f (2) by passing to an infinite number of infinitesimally spaced unknowns, the transposed equations a 1 r z 1 + a 2 r z 2 + ... + a nr z n = g r (3) merge into the adjoint equation M ( z ) Ξ (—) m d m / dx m ( a m z ) + ... - d / dx ( a 1 z ) + a o z = g .(4)

Self-adjoint Sturm-Liouville problems with an infinite number of boundary conditions

2016 ◽  
Vol 289 (8-9) ◽  
pp. 1148-1169 ◽  
Author(s):  
Yingchun Zhao ◽  
Jiong Sun ◽  
Anton Zettl
Keyword(s):  
Boundary Conditions ◽  
Infinite Number ◽  
Sturm Liouville
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