scholarly journals Benign ghosts in higher-derivative systems

2021 ◽  
Vol 2038 (1) ◽  
pp. 012023
Author(s):  
Andrei Smilga
Keyword(s):  
Ground State ◽  
Necessary Condition ◽  
Exact Solvability ◽  
Higher Derivative ◽  
Higher Dimensional ◽  
Special Cases ◽  
Exactly Solvable ◽  
Theory Of Everything ◽  
Higher Derivatives ◽  
Benign Nature

Abstract A brief review of the physics of systems including higher derivatives in the Lagrangian is given. All such systems involve ghosts i.e. the spectrum of the Hamiltonian is not bounded from below and the vacuum ground state is absent. Usually this leads to collapse and loss of unitarity. In certain special cases, this does not happen, however: ghosts are benign. This happens, in particular, in exactly solvable higher-derivative theories, but exact solvability seems to be a sufficient but not a necessary condition for the benign nature of the ghosts. We speculate that the Theory of Everything is a higher-derivative field theory, characterized by the presence of such benign ghosts and defined in a higher-dimensional bulk. Our Universe represents then a classical solution in this theory, having the form of a 3-brane embedded in the bulk.

scholarly journals Classical and quantum dynamics of higher-derivative systems

2017 ◽  
Vol 32 (33) ◽  
pp. 1730025 ◽  
Author(s):  
Andrei Smilga
Keyword(s):  
Field Theory ◽  
Classical Solution ◽  
Ground State ◽  
Quantum Dynamics ◽  
Higher Derivative ◽  
Higher Dimensional ◽  
Special Cases ◽  
Theory Of Everything ◽  
Higher Derivatives

A brief review of the physics of systems including higher derivatives in the Lagrangian is given. All such systems involve ghosts, i.e. the spectrum of the Hamiltonian is not bounded from below and the vacuum ground state is absent. Usually, this leads to collapse and loss of unitarity. In certain special cases, this does not happen, however, ghosts are benign. We speculate that the Theory of Everything is a higher-derivative field theory, characterized by the presence of such benign ghosts and defined in a higher-dimensional bulk. Our Universe then represents a classical solution in this theory, having the form of a 3-brane embedded in the bulk.

scholarly journals HIGHER DIMENSIONAL OPERATORS AND THEIR EFFECTS IN (NON)SUPERSYMMETRIC MODELS

2008 ◽  
Vol 23 (10) ◽  
pp. 711-720 ◽  
Author(s):  
D. M. GHILENCEA
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Space Time ◽  
Analytical Continuation ◽  
Power Counting ◽  
Higher Derivative ◽  
Minkowski Space Time ◽  
Higher Dimensional ◽  
Supersymmetric Models ◽  
Higher Derivatives

It is shown that a 4D N = 1 softly broken supersymmetric theory with higher derivative operators in the Kahler or the superpotential part of the Lagrangian and with an otherwise arbitrary superpotential, can be re-formulated as a theory without higher derivatives but with additional (ghost) superfields and modified interactions. The importance of the analytical continuation Minkowski–Euclidean space–time for the UV behaviour of such theories is discussed in detail. In particular it is shown that power counting for divergences in Minkowski space–time does not always work in models with higher dimensional (derivative) operators.

scholarly journals Simple prescription for computing the nonrelativistic interparticle potential energy related to dual models

2016 ◽  
Vol 31 (12) ◽  
pp. 1650070 ◽  
Author(s):  
G. B. de Gracia ◽  
G. P. de Brito
Keyword(s):  
Vector Field ◽  
Potential Energy ◽  
Nonrelativistic Limit ◽  
External Current ◽  
Interparticle Potential ◽  
Higher Derivative ◽  
Higher Derivatives ◽  
Rank 2 ◽  
Electromagnetic Models ◽  
Dual Models

Following a procedure recently utilized by Accioly et al. to obtain the D-dimensional interparticle potential energy for electromagnetic models in the nonrelativistic limit, and relaxing the condition assumed by the authors concerning the conservation of the external current, the prescription found out by them is generalized so that dual models can also be contemplated. Specific models in which the interaction is mediated by a spin-0 particle described first by a vector field and then by a higher-derivative vector field, are analyzed. Systems mediated by spin-1 particles described, respectively, by symmetric rank-2 tensors, symmetric rank-2 tensors augmented by higher derivatives and antisymmetric rank-2 tensors, are considered as well.

Maximin: a direct approach to sustainability

2006 ◽  
Vol 11 (3) ◽  
pp. 275-300 ◽  
Author(s):  
ROBERT D. CAIRNS ◽  
NGO VAN LONG
Keyword(s):  
Precautionary Principle ◽  
Direct Approach ◽  
Necessary Condition ◽  
Hyperbolic Discount ◽  
Discount Factors ◽  
Discounted Utility ◽  
Special Cases ◽  
Analytic Expression ◽  
Hotelling's Rule ◽  
Competitive Economy

We solve directly a general maximin (sustainment, intergenerational-equity) problem. Because the shadow values of a maximin problem do not correspond to the shadow values from a general discounted-utility solution, they correspond to the prices of only a very special competitive economy. Virtual discount factors for the economy arise. They do not correspond to hyperbolic discount factors. Hartwick's rule is derived and generalized naturally to take into account non-autonomous and non-deterministic features of the economy. Under uncertainty, Hartwick's rule is the analytic expression of a form of precautionary principle. Hotelling's rule is a necessary condition, but may be more complex than has been appreciated in simple models. Some interpretations of strong sustainment are special cases of weak sustainment but, paradoxically, may be more difficult to solve.

scholarly journals Composing effective prediction at five points

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
John Joseph M. Carrasco ◽  
Laurentiu Rodina ◽  
Suna Zekioğlu
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitude ◽  
Building Blocks ◽  
Tree Level ◽  
Critical Aspect ◽  
Higher Derivative ◽  
Higher Dimensional ◽  
Single Trace ◽  
The Relationship ◽  
Double Copy

Abstract Color-kinematics duality in the adjoint has proven key to the relationship between gauge and gravity theory scattering amplitude predictions. In recent work, we demonstrated that at four-point tree-level, a small number of color-dual EFT building blocks could encode all higher-derivative single-trace massless corrections to gauge and gravity theories compatible with adjoint double-copy. One critical aspect was the trivialization of building higher-derivative color-weights — indeed, it is the mixing of kinematics with non-adjoint-type color-weights (like the permutation-invariant d4) which permits description via adjoint double-copy. Here we find that such ideas clarify the predictions of local five-point higher-dimensional operators as well. We demonstrate how a single scalar building block can be combined with color structures to build higher-derivative color factors that generate, through double copy, the amplitudes associated with higher-derivative gauge-theory operators. These may then be suitably mapped, through another double-copy, to higher-derivative corrections in gravity.

Exploring scalar quantum walks on Cayley graphs

2008 ◽  
Vol 8 (1&2) ◽  
pp. 68-81
Author(s):  
O.L. Acevedo ◽  
J. Roland ◽  
N.J. Cerf
Keyword(s):  
Evolution Operator ◽  
Cayley Graphs ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Constructive Method ◽  
Quantum Evolution ◽  
Necessary Condition ◽  
Internal Space ◽  
Special Cases ◽  
Scalar Quantum

A quantum walk, \emph{i.e.}, the quantum evolution of a particle on a graph, is termed \emph{scalar} if the internal space of the moving particle (often called the coin) has dimension one. Here, we study the existence of scalar quantum walks on Cayley graphs, which are built from the generators of a group. After deriving a necessary condition on these generators for the existence of a scalar quantum walk, we present a general method to express the evolution operator of the walk, assuming homogeneity of the evolution. We use this necessary condition and the subsequent constructive method to investigate the existence of scalar quantum walks on Cayley graphs of groups presented with two or three generators. In this restricted framework, we classify all groups -- in terms of relations between their generators -- that admit scalar quantum walks, and we also derive the form of the most general evolution operator. Finally, we point out some interesting special cases, and extend our study to a few examples of Cayley graphs built with more than three generators.

scholarly journals On Reay's Relaxed Tverberg Conjecture and Generalizations of Conway's Thrackle Conjecture

10.37236/6516 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Megumi Asada ◽  
Ryan Chen ◽  
Florian Frick ◽  
Frederick Huang ◽  
Maxwell Polevy ◽  
...  
Keyword(s):  
Geometric Property ◽  
Convex Sets ◽  
Convex Hulls ◽  
Open Problems ◽  
Higher Dimensional ◽  
Special Cases ◽  
Minimum Number ◽  
Point Set ◽  
Colored Version ◽  
Special Case

Reay's relaxed Tverberg conjecture and Conway's thrackle conjecture are open problems about the geometry of pairwise intersections. Reay asked for the minimum number of points in Euclidean $d$-space that guarantees any such point set admits a partition into $r$ parts, any $k$ of whose convex hulls intersect. Here we give new and improved lower bounds for this number, which Reay conjectured to be independent of $k$. We prove a colored version of Reay's conjecture for $k$ sufficiently large, but nevertheless $k$ independent of dimension $d$. Pairwise intersecting convex hulls have severely restricted combinatorics. This is a higher-dimensional analogue of Conway's thrackle conjecture or its linear special case. We thus study convex-geometric and higher-dimensional analogues of the thrackle conjecture alongside Reay's problem and conjecture (and prove in two special cases) that the number of convex sets in the plane is bounded by the total number of vertices they involve whenever there exists a transversal set for their pairwise intersections. We thus isolate a geometric property that leads to bounds as in the thrackle conjecture. We also establish tight bounds for the number of facets of higher-dimensional analogues of linear thrackles and conjecture their continuous generalizations.

scholarly journals CCNV Space-Times as Potential Supergravity Solutions

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
A. Coley ◽  
D. McNutt ◽  
N. Pelavas
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Space Time ◽  
Null Vector ◽  
Killing Spinor ◽  
Necessary Condition ◽  
Killing Vector Field ◽  
Higher Dimensional

It is of interest to study supergravity solutions preserving a nonminimal fraction of supersymmetries. A necessary condition for supersymmetry to be preserved is that the space-time admits a Killing spinor and hence a null or time-like Killing vector field. Any space-time admitting a covariantly constant null vector (CCNV) field belongs to the Kundt class of metrics and more importantly admits a null Killing vector field. We investigate the existence of additional non-space-like isometries in the class of higher-dimensional CCNV Kundt metrics in order to produce potential solutions that preserve some supersymmetries.

scholarly journals Higher derivatives driven symmetry breaking in holographic superconductors

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
Hai-Li Li ◽  
Guoyang Fu ◽  
Yan Liu ◽  
Jian-Pin Wu ◽  
Xin Zhang
Keyword(s):  
High Temperature Superconductor ◽  
Energy Gap ◽  
Coupling Term ◽  
Holographic Superconductor ◽  
Complex Scalar ◽  
Holographic Superconductors ◽  
Higher Derivative ◽  
Superconducting Energy Gap ◽  
Higher Derivatives ◽  
Complex Scalar Field

Abstract In this paper, we construct a novel holographic superconductor from higher derivative (HD) gravity involving a coupling between the complex scalar field and the Weyl tensor. This HD coupling term provides a near horizon effective mass squared, which can violates IR Breitenlohner–Freedman (BF) bound by tuning the HD coupling and induces the instability of black brane such that the superconducting phase transition happens. We also study the properties of the condensation and the conductivity in the probe limit. We find that a wider extension of the superconducting energy gap ranging from 4.6 to 10.5 may provide a novel platform to model and interpret the phenomena in the real materials of high temperature superconductor.

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